Algebra 1 Grade 8 CA Common Core Review

 

8.A8.N Number and Quantity

8.A8.A Algebra

8.A8.F Functions

8.A8.G Geometry

8.A8.SP Statistics and Probability

8.A8.VA Constructing Viable Arguments

  • 8.A8.VA.VA Constructing Viable Arguments

    • 8.A8.VA.VA.1 Use and know simple aspects of a logical argument.

      • 8.A8.VA.VA.1.a Use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

    • 8.A8.VA.VA.2 Use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:

      • 8.A8.VA.VA.2.a Use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

      • 8.A8.VA.VA.2.b Judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

      • 8.A8.VA.VA.2.c Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, determine whether the statement is true sometimes, always, or never.

Grade 1 – CA Common Care – Standards & Learning Objectives

1.1.OA Operations and Algebraic Thinking

 

1 Represent and solve problems involving addition and subtraction.

 

1.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Addition with pictures – sums to 10 (First grade – B.1)

Addition sentences – sums to 10 (First grade – B.2)

Addition word problems – sums to 10 (First grade – B.4)

Word problems – write the addition sentence (First grade – B.5)

Addition word problems – sums to 18 (First grade – B.15)

Complete the addition sentence (First grade – B.16)

Subtraction with pictures – numbers up to 10 (First grade – D.1)

Subtraction sentences – numbers up to 10 (First grade – D.2)

Subtraction word problems – one-digit numbers (First grade – D.4)

Word problems – write the subtraction sentence (First grade – D.5)

Subtraction word problems – numbers up to 18 (First grade – D.14)

Complete the subtraction sentence (First grade – D.15)

Addition and subtraction word problems (First grade – F.6)

Comparison word problems (First grade – G.4)

Customary units of length: word problems (First grade – N.6)

Metric units of length: word problems (First grade – N.10)

 

1.1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Adding three numbers (First grade – B.17)

Word problems – adding three numbers (First grade – B.18)

 

1 Understand and apply properties of operations and the relationship between addition and subtraction.

 

1.1.OA.3 Apply properties of operations as strategies to add and subtract.

Adding three numbers (First grade – B.17)

Word problems – adding three numbers (First grade – B.18)

Related addition facts (First grade – B.19)

Related subtraction facts (First grade – D.16)

Fact families (First grade – F.3)

 

1.1.OA.4 Understand subtraction as an unknown-addend problem.

Complete the addition sentence (First grade – B.16)

Fact families (First grade – F.3)

 

1 Add and subtract within 20.

 

1.1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Counting forward and backward (First grade – A.11)

Skip-counting patterns – with tables (First grade – A.19)

Sequences – count up and down by 1, 2, 3, 5, and 10 (First grade – A.20)

Addition sentences to 10 using number lines (First grade – B.3)

Subtraction sentences within 10 using number lines (First grade – D.3)

 

1.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Ways to make a number using addition (First grade – B.6)

Ways to make a number – addition sentences (First grade – B.7)

Adding zero (First grade – B.8)

Adding doubles (First grade – B.10)

Addition facts – sums to 10 (First grade – B.12)

Addition sentences to 18 using number lines (First grade – B.13)

Addition facts – sums to 18 (First grade – B.14)

Add using doubles plus 1 (First grade – B.20)

Add using doubles minus 1 (First grade – B.21)

Addition facts – sums to 20 (First grade – B.22)

Adding 0 (First grade – C.1)

Adding 1 (First grade – C.2)

Adding 2 (First grade – C.3)

Adding 3 (First grade – C.4)

Adding 4 (First grade – C.5)

Adding 5 (First grade – C.6)

Adding 6 (First grade – C.7)

Adding 7 (First grade – C.8)

Adding 8 (First grade – C.9)

Adding 9 (First grade – C.10)

Ways to make a number using subtraction (First grade – D.6)

Ways to make a number – subtraction sentences (First grade – D.7)

Ways to subtract from a number – subtraction sentences (First grade – D.8)

Subtracting zero and all (First grade – D.9)

Subtracting doubles (First grade – D.10)

Subtraction facts – numbers up to 10 (First grade – D.11)

Subtraction sentences within 18 using number lines (First grade – D.12)

Subtraction facts – numbers up to 18 (First grade – D.13)

Subtract one-digit numbers from two-digit numbers (First grade – D.20)

Subtracting 0 (First grade – E.1)

Subtracting 1 (First grade – E.2)

Subtracting 2 (First grade – E.3)

Subtracting 3 (First grade – E.4)

Subtracting 4 (First grade – E.5)

Subtracting 5 (First grade – E.6)

Subtracting 6 (First grade – E.7)

Subtracting 7 (First grade – E.8)

Subtracting 8 (First grade – E.9)

Subtracting 9 (First grade – E.10)

Addition and subtraction – ways to make a number (First grade – F.1)

Addition and subtraction facts – numbers up to 10 (First grade – F.4)

Addition and subtraction facts – numbers up to 18 (First grade – F.5)

 

1 Work with addition and subtraction equations.

 

1.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Addition sentences: true or false? (First grade – B.23)

Subtraction sentences: true or false? (First grade – D.17)

Which sign makes the number sentence true? (First grade – F.2)

Addition and subtraction sentences: true or false? (First grade – F.7)

 

1.1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

Complete the addition sentence (First grade – B.16)

Complete the subtraction sentence (First grade – D.15)

1.1.NBT Number and Operations in Base Ten

 

1 Extend the counting sequence.

 

1.1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Counting review – 0 to 10 (First grade – A.1)

Counting review – up to 20 (First grade – A.3)

Counting – up to 30 (First grade – A.5)

Counting – up to 100 (First grade – A.6)

Counting on the hundred chart (First grade – A.13)

Writing numbers in words (First grade – A.22)

 

1 Understand place value.

 

1.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

 

1.1.NBT.2.a 10 can be thought of as a bundle of ten ones – called a “ten.”

Counting tens and ones – up to 20 (First grade – A.4)

Counting tens and ones – up to 99 (First grade – A.8)

Hundred chart (First grade – A.14)

Convert between tens and ones (First grade – I.4)

 

1.1.NBT.2.b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Counting review – up to 20 (First grade – A.3)

Counting tens and ones – up to 20 (First grade – A.4)

Place value models up to 20 (First grade – I.1)

Write numbers as tens and ones up to 20 (First grade – I.2)

 

1.1.NBT.2.c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Counting by tens – up to 100 (First grade – A.7)

 

1.1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Comparing numbers up to 100 (First grade – G.3)

Put numbers in order (First grade – R.3)

 

1 Use place value understanding and properties of operations to add and subtract.

 

1.1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Add tens I (First grade – B.24)

Add tens II (First grade – B.25)

Add a one-digit number to a two-digit number – without regrouping (First grade – B.26)

Regrouping tens and ones I (First grade – B.27)

Regrouping tens and ones II (First grade – B.28)

Add a one-digit number to a two-digit number – with regrouping (First grade – B.29)

Add and subtract tens (First grade – F.9)

 

1.1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Ten more or less (First grade – F.8)

 

1.1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Subtract tens I (First grade – D.18)

Add and subtract tens (First grade – F.9)

1.1.MD Measurement and Data

 

1 Measure lengths indirectly and by iterating length units.

 

1.1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Compare objects: length and height (First grade – N.2)

Customary units of length: word problems (First grade – N.6)

Metric units of length: word problems (First grade – N.10)

 

1.1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

Measure using objects (First grade – N.3)

 

1 Tell and write time.

 

1.1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

Match analog clocks and times (First grade – S.1)

Match digital clocks and times (First grade – S.2)

Match analog and digital clocks (First grade – S.3)

Read clocks and write times (First grade – S.4)

Compare clocks (First grade – S.7)

Choose the appropriate time units (First grade – S.9)

 

1 Represent and interpret data.

 

1.1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Comparing – review (First grade – G.1)

Record data with tally charts, picture graphs, tables (First grade – M.1)

Interpret data in tally charts, picture graphs, tables (First grade – M.2)

Interpret bar graphs (First grade – M.3)

Which bar graph is correct? (First grade – M.4)

Sort shapes into a Venn diagram (First grade – R.1)

Count shapes in a Venn diagram (First grade – R.2)

1.1.G Geometry

 

1 Reason with shapes and their attributes.

 

1.1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Identify 2-dimensional shapes (First grade – K.1)

Count sides and vertices (First grade – K.6)

Count edges, vertices, and faces (First grade – K.7)

Compare sides and vertices (First grade – K.8)

Compare edges, vertices, and faces (First grade – K.9)

Open and closed shapes (First grade – K.10)

Same shape (First grade – K.13)

 

1.1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

 

1.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Halves, thirds, and fourths (First grade – J.1)

Equal parts (First grade – J.2)

Simple fractions: what fraction does the shape show? (First grade – J.3)

Simple fractions: which shape matches the fraction? (First grade – J.4)

Compare fractions (First grade – J.7)

Fraction models equivalent to whole numbers (First grade – J.8)

Grade 5 – CA Common Core Standards and Learning Objectives

5.5.OA Operations and Algebraic Thinking

 

5 Write and interpret numerical expressions.

 

5.5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Perform multiple operations with whole numbers (Fifth grade – O.4)

 

5.5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Write numerical expressions (Fifth grade – O.3)

 

5.5.OA.2.1 Express a whole number in the range 2-50 as a product of its prime factors.

Prime factorization (Fifth grade – F.2)

 

5 Analyze patterns and relationships.

 

5.5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Complete a table for a two-variable relationship (Fifth grade – U.8)

Complete a table from a graph (Fifth grade – U.9)

Graph a two-variable relationship (Fifth grade – U.10)

5.5.NBT Number and Operations in Base Ten

 

5 Understand the place value system.

 

5.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Place values (Fifth grade – A.1)

Convert between place values (Fifth grade – A.2)

Place values in decimal numbers (Fifth grade – G.4)

 

5.5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Scientific notation (Fifth grade – A.11)

Multiplication patterns over increasing place values (Fifth grade – C.3)

Multiply numbers ending in zeroes (Fifth grade – C.4)

Multiply numbers ending in zeroes: word problems (Fifth grade – C.5)

Division patterns over increasing place values (Fifth grade – D.7)

Multiply a decimal by a power of ten (Fifth grade – I.2)

Divide by powers of ten (Fifth grade – J.1)

Decimal division patterns over increasing place values (Fifth grade – J.2)

 

5.5.NBT.3 Read, write, and compare decimals to thousandths.

 

5.5.NBT.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

What decimal number is illustrated? (Fifth grade – G.1)

Model decimals and fractions (Fifth grade – G.2)

Understanding decimals expressed in words (Fifth grade – G.3)

Place values in decimal numbers (Fifth grade – G.4)

Convert decimals between standard and expanded form (Fifth grade – G.5)

Convert decimals between standard and expanded form using fractions (Fifth grade – G.14)

 

5.5.NBT.3.b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Equivalent decimals (Fifth grade – G.6)

Decimal number lines (Fifth grade – G.8)

Compare decimals on number lines (Fifth grade – G.9)

Compare decimal numbers (Fifth grade – G.10)

Put decimal numbers in order (Fifth grade – G.11)

Compare decimals and fractions on number lines (Fifth grade – G.15)

Inequalities with decimal multiplication (Fifth grade – I.10)

 

5.5.NBT.4 Use place value understanding to round decimals to any place.

Round decimals (Fifth grade – G.7)

Estimate sums and differences of decimals (Fifth grade – H.8)

 

5 Perform operations with multi-digit whole numbers and with decimals to hundredths.

 

5.5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Multiply by 2-digit numbers: complete the missing steps (Fifth grade – C.12)

Multiply 2-digit numbers by 2-digit numbers (Fifth grade – C.13)

Multiply 2-digit numbers by 3-digit numbers (Fifth grade – C.14)

Multiply 2-digit numbers by larger numbers (Fifth grade – C.15)

Multiply by 2-digit numbers: word problems (Fifth grade – C.16)

Multiply three or more numbers up to 2 digits each (Fifth grade – C.17)

Multiply by 3-digit numbers (Fifth grade – C.18)

Multiply three numbers up to 3 digits each (Fifth grade – C.19)

Multiply three or more numbers: word problems (Fifth grade – C.20)

 

5.5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Properties of multiplication (Fifth grade – C.6)

Division facts to 12 (Fifth grade – D.1)

Division facts to 12: word problems (Fifth grade – D.2)

Divide multi-digit numbers by 1-digit numbers (Fifth grade – D.3)

Divide multi-digit numbers by 1-digit numbers: word problems (Fifth grade – D.4)

Divide numbers ending in zeroes (Fifth grade – D.8)

Divide numbers ending in zeroes: word problems (Fifth grade – D.9)

Divide 2-digit and 3-digit numbers by 2-digit numbers (Fifth grade – D.10)

Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems (Fifth grade – D.11)

Divide larger numbers by 2-digit numbers (Fifth grade – D.12)

Divide larger numbers by 2-digit numbers: word problems (Fifth grade – D.13)

Choose numbers with a particular quotient (Fifth grade – D.16)

 

5.5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Add and subtract money: word problems (Fifth grade – B.4)

Divide money amounts: word problems (Fifth grade – D.14)

Add decimal numbers (Fifth grade – H.1)

Subtract decimal numbers (Fifth grade – H.2)

Add and subtract decimal numbers (Fifth grade – H.3)

Add and subtract decimals: word problems (Fifth grade – H.4)

Choose decimals with a particular sum or difference (Fifth grade – H.5)

Complete the addition or subtraction sentence (Fifth grade – H.6)

Inequalities with decimal addition and subtraction (Fifth grade – H.7)

Multiply a decimal by a one-digit whole number (Fifth grade – I.3)

Multiply a decimal by a multi-digit whole number (Fifth grade – I.4)

Multiply decimals and whole numbers: word problems (Fifth grade – I.5)

Multiply money amounts: word problems (Fifth grade – I.6)

Multiply three or more numbers, one of which is a decimal (Fifth grade – I.7)

Multiply two decimals using grids (Fifth grade – I.8)

Multiply two decimals (Fifth grade – I.9)

Division with decimal quotients (Fifth grade – J.3)

Division with decimal quotients and rounding (Fifth grade – J.4)

Division with decimal quotients: word problems (Fifth grade – J.5)

Add, subtract, multiply, and divide decimals (Fifth grade – O.5)

Add, subtract, multiply, and divide decimals: word problems (Fifth grade – O.6)

Price lists (Fifth grade – R.1)

Unit prices (Fifth grade – R.2)

5.5.NF Number and Operations-Fractions

 

5 Use equivalent fractions as a strategy to add and subtract fractions.

 

5.5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Equivalent fractions (Fifth grade – K.3)

Reduce fractions to lowest terms (Fifth grade – K.4)

Convert between improper fractions and mixed numbers (Fifth grade – K.5)

Add fractions with unlike denominators using models (Fifth grade – L.6)

Add up to 4 fractions with denominators of 10 and 100 (Fifth grade – L.7)

Add fractions with unlike denominators (Fifth grade – L.8)

Subtract fractions with unlike denominators using models (Fifth grade – L.9)

Subtract fractions with unlike denominators (Fifth grade – L.10)

Add 3 or more fractions with unlike denominators (Fifth grade – L.12)

Complete addition and subtraction sentences with fractions (Fifth grade – L.15)

Inequalities with addition and subtraction of fractions (Fifth grade – L.16)

Add mixed numbers with unlike denominators (Fifth grade – L.18)

Subtract mixed numbers with unlike denominators (Fifth grade – L.19)

Complete addition and subtraction sentences with mixed numbers (Fifth grade – L.22)

Inequalities with addition and subtraction of mixed numbers (Fifth grade – L.23)

 

5.5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Add and subtract fractions with like denominators: word problems (Fifth grade – L.4)

Add and subtract fractions with unlike denominators: word problems (Fifth grade – L.11)

Add 3 or more fractions: word problems (Fifth grade – L.13)

Compare sums and differences of unit fractions (Fifth grade – L.14)

Add and subtract mixed numbers: word problems (Fifth grade – L.20)

Add and subtract fractions in recipes (Fifth grade – L.21)

 

5 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

 

5.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Fractions review (Fifth grade – K.1)

Divide fractions by whole numbers (Fifth grade – N.4)

 

5.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

 

5.5.NF.4.a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.

Multiply fractions by whole numbers I (Fifth grade – M.5)

Multiply fractions by whole numbers II (Fifth grade – M.8)

Multiply fractions by whole numbers: input/output tables (Fifth grade – M.11)

 

5.5.NF.4.b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Multiply two unit fractions using models (Fifth grade – M.12)

Multiply two fractions using models: fill in the missing factor (Fifth grade – M.13)

Multiply two fractions using models (Fifth grade – M.14)

Area of squares and rectangles (Fifth grade – Z.16)

Area and perimeter: word problems (Fifth grade – Z.22)

 

5.5.NF.5 Interpret multiplication as scaling (resizing), by:

 

5.5.NF.5.a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Scaling whole numbers by fractions (Fifth grade – M.17)

Scaling fractions by fractions (Fifth grade – M.18)

Scaling mixed numbers by fractions (Fifth grade – M.19)

 

5.5.NF.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

Multiply two fractions using models (Fifth grade – M.14)

 

5.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Multiply fractions by whole numbers: word problems (Fifth grade – M.10)

Multiply two fractions (Fifth grade – M.15)

Multiply two fractions: word problems (Fifth grade – M.16)

Multiply a mixed number by a whole number (Fifth grade – M.23)

Multiply a mixed number by a fraction (Fifth grade – M.24)

Multiply two mixed numbers (Fifth grade – M.25)

Multiplication with mixed numbers: word problems (Fifth grade – M.27)

Multiply fractions and mixed numbers in recipes (Fifth grade – M.28)

Add, subtract, multiply, and divide fractions and mixed numbers (Fifth grade – O.7)

Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Fifth grade – O.8)

 

5.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

 

5.5.NF.7.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

Divide unit fractions by whole numbers (Fifth grade – N.1)

Divide fractions by whole numbers (Fifth grade – N.4)

 

5.5.NF.7.b Interpret division of a whole number by a unit fraction, and compute such quotients.

Divide whole numbers by unit fractions (Fifth grade – N.2)

Divide whole numbers by unit fractions using models (Fifth grade – N.7)

Divide whole numbers by fractions (Fifth grade – N.8)

 

5.5.NF.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Divide whole numbers and unit fractions (Fifth grade – N.3)

Divide unit fractions by whole numbers: word problems (Fifth grade – N.6)

5.5.MD Measurement and Data

 

5 Convert like measurement units within a given measurement system.

 

5.5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Compare and convert customary units of length (Fifth grade – Y.2)

Compare and convert customary units of weight (Fifth grade – Y.3)

Compare and convert customary units of volume (Fifth grade – Y.4)

Compare and convert customary units (Fifth grade – Y.5)

Conversion tables – customary units (Fifth grade – Y.6)

Compare and convert metric units of length (Fifth grade – Y.8)

Compare and convert metric units of weight (Fifth grade – Y.9)

Compare and convert metric units of volume (Fifth grade – Y.10)

Compare and convert metric units (Fifth grade – Y.11)

Conversion tables – metric units (Fifth grade – Y.12)

Compare customary units by multiplying (Fifth grade – Y.13)

Convert customary units involving fractions (Fifth grade – Y.14)

Convert mixed customary units (Fifth grade – Y.15)

Add and subtract mixed customary units (Fifth grade – Y.16)

 

5 Represent and interpret data.

 

5.5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Interpret line plots (Fifth grade – V.10)

Create line plots (Fifth grade – V.11)

Create and interpret line plots with fractions (Fifth grade – V.12)

 

5 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

 

5.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

 

5.5.MD.3.a A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

Volume of rectangular prisms made of unit cubes (Fifth grade – Z.23)

 

5.5.MD.3.b A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Volume of rectangular prisms made of unit cubes (Fifth grade – Z.23)

 

5.5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Volume of rectangular prisms made of unit cubes (Fifth grade – Z.23)

 

5.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

 

5.5.MD.5.a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Volume of rectangular prisms made of unit cubes (Fifth grade – Z.23)

Volume of cubes and rectangular prisms (Fifth grade – Z.25)

 

5.5.MD.5.b Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Volume of cubes and rectangular prisms (Fifth grade – Z.25)

 

5.5.MD.5.c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Volume of irregular figures made of unit cubes (Fifth grade – Z.24)

5.5.G Geometry

 

5 Graph points on the coordinate plane to solve real-world and mathematical problems.

 

5.5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Coordinate graphs review – whole numbers only (Fifth grade – T.1)

Coordinate graphs with decimals and negative numbers (Fifth grade – T.2)

Graph points on a coordinate plane (Fifth grade – T.3)

 

5.5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Graph points on a coordinate plane (Fifth grade – T.3)

Coordinate graphs as maps (Fifth grade – T.4)

Relative coordinates: follow directions (Fifth grade – T.5)

 

5 Classify two-dimensional figures into categories based on their properties.

 

5.5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

Classify quadrilaterals (Fifth grade – Z.7)

 

5.5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

Identify 2-dimensional and 3-dimensional shapes (Fifth grade – Z.1)

Types of triangles (Fifth grade – Z.2)

Open and closed shapes and qualities of polygons (Fifth grade – Z.3)

Regular and irregular polygons (Fifth grade – Z.4)

Number of sides in polygons (Fifth grade – Z.5)

Which figure is being described? (Fifth grade – Z.6)

Classify quadrilaterals (Fifth grade – Z.7)

Grade 8 – CA Common Core Standards & Learning Objectives

8.8.NS The Number System

 

8 Know that there are numbers that are not rational, and approximate them by rational numbers.

 

8.8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Identify rational and irrational numbers (Eighth grade – D.1)

Convert between decimals and fractions or mixed numbers (Eighth grade – D.6)

 

8.8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi²).

Estimate positive and negative square roots (Eighth grade – F.16)

Estimate cube roots (Eighth grade – F.21)

8.8.EE Expressions and Equations

 

8 Work with radicals and integer exponents.

 

8.8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

Understanding exponents (Eighth grade – F.1)

Evaluate exponents (Eighth grade – F.2)

Solve equations with variable exponents (Eighth grade – F.3)

Exponents with negative bases (Eighth grade – F.4)

Exponents with decimal and fractional bases (Eighth grade – F.5)

Understanding negative exponents (Eighth grade – F.6)

Evaluate negative exponents (Eighth grade – F.7)

Multiplication with exponents (Eighth grade – F.8)

Division with exponents (Eighth grade – F.9)

Multiplication and division with exponents (Eighth grade – F.10)

Power rule (Eighth grade – F.11)

Evaluate expressions involving exponents (Eighth grade – F.12)

Identify equivalent expressions involving exponents (Eighth grade – F.13)

Multiply monomials (Eighth grade – Z.6)

Divide monomials (Eighth grade – Z.7)

Multiply and divide monomials (Eighth grade – Z.8)

Powers of monomials (Eighth grade – Z.9)

 

8.8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

Identify rational and irrational numbers (Eighth grade – D.1)

Square roots of perfect squares (Eighth grade – F.14)

Positive and negative square roots (Eighth grade – F.15)

Relationship between squares and square roots (Eighth grade – F.17)

Cube roots of perfect cubes (Eighth grade – F.19)

Solve equations involving cubes and cube roots (Eighth grade – F.20)

Evaluate radical expressions (Eighth grade – S.7)

 

8.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Convert between standard and scientific notation (Eighth grade – G.1)

Compare numbers written in scientific notation (Eighth grade – G.2)

 

8.8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Convert between standard and scientific notation (Eighth grade – G.1)

Multiply numbers written in scientific notation (Eighth grade – G.3)

Divide numbers written in scientific notation (Eighth grade – G.4)

 

8 Understand the connections between proportional relationships, lines, and linear equations.

 

8.8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Unit rates (Eighth grade – H.5)

Do the ratios form a proportion? (Eighth grade – H.6)

Do the ratios form a proportion: word problems (Eighth grade – H.7)

Solve proportions (Eighth grade – H.8)

Solve proportions: word problems (Eighth grade – H.9)

Find the constant of proportionality from a graph (Eighth grade – I.3)

Graph proportional relationships (Eighth grade – I.5)

Solve problems involving proportional relationships (Eighth grade – I.8)

 

8.8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Write equations for proportional relationships (Eighth grade – I.4)

Find the slope of a graph (Eighth grade – W.1)

Find the slope from two points (Eighth grade – W.2)

Find the slope of an equation (Eighth grade – W.4)

Graph a linear equation (Eighth grade – W.5)

Write a linear equation from a graph (Eighth grade – W.7)

Graph a line from an equation (Eighth grade – X.9)

 

8 Analyze and solve linear equations and pairs of simultaneous linear equations.

 

8.8.EE.7 Solve linear equations in one variable.

 

8.8.EE.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Find the number of solutions (Eighth grade – U.12)

 

8.8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Solve equations involving squares and square roots (Eighth grade – F.18)

Model and solve equations using algebra tiles (Eighth grade – U.3)

Write and solve equations that represent diagrams (Eighth grade – U.4)

Solve one-step equations (Eighth grade – U.5)

Solve two-step equations (Eighth grade – U.6)

Solve multi-step equations (Eighth grade – U.7)

Solve equations involving like terms (Eighth grade – U.8)

Solve equations with variables on both sides (Eighth grade – U.9)

Solve equations: mixed review (Eighth grade – U.10)

Solve equations: word problems (Eighth grade – U.11)

 

8.8.EE.8 Analyze and solve pairs of simultaneous linear equations.

 

8.8.EE.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Is (x, y) a solution to the system of equations? (Eighth grade – Y.1)

Solve a system of equations by graphing (Eighth grade – Y.2)

Find the number of solutions to a system of equations by graphing (Eighth grade – Y.4)

 

8.8.EE.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

Find the number of solutions to a system of equations (Eighth grade – Y.5)

Classify a system of equations by graphing (Eighth grade – Y.6)

Classify a system of equations (Eighth grade – Y.7)

Solve a system of equations using substitution (Eighth grade – Y.8)

Solve a system of equations using elimination (Eighth grade – Y.10)

 

8.8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables.

Solve a system of equations by graphing: word problems (Eighth grade – Y.3)

Solve a system of equations using substitution: word problems (Eighth grade – Y.9)

Solve a system of equations using elimination: word problems (Eighth grade – Y.11)

8.8.F Functions

 

8 Define, evaluate, and compare functions.

 

8.8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Identify functions (Eighth grade – X.1)

Complete a table for a linear function (Eighth grade – X.7)

Graph a line from a function table (Eighth grade – X.8)

Evaluate a function graphically (Eighth grade – X.10)

 

8.8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Graph a line from a function table (Eighth grade – X.8)

Graph a line from an equation (Eighth grade – X.9)

Write a linear function from a table (Eighth grade – X.11)

Identify linear and nonlinear functions (Eighth grade – X.14)

 

8.8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Graph a line from an equation (Eighth grade – X.9)

Identify linear and nonlinear functions (Eighth grade – X.14)

 

8 Use functions to model relationships between quantities.

 

8.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Find the constant of proportionality from a graph (Eighth grade – I.3)

Write equations for proportional relationships (Eighth grade – I.4)

Find the constant of proportionality: word problems (Eighth grade – I.7)

Solve problems involving proportional relationships (Eighth grade – I.8)

Find the slope of a graph (Eighth grade – W.1)

Find the slope from two points (Eighth grade – W.2)

Find a missing coordinate using slope (Eighth grade – W.3)

Write a linear equation from a graph (Eighth grade – W.7)

Write a linear equation from two points (Eighth grade – W.9)

Rate of change (Eighth grade – X.4)

Constant rate of change (Eighth grade – X.5)

Write a linear function from a table (Eighth grade – X.11)

Write linear functions: word problems (Eighth grade – X.12)

 

8.8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Write linear functions: word problems (Eighth grade – X.12)

8.8.G Geometry

 

8 Understand congruence and similarity using physical models, transparencies, or geometry software.

 

8.8.G.1 Verify experimentally the properties of rotations, reflections, and translations:

 

8.8.G.1.a Lines are taken to lines, and line segments to line segments of the same length.

Identify reflections, rotations, and translations (Eighth grade – Q.1)

Translations: graph the image (Eighth grade – Q.2)

Reflections: graph the image (Eighth grade – Q.4)

Rotations: graph the image (Eighth grade – Q.6)

 

8.8.G.1.b Angles are taken to angles of the same measure.

Identify reflections, rotations, and translations (Eighth grade – Q.1)

Translations: graph the image (Eighth grade – Q.2)

Reflections: graph the image (Eighth grade – Q.4)

Rotations: graph the image (Eighth grade – Q.6)

 

8.8.G.1.c Parallel lines are taken to parallel lines.

Identify reflections, rotations, and translations (Eighth grade – Q.1)

Translations: graph the image (Eighth grade – Q.2)

Reflections: graph the image (Eighth grade – Q.4)

Rotations: graph the image (Eighth grade – Q.6)

 

8.8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Similar and congruent figures (Eighth grade – N.10)

Congruent figures: side lengths and angle measures (Eighth grade – N.12)

Congruence statements and corresponding parts (Eighth grade – N.13)

 

8.8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Translations: find the coordinates (Eighth grade – Q.3)

Reflections: find the coordinates (Eighth grade – Q.5)

Rotations: find the coordinates (Eighth grade – Q.7)

Dilations: graph the image (Eighth grade – Q.8)

Dilations: find the coordinates (Eighth grade – Q.9)

 

8.8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Similar and congruent figures (Eighth grade – N.10)

Similar figures: side lengths and angle measures (Eighth grade – N.11)

 

8.8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Identify complementary, supplementary, vertical, adjacent, and congruent angles (Eighth grade – N.1)

Find measures of complementary, supplementary, vertical, and adjacent angles (Eighth grade – N.2)

Transversal of parallel lines (Eighth grade – N.3)

Find missing angles in triangles and quadrilaterals (Eighth grade – N.6)

Exterior Angle Theorem (Eighth grade – N.7)

Interior angles of polygons (Eighth grade – N.9)

Congruent triangles: SSS, SAS, and ASA (Eighth grade – N.14)

 

8 Understand and apply the Pythagorean Theorem.

 

8.8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

Converse of the Pythagorean theorem: is it a right triangle? (Eighth grade – O.5)

 

8.8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Pythagorean theorem: find the length of the hypotenuse (Eighth grade – O.1)

Pythagorean theorem: find the missing leg length (Eighth grade – O.2)

Pythagorean theorem: find the perimeter (Eighth grade – O.3)

Pythagorean theorem: word problems (Eighth grade – O.4)

 

8.8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Distance between two points (Eighth grade – P.4)

 

8 Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

 

8.8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Volume of cylinders and cones (Eighth grade – N.31)

Volume of spheres (Eighth grade – N.32)

8.8.SP Statistics and Probability

 

8 Investigate patterns of association in bivariate data.

 

8.8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Scatter plots (Eighth grade – AA.14)

Outliers in scatter plots (Eighth grade – BB.8)

 

8.8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

 

8.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Find the slope of a graph (Eighth grade – W.1)

Constant rate of change (Eighth grade – X.5)

Graph a line from an equation (Eighth grade – X.9)

Write linear functions: word problems (Eighth grade – X.12)

 

8.8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Interpret stem-and-leaf plots (Eighth grade – AA.9)

Interpret histograms (Eighth grade – AA.10)

Create histograms (Eighth grade – AA.11)

Create frequency charts (Eighth grade – AA.12)

Grade 7 – CA Common Core Standards & IXL Practice

7.7.RP    Ratios and Proportional Relationships
7    Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.7.RP.1     Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Understanding ratios (Seventh grade – J.1)

Unit rates (Seventh grade – J.5)

Unit prices (Seventh grade – M.3)

Unit prices with unit conversions (Seventh grade – M.4)

 

7.7.RP.2      Recognize and represent proportional relationships between quantities.
7.7.RP.2.a     Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Equivalent ratios (Seventh grade – J.2)

Equivalent ratios: word problems (Seventh grade – J.3)

Do the ratios form a proportion? (Seventh grade – J.6)

Do the ratios form a proportion: word problems (Seventh grade – J.7)

Identify proportional relationships (Seventh grade – K.6)

 

7.7.RP.2.b     Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Find the constant of proportionality from a table (Seventh grade – K.1)

Find the constant of proportionality from a graph (Seventh grade – K.3)

Find the constant of proportionality: word problems (Seventh grade – K.7)

 

7.7.RP.2.c     Represent proportional relationships by equations.

Solve proportions: word problems (Seventh grade – J.9)

Write equations for proportional relationships (Seventh grade – K.4)

Write equations for proportional relationships (Eighth grade – I.4)

 

7.7.RP.2.d     Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
7.7.RP.3  Use proportional relationships to solve multistep ratio and percent problems.

Estimate population size using proportions (Seventh grade – J.10)

Estimate percents of numbers (Seventh grade – L.4)

Percents of numbers and money amounts (Seventh grade – L.5)

Percents of numbers: word problems (Seventh grade – L.6)

Solve percent equations (Seventh grade – L.7)

Solve percent equations: word problems (Seventh grade – L.8)

Percent of change (Seventh grade – L.9)

Percent of change: word problems (Seventh grade – L.10)

Unit prices with unit conversions (Seventh grade – M.4)

Unit prices: find the total price (Seventh grade – M.5)

Percent of a number: tax, discount, and more (Seventh grade – M.6)

Find the percent: tax, discount, and more (Seventh grade – M.7)

Sale prices: find the original price (Seventh grade – M.8)

Multi-step problems with percents (Seventh grade – M.9)

Estimate tips (Seventh grade – M.10)

Simple interest (Seventh grade – M.11)

Compound interest (Seventh grade – M.12)

Experimental probability (Seventh grade – CC.3)

7.7.NS    The Number System
7     Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
7.7.NS.1     Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.7.NS.1.a     Describe situations in which opposite quantities combine to make 0.

Absolute value and opposite integers (Seventh grade – B.4)

7.7.NS.1.b       Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Integers on number lines (Seventh grade – B.2)

Absolute value and opposite integers (Seventh grade – B.4)

Integer inequalities with absolute values (Seventh grade – B.6)

Integer addition and subtraction rules (Seventh grade – C.1)

Add and subtract integers (Seventh grade – C.3)

Complete addition and subtraction equations with integers (Seventh grade – C.4)

Add and subtract integers: word problems (Seventh grade – C.5)

Decimal number lines (Seventh grade – D.3)

Absolute value of rational numbers (Seventh grade – H.3)

Add and subtract rational numbers (Seventh grade – H.6)

 

7.7.NS.1.c     Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Understanding integers (Seventh grade – B.1)

Integers on number lines (Seventh grade – B.2)

Integer addition and subtraction rules (Seventh grade – C.1)

Add and subtract integers (Seventh grade – C.3)

Complete addition and subtraction equations with integers (Seventh grade – C.4)

Add and subtract integers: word problems (Seventh grade – C.5)

Decimal number lines (Seventh grade – D.3)

Add and subtract rational numbers (Seventh grade – H.6)

 

7.7.NS.1.d    Apply properties of operations as strategies to add and subtract rational numbers.

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Add and subtract decimals (Seventh grade – E.1)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

Add and subtract fractions (Seventh grade – G.1)

Add and subtract mixed numbers (Seventh grade – G.3)

Apply addition and subtraction rules (Seventh grade – H.7)

Properties of addition and multiplication (Seventh grade – S.1)

 

7.7.NS.2     Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.7.NS.2.a     Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Multiply and divide rational numbers (Seventh grade – H.8)

Distributive property (Seventh grade – S.2)

 

7.7.NS.2.b     Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Multiplicative inverses (Seventh grade – A.3)

Divisibility rules (Seventh grade – A.4)

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Divide decimals by whole numbers: word problems (Seventh grade – E.6)

Understanding fractions: word problems (Seventh grade – F.3)

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Multiply and divide rational numbers (Seventh grade – H.8)

 

7.7.NS.2.c     Apply properties of operations as strategies to multiply and divide rational numbers.

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Multiply decimals (Seventh grade – E.3)

Divide decimals (Seventh grade – E.5)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

Multiply fractions and whole numbers (Seventh grade – G.7)

Multiply fractions (Seventh grade – G.9)

Multiply mixed numbers (Seventh grade – G.10)

Divide fractions (Seventh grade – G.12)

Divide mixed numbers (Seventh grade – G.13)

Apply multiplication and division rules (Seventh grade – H.9)

Properties of addition and multiplication (Seventh grade – S.1)

 

7.7.NS.2.d     Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Classify numbers (Seventh grade – A.10)

Convert between decimals and fractions or mixed numbers (Seventh grade – H.2)

 

7.7.NS.3     Solve real-world and mathematical problems involving the four operations with rational numbers.

Add and subtract integers (Seventh grade – C.3)

Complete addition and subtraction equations with integers (Seventh grade – C.4)

Add and subtract integers: word problems (Seventh grade – C.5)

Integer multiplication and division rules (Seventh grade – C.6)

Multiply and divide integers (Seventh grade – C.7)

Complete multiplication and division equations with integers (Seventh grade – C.8)

Add and subtract decimals (Seventh grade – E.1)

Add and subtract decimals: word problems (Seventh grade – E.2)

Multiply decimals (Seventh grade – E.3)

Multiply decimals and whole numbers: word problems (Seventh grade – E.4)

Divide decimals (Seventh grade – E.5)

Divide decimals by whole numbers: word problems (Seventh grade – E.6)

Add, subtract, multiply, and divide decimals: word problems (Seventh grade – E.8)

Add and subtract fractions (Seventh grade – G.1)

Add and subtract fractions: word problems (Seventh grade – G.2)

Add and subtract mixed numbers (Seventh grade – G.3)

Add and subtract mixed numbers: word problems (Seventh grade – G.4)

Inequalities with addition and subtraction of fractions and mixed numbers (Seventh grade – G.5)

Multiply fractions and whole numbers (Seventh grade – G.7)

Multiply fractions (Seventh grade – G.9)

Multiply mixed numbers (Seventh grade – G.10)

Multiply fractions and mixed numbers: word problems (Seventh grade – G.11)

Divide fractions (Seventh grade – G.12)

Divide mixed numbers (Seventh grade – G.13)

Divide fractions and mixed numbers: word problems (Seventh grade – G.14)

Add, subtract, multiply, and divide fractions and mixed numbers: word problems (Seventh grade – G.16)

Add and subtract rational numbers (Seventh grade – H.6)

Multiply and divide rational numbers (Seventh grade – H.8)

Add, subtract, multiply, and divide money amounts: word problems (Seventh grade – M.1)

Price lists (Seventh grade – M.2)

7.7.EE     Expressions and Equations
7     Use properties of operations to generate equivalent expressions.
7.7.EE.1     Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Add and subtract like terms (Seventh grade – R.8)

Add, subtract, and multiply linear expressions (Seventh grade – R.9)

Factor linear expressions (Seventh grade – R.10)

Identify equivalent linear expressions (Seventh grade – R.11)

Properties of addition and multiplication (Seventh grade – S.1)

Distributive property (Seventh grade – S.2)

Write equivalent expressions using properties (Seventh grade – S.3)

 

7.7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

7 Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Scientific notation (Seventh grade – A.8)

Compare numbers written in scientific notation (Seventh grade – A.9)

Evaluate numerical expressions involving integers (Seventh grade – C.9)

Round decimals (Seventh grade – D.4)

Estimate sums, differences, and products of decimals (Seventh grade – E.7)

Multi-step inequalities with decimals (Seventh grade – E.9)

Maps with decimal distances (Seventh grade – E.10)

Evaluate numerical expressions involving decimals (Seventh grade – E.11)

Equivalent fractions (Seventh grade – F.1)

Simplify fractions (Seventh grade – F.2)

Compare and order fractions (Seventh grade – F.5)

Compare fractions: word problems (Seventh grade – F.6)

Convert between mixed numbers and improper fractions (Seventh grade – F.7)

Compare mixed numbers and improper fractions (Seventh grade – F.8)

Round mixed numbers (Seventh grade – F.9)

Estimate sums and differences of mixed numbers (Seventh grade – G.6)

Estimate products and quotients of fractions and mixed numbers (Seventh grade – G.15)

Maps with fractional distances (Seventh grade – G.17)

Convert between decimals and fractions or mixed numbers (Seventh grade – H.2)

Compare ratios: word problems (Seventh grade – J.4)

Convert between percents, fractions, and decimals (Seventh grade – L.2)

Compare percents to fractions and decimals (Seventh grade – L.3)

Unit prices with unit conversions (Seventh grade – M.4)

Unit prices: find the total price (Seventh grade – M.5)

Estimate to solve word problems (Seventh grade – N.1)

Multi-step word problems (Seventh grade – N.2)

Guess-and-check word problems (Seventh grade – N.3)

Use Venn diagrams to solve problems (Seventh grade – N.4)

Find the number of each type of coin (Seventh grade – N.5)

Elapsed time word problems (Seventh grade – N.6)

 

7.7.EE.4     Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.7.EE.4.a     Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve proportions: word problems (Seventh grade – J.9)

Solve equations using properties (Seventh grade – S.4)

Model and solve equations using algebra tiles (Seventh grade – T.3)

Solve one-step equations (Seventh grade – T.5)

Solve two-step equations (Seventh grade – T.6)

Solve equations: word problems (Seventh grade – T.7)

Solve equations involving like terms (Seventh grade – T.8)

Solve word problems involving two-variable equations (Seventh grade – V.4)

 

7.7.EE.4.b     Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Solutions to inequalities (Seventh grade – U.1)

Write inequalities from number lines (Seventh grade – U.2)

Graph inequalities on number lines (Seventh grade – U.3)

Solve one-step inequalities (Seventh grade – U.4)

Graph solutions to one-step inequalities (Seventh grade – U.5)

Solve two-step inequalities (Seventh grade – U.6)

Graph solutions to two-step inequalities (Seventh grade – U.7)

7.7.G Geometry
7     Draw, construct, and describe geometrical figures and describe the relationships between them.

 

7.7.G.     Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Scale drawings and scale factors (Seventh grade – J.13)

Similar and congruent figures (Seventh grade – X.12)

Similar figures: side lengths and angle measures (Seventh grade – X.13)

Similar figures and indirect measurement (Seventh grade – X.14)

Congruent figures: side lengths and angle measures (Seventh grade – X.15)

Congruence statements and corresponding parts (Seventh grade – X.16)

Perimeter, area, and volume: changes in scale (Seventh grade – X.30)

 

7.7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

 

7.7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Front, side, and top view (Seventh grade – X.25)

Names and bases of 3-dimensional figures (Seventh grade – X.26)

 

7 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

 

7.7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Parts of a circle (Seventh grade – X.21)

Circles: calculate area, circumference, radius, and diameter (Seventh grade – X.22)

Circles: word problems (Seventh grade – X.23)

 

7.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Identify complementary, supplementary, vertical, adjacent, and congruent angles (Seventh grade – X.4)

Find measures of complementary, supplementary, vertical, and adjacent angles (Seventh grade – X.5)

 

7.7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Area of rectangles and parallelograms (Seventh grade – X.18)

Area of triangles and trapezoids (Seventh grade – X.19)

Area and perimeter: word problems (Seventh grade – X.20)

Nets of 3-dimensional figures (Seventh grade – X.27)

Surface area (Seventh grade – X.28)

Volume (Seventh grade – X.29)

7.7.SP Statistics and Probability

 

7 Use random sampling to draw inferences about a population.

 

7.7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Identify representative, random, and biased samples (Seventh grade – BB.5)

 

7.7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Estimate population size using proportions (Seventh grade – J.10)

 

7 Draw informal comparative inferences about two populations.

 

7.7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

 

7.7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Calculate mean, median, mode, and range (Seventh grade – BB.1)

Interpret charts to find mean, median, mode, and range (Seventh grade – BB.2)

Mean, median, mode, and range: find the missing number (Seventh grade – BB.3)

Changes in mean, median, mode, and range (Seventh grade – BB.4)

 

7     Investigate chance processes and develop, use, and evaluate probability models.
7.7.SP.5     Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Probability of simple events (Seventh grade – CC.1)

 

7.7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

Experimental probability (Seventh grade – CC.3)

Make predictions (Seventh grade – CC.4)

 

7.7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

 

7.7.SP.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Probability of simple events (Seventh grade – CC.1)

 

7.7.SP.7.b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

Experimental probability (Seventh grade – CC.3)

 

7.7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

 

7.7.SP.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Probability of opposite, mutually exclusive, and overlapping events (Seventh grade – CC.2)

Identify independent and dependent events (Seventh grade – CC.6)

Probability of independent and dependent events (Seventh grade – CC.7)

 

7.7.SP.8.b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Compound events: find the number of outcomes (Seventh grade – CC.5)

Factorials (Seventh grade – CC.8)

Permutations (Seventh grade – CC.9)

Counting principle (Seventh grade – CC.10)

Combination and permutation notation (Seventh grade – CC.11)

 

7.7.SP.8.c Design and use a simulation to generate frequencies for compound events.

Grade 6 CA Common Core – Standards with Learning Objectives

6.6.RP Ratios and Proportional Relationships

 

6 Understand ratio concepts and use ratio reasoning to solve problems.

 

6.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Interpret ratios of two quantities  Write a ratio to describe objects in a picture (Sixth grade – R.1)

Use ratios to solve  word problems (Sixth grade – R.3)

 

6.6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b is not equal to 0, and use rate language in the context of a ratio relationship.

Interpret and calculate nit rates and equivalent rates (Sixth grade – R.8)

Calculate unit rates.  Unit rates: word problems (Sixth grade – R.9)

 

6.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

 

6.6.RP.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Determine ratio tables (Sixth grade – R.2)

Equivalent ratios (Sixth grade – R.4)

Equivalent ratios: word problems (Sixth grade – R.5)

Compare ratios using tables: word problems (Sixth grade – R.6)

Coordinate graphs review (Sixth grade – W.1)

 

6.6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed.

Unit rates and equivalent rates (Sixth grade – R.8)

Unit rates: word problems (Sixth grade – R.9)

Unit prices with fractions and decimals (Sixth grade – U.3)

Unit prices with customary unit conversions (Sixth grade – U.4)

 

6.6.RP.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Percents of numbers and money amounts (Sixth grade – R.14)

Percents of numbers: word problems (Sixth grade – R.15)

Which is the better coupon? (Sixth grade – U.1)

Unit prices: which is the better buy? (Sixth grade – U.2)

Sale prices (Sixth grade – U.5)

Sale prices: find the original price (Sixth grade – U.6)

Percents – calculate tax, tip, mark-up, and more (Sixth grade – U.7)

 

6.6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Convert and compare customary units (Sixth grade – S.3)

Convert, compare, add, and subtract mixed customary units (Sixth grade – S.4)

Multiply and divide mixed customary units (Sixth grade – S.5)

Customary unit conversions involving fractions and mixed numbers (Sixth grade – S.6)

Convert and compare metric units (Sixth grade – S.7)

Convert between customary and metric systems (Sixth grade – S.8)

Unit prices with customary unit conversions (Sixth grade – U.4)

6.6.NS The Number System

 

6 Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

 

6.6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Divide whole numbers by unit fractions using models (Sixth grade – L.1)

Reciprocals (Sixth grade – L.2)

Divide whole numbers and unit fractions (Sixth grade – L.3)

Divide fractions (Sixth grade – L.5)

Estimate quotients when dividing mixed numbers (Sixth grade – L.6)

Divide fractions and mixed numbers (Sixth grade – L.7)

Divide fractions and mixed numbers: word problems (Sixth grade – L.8)

Add, subtract, multiply, or divide two fractions (Sixth grade – O.7)

Add, subtract, multiply, or divide two fractions: word problems (Sixth grade – O.8)

 

6 Compute fluently with multi-digit numbers and find common factors and multiples.

 

6.6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

Divisibility rules (Sixth grade – C.1)

Division patterns with zeroes (Sixth grade – C.2)

Divide numbers ending in zeroes: word problems (Sixth grade – C.3)

Estimate quotients (Sixth grade – C.4)

Divide whole numbers – 2-digit divisors (Sixth grade – C.5)

Divide whole numbers – 3-digit divisors (Sixth grade – C.6)

Add, subtract, multiply, or divide two whole numbers (Sixth grade – O.1)

Add, subtract, multiply, or divide two whole numbers: word problems (Sixth grade – O.2)

 

6.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Add and subtract decimal numbers (Sixth grade – G.1)

Add and subtract decimals: word problems (Sixth grade – G.2)

Estimate sums and differences of decimals (Sixth grade – G.3)

Maps with decimal distances (Sixth grade – G.4)

Multiply decimals (Sixth grade – H.1)

Estimate products of decimal numbers (Sixth grade – H.2)

Inequalities with decimal multiplication (Sixth grade – H.3)

Divide decimals by whole numbers (Sixth grade – H.4)

Divide decimals by whole numbers: word problems (Sixth grade – H.5)

Multiply and divide decimals by powers of ten (Sixth grade – H.6)

Division with decimal quotients (Sixth grade – H.7)

Inequalities with decimal division (Sixth grade – H.8)

Add, subtract, multiply, or divide two decimals (Sixth grade – O.4)

Add, subtract, multiply, or divide two decimals: word problems (Sixth grade – O.5)

Perform multiple operations with decimals (Sixth grade – O.6)

 

6.6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Identify factors (Sixth grade – E.4)

Greatest common factor (Sixth grade – E.7)

Least common multiple (Sixth grade – E.8)

GCF and LCM: word problems (Sixth grade – E.9)

 

6 Apply and extend previous understandings of numbers to the system of rational numbers.

 

6.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Understanding integers (Sixth grade – M.1)

Working with temperatures above and below zero (Sixth grade – S.9)

 

6.6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

 

6.6.NS.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

Absolute value and opposite integers (Sixth grade – M.2)

Integers on number lines (Sixth grade – M.3)

 

6.6.NS.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Reflections: graph the image (Sixth grade – BB.18)

 

6.6.NS.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Decimal number lines (Sixth grade – F.9)

Integers on number lines (Sixth grade – M.3)

Graph integers on horizontal and vertical number lines (Sixth grade – M.4)

Rational numbers: find the sign (Sixth grade – P.6)

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Coordinate graphs as maps (Sixth grade – W.3)

Translations: graph the image (Sixth grade – BB.17)

 

6.6.NS.7 Understand ordering and absolute value of rational numbers.

 

6.6.NS.7.a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

Write inequalities from number lines (Sixth grade – Z.2)

 

6.6.NS.7.b Write, interpret, and explain statements of order for rational numbers in real-world contexts.

Compare rational numbers (Sixth grade – P.1)

Put rational numbers in order (Sixth grade – P.2)

 

6.6.NS.7.c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

Absolute value and opposite integers (Sixth grade – M.2)

Absolute value of rational numbers (Sixth grade – P.3)

 

6.6.NS.7.d Distinguish comparisons of absolute value from statements about order.

Put rational numbers in order (Sixth grade – P.2)

Absolute value of rational numbers (Sixth grade – P.3)

 

6.6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Coordinate graphs review (Sixth grade – W.1)

Graph points on a coordinate plane (Sixth grade – W.2)

Coordinate graphs as maps (Sixth grade – W.3)

Distance between two points (Sixth grade – W.4)

Relative coordinates (Sixth grade – W.5)

6.6.EE Expressions and Equations

 

6 Apply and extend previous understandings of arithmetic to algebraic expressions.

 

6.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

Write multiplication expressions using exponents (Sixth grade – D.1)

Evaluate exponents (Sixth grade – D.2)

Find the missing exponent or base (Sixth grade – D.3)

Exponents with decimal bases (Sixth grade – D.4)

Exponents with fractional bases (Sixth grade – D.5)

 

6.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

 

6.6.EE.2.a Write expressions that record operations with numbers and with letters standing for numbers.

Write variable expressions (Sixth grade – X.1)

Write variable expressions: word problems (Sixth grade – X.2)

Write a two-variable equation (Sixth grade – AA.6)

 

6.6.EE.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

Identify terms and coefficients (Sixth grade – X.6)

 

6.6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Perform multiple operations with whole numbers (Sixth grade – O.3)

Convert between Celsius and Fahrenheit (Sixth grade – S.10)

Evaluate variable expressions with whole numbers (Sixth grade – X.3)

Evaluate multi-variable expressions (Sixth grade – X.4)

Evaluate variable expressions with decimals, fractions, and mixed numbers (Sixth grade – X.5)

Complete a table for a two-variable relationship (Sixth grade – AA.5)

 

6.6.EE.3 Apply the properties of operations to generate equivalent expressions.

Properties of addition (Sixth grade – X.7)

Properties of multiplication (Sixth grade – X.8)

Distributive property (Sixth grade – X.9)

Write equivalent expressions using properties (Sixth grade – X.11)

 

6.6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

Add and subtract like terms (Sixth grade – X.12)

Identify equivalent expressions (Sixth grade – X.13)

 

6 Reason about and solve one-variable equations and inequalities.

 

6.6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Does x satisfy an equation? (Sixth grade – Y.1)

Find the solution from a set (Sixth grade – Y.2)

Solve one-step equations with whole numbers (Sixth grade – Y.6)

Solutions to inequalities (Sixth grade – Z.1)

Solve one-step inequalities (Sixth grade – Z.4)

 

6.6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Convert between Celsius and Fahrenheit (Sixth grade – S.10)

Write variable expressions: word problems (Sixth grade – X.2)

Write an equation from words (Sixth grade – Y.3)

Solve word problems involving two-variable equations (Sixth grade – AA.4)

 

6.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Model and solve equations using algebra tiles (Sixth grade – Y.4)

Write and solve equations that represent diagrams (Sixth grade – Y.5)

Solve one-step equations with whole numbers (Sixth grade – Y.6)

Solve one-step equations with decimals, fractions, and mixed numbers (Sixth grade – Y.7)

Solve one-step equations: word problems (Sixth grade – Y.8)

 

6.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Write inequalities from number lines (Sixth grade – Z.2)

Graph inequalities on number lines (Sixth grade – Z.3)

 

6 Represent and analyze quantitative relationships between dependent and independent variables.

 

6.6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

Solve one-step equations: word problems (Sixth grade – Y.8)

Identify independent and dependent variables (Sixth grade – AA.2)

Find a value using two-variable equations (Sixth grade – AA.3)

Solve word problems involving two-variable equations (Sixth grade – AA.4)

Complete a table for a two-variable relationship (Sixth grade – AA.5)

Write a two-variable equation (Sixth grade – AA.6)

Identify the graph of an equation (Sixth grade – AA.7)

Graph a two-variable equation (Sixth grade – AA.8)

Interpret a graph: word problems (Sixth grade – AA.9)

Write an equation from a graph using a table (Sixth grade – AA.10)

6.6.G Geometry

 

6 Solve real-world and mathematical problems involving area, surface area, and volume.

 

6.6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Area (Sixth grade – BB.23)

Area of compound figures (Sixth grade – BB.24)

Compare area and perimeter of two figures (Sixth grade – BB.28)

 

6.6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Volume of cubes and rectangular prisms (Sixth grade – BB.36)

 

6.6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Coordinate graphs review (Sixth grade – W.1)

Distance between two points (Sixth grade – W.4)

 

6.6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Nets of 3-dimensional figures (Sixth grade – BB.35)

Surface area of cubes and rectangular prisms (Sixth grade – BB.37)

Volume and surface area of triangular prisms (Sixth grade – BB.38)

6.6.SP Statistics and Probability

 

6 Develop understanding of statistical variability.

 

6.6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

Identify representative, random, and biased samples (Sixth grade – DD.4)

 

6.6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Stem-and-leaf plots (Sixth grade – CC.3)

Create line plots (Sixth grade – CC.5)

Interpret box-and-whisker plots (Sixth grade – CC.19)

 

6.6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Calculate mean, median, mode, and range (Sixth grade – DD.1)

Interpret charts to find mean, median, mode, and range (Sixth grade – DD.2)

Mean, median, mode, and range: find the missing number (Sixth grade – DD.3)

 

6 Summarize and describe distributions.

 

6.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Interpret pictographs (Sixth grade – CC.1)

Create pictographs (Sixth grade – CC.2)

Stem-and-leaf plots (Sixth grade – CC.3)

Interpret line plots (Sixth grade – CC.4)

Create line plots (Sixth grade – CC.5)

Create frequency tables (Sixth grade – CC.7)

Interpret bar graphs (Sixth grade – CC.8)

Create bar graphs (Sixth grade – CC.9)

Interpret double bar graphs (Sixth grade – CC.10)

Create double bar graphs (Sixth grade – CC.11)

Create histograms (Sixth grade – CC.13)

Circle graphs with fractions (Sixth grade – CC.14)

Interpret line graphs (Sixth grade – CC.15)

Create line graphs (Sixth grade – CC.16)

Interpret double line graphs (Sixth grade – CC.17)

Create double line graphs (Sixth grade – CC.18)

Interpret box-and-whisker plots (Sixth grade – CC.19)

Choose the best type of graph (Sixth grade – CC.20)

 

6.6.SP.5 Summarize numerical data sets in relation to their context, such as by:

 

6.6.SP.5.a Reporting the number of observations.

Create frequency tables (Sixth grade – CC.7)

Create histograms (Sixth grade – CC.13)

 

6.6.SP.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Identify representative, random, and biased samples (Sixth grade – DD.4)

 

6.6.SP.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Calculate mean, median, mode, and range (Sixth grade – DD.1)

Interpret charts to find mean, median, mode, and range (Sixth grade – DD.2)

Mean, median, mode, and range: find the missing number (Sixth grade – DD.3)

 

6.6.SP.5.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Iowa Math Test

Mathematics

The chart below explains what this test assesses at various developmental levels.

Test Description
Level 5/6 This assessment consists of questions about beginning Mathematics concepts, problem solving, and mathematics operations.

The content standards include numeration, geometry, measurement, and applications of addition and subtraction in word problems. Items are read aloud, and responses are pictures and numbers.

Level 7 All questions are read aloud in this assessment, which is administered in two separate sessions.

In Part 1, the response options for each question are either pictorial or numerical. Students are required to demonstrate their understanding of, and ability to apply, a variety of concepts in the areas of number sense and operations, geometry, measurement, and number sentences.

In Part 2, some questions involve the interpretation of data presented in graphs or tables: students locate data, compare amounts, or develop generalizations.

For other questions, brief word problems are presented, students solve the problems, and then they record their answers according to the choices provided. One choice in each set is N, meaning that the problem’s solution is not given among the choices presented.

Level 8 The same description as Level 7 with this addition to Part 2:

For other questions, students select a number sentence that could be used to solve the problem.

Levels 9–14 Administered in two parts, this assessment requires students to demonstrate an understanding of Mathematics concepts, relationships, visual representations, and problem solving. Questions deal with number sense and operations, algebraic patterns and connections, data analysis, probability, statistics, geometry, and measurement.
Levels 15–17/18 This assessment measures students’ ability to solve quantitative problems.

The questions present problems that require basic arithmetic and measurement, estimation, data interpretation, and logical thinking. The questions are drawn from the areas of number sense and operations, algebraic patterns and connections, data analysis, probability, statistics, geometry, and measurement

CBEST Administration

The Basic Skills Requirement (CBEST)

Source:

The Commission on Teacher Credentialing has the responsibility to select, administer and interpret examinations used to meet certification requirements. The Commission uses examinations in various areas of certification.

Information on the examinations required for the type of certification you are seeking can be found in the Credential Requirements section of the Commission website.

This article covers: California Basic Educational Skills Test (CBEST) Information Leaflet CL-667 [PDF] Coded Correspondence: 06-0014 [PDF], 06-0021 [PDF], and 06-0028 [PDF] California Education Code: § 44252 Title 5: § 80071.4

CBEST verifies an individual’s basic skills proficiency in the areas of reading, writing and mathematics. Evaluation Systems, Pearson is the testing contractor responsible for the administration of the CBEST.

Information regarding CBEST content, registration, administration, test schedule, fees, scoring, passing scores, and sample test material may be obtained by visiting the testing website: http://www.ctcexams.nesinc.com

Candidates enrolling in a Commission-approved credential program who have not satisfied the basic skills requirement must take the CBEST or other approved basic skills test for diagnostic purposes unless the individual is otherwise exempt.

The basic skills test must be passed prior to obtaining certification, serving as an intern or, for Multiple Subject, Single Subject, and Education Specialist Teaching Credential candidates, prior to being assigned to daily responsibility for whole class instruction in student teaching.

However, institutions may require passage prior to program enrollment. When registering for the CBEST, examinees may request that up to three institutions received a score report directly from the testing contractor in addition to the official score sent to the examinee.

The Commission has no authority to interpret regulations on the use of the basic skills requirement for employment purposes. Questions regarding employment issues should be directed to the employing agency. See California Education Code 44830 for more information.

The following documents may be issued

pending the completion of the basic skills requirement:
1. Preliminary Credentials — Out-of-state individuals may be issued a five-year preliminary Multiple or Single Subject Teaching Credential or Education Specialist Instruction Credential without the completion of the basic skills requirement with the understanding that they must verify completion of the basic skills requirement within one year from the issuance date of the credential in order for the holder to continue teaching.

2. Out-of-state prepared applicants for credentials that require basic skills (other than Multiple Subject, Single Subject, or Education Specialist Instruction Credentials); California public school employers of certain qualified individuals may request that the Commission issue a One-Year Nonrenewable (OYNR) credential pending the passage of the basic skills requirement.

3. Exchange/Sojourn Credentials – The Commission will issue Exchange or Sojourn Credentials for one year to individuals who meet all of the requirements for the document but have not yet met the basic skills requirement. The credentials will be renewed for the remainder of their term as prescribed in Title 5 regulations once the basic skills requirement has been met.

Pass, Fail and Retake

In order to pass CBEST, one must obtain a score of 41 or higher in each of the three sections (reading, writing and mathematics). However, a section score of 37 is acceptable if the total score is at least 123.

Individuals who pass the CBEST receive an “Examinee Score Report” listing the scores for the test and an overall score, a “Permanent Verification Card” verifying passage of the CBEST, and two copies of a “Verification Transcript.”

Individuals who do not pass the CBEST will only receive the “Examinee Score Report” which lists their numerical scores for each of the three parts of the test (passed and failed), the total numerical score and information about retaking the examination.

The CBEST may be taken as many times as needed. Individuals who receive a minimum passing score of 41 in a section but do not pass the entire examination need only to retake the failed section(s). The passing scores will be computed using the highest score on each section obtained at any test administration.

The minimum passing score for each of the three subtests of the CSET: Multiple Subjects examination plus the CSET:

Writing skills examination is 220. The minimum passing scores for both of the English and Mathematics sections of the California State University (CSU) Early Assessment Program (EAP) are a status as “College Ready” or “Exempt” in each section.

To pass the combined English Placement Test (EPT) and Entry Level Mathematics (ELM) option, the following minimum scores must be met: (1) An EPT score of 151 plus (2) an ELM score of 50 for tests administered since March 2003 or a score of 550 for tests administered prior to March 2003.

Period of Validity

Once the basic skills examination(s) has been passed, it need not be taken again since it indefinitely satisfies the basic skills requirement necessary for certification, program enrollment, and employment.

For the basic skills requirement only, the passing scores for the CSET: Writing Skills plus three subtests of the CSET: Multiple Subjects are valid indefinitely.

Please note that the validity period of the three CSET: Multiple Subjects Subtests scores used to satisfy the subject matter requirement is five years from the individual passing date of each subtest. See Coded Correspondence 00-0006 [PDF]for more information on exam score validity.

Verifying Passage of the Basic Skills Requirement

CBEST, CSET: Multiple Subjects, and CSET: Writing Skills scores are transmitted electronically into the Commission’s databases. In most cases it is not necessary to submit the “Verification Transcript,” however the Commission reserves the right to request evidence of passage when necessary.

Credential applicants must submit official score reports when verifying the California State University (CSU) Early Assessment Program (EAP) option or the English Placement Test (EPT) plus the Entry Level Mathematics (ELM) option. T

hose who have lost their official score reports must contact ETS and request ETS to send, via email, the duplicate exam score information to the Commission.

Special Administration of CBEST

The CBEST is normally offered throughout California as a paper-based test six times a year and nationally as a computer-based test twelve times a year.

Beginning August 6, 2011, the CBEST is available for computer-based testing by appointment, year-round, Monday through Saturday (excluding holidays), on a first-come, first-served basis. Computer-based testing will be offered at numerous test centers in California and over 225 test centers nationwide.

The Commission can arrange for a special administration of CBEST for a school district, a group of school districts, a county office of education, or a group of counties in the event of an emergency employment situation.

No special administrations will be scheduled for a college or university.

An emergency is defined as a reasonably unforeseeable circumstance which cannot be avoided or a foreseeable one that cannot be accommodated because of special and unique staff recruitment problems.

The special administration cannot be scheduled within three weeks prior to a regularly scheduled exam and at least 40 people must be scheduled to take the test. For more information, refer to Title 5 80071.4(g)-(i) or contact the Commission’s Examination and Research Unit exams@ctc.ca.gov.

CBEST Math Content Specification

CALIFORNIA BASIC EDUCATIONAL SKILLS TEST™ (CBEST ®)

TEST SPECIFICATIONS MATHEMATICS – Three Skill Factors

Skill Factor 1: Estimation, Measurement, & Statistical Principles

Skill Factor 2: Computation & Problem Solving

Skill Factor 3: Numerical & Graphic Relationships


-1-  ESTIMATION, MEASUREMENT, & STATISTICAL PRINCIPLES

A. Estimation and Measurement:

Understand and use standard units of length, temperature, weight, and
capacity in the U.S. measurement system.

Measure length and perimeter.

Understand and use estimates of time to plan and achieve work-related
objectives.

Estimate the results of problems involving addition, subtraction,
multiplication, and division prior to computation.

B. Statistical Principles:

Perform arithmetic operations with basic statistical data related to test scores
(e.g., averages, ratios, proportions, and percentile scores).

Understand basic principles of probability and predict likely outcomes based
on data provided (e.g., estimate the likelihood that an event will occur).

Interpret the meaning of standardized test scores (e.g., stanine scores,
percentiles) to determine how individuals performed relative to other
students.


-2-  COMPUTATION & PROBLEM SOLVING

Add, subtract, multiply, and divide with whole numbers.

Add and subtract with positive and negative numbers.

Add, subtract, multiply, and divide with fractions, decimals, and percentages.

Determine and perform necessary arithmetic operations to solve a practical
mathematics problem (e.g., determine the total invoice cost for ordered
supplies by multiplying quantity by unit price, summing all items).

Solve simple algebraic problems (e.g., equations with one unknown).

Determine whether enough information is given to solve a problem; identify
the facts given in a problem.

Recognize alternative mathematical methods of solving a problem.


-3-  NUMERICAL & GRAPHIC RELATIONSHIPS

Recognize relationships in numerical data (e.g., compute a percentage
change from one year to the next).

Recognize the position of numbers in relation to each other (e.g., 1/3 is
between 1/4 and 1/2; -7<-4).

Use the relations less than, greater than, or equal to, and their associated
symbols to express a numerical relationship.

Identify numbers, formulas, and mathematical expressions that are
mathematically equivalent (e.g., 2/4 = 1/2, 1/4 = 25%).

Understand and use rounding rules when solving problems.

Understand and apply the meaning of logical connectives (e.g., and, or,
if-then) and quantifiers (e.g., some, all, noUse numerical information contained in tables, spreadsheets, and various kinds of graphs (e.g., bar, line, circle) to solve mathematics problems.


PLEASE NOTE:  Copyright © 2007 by the Commission on Teacher Credentialing

California Basic Educational Skills Test, CBEST, and the CBEST logo are trademarks, in the U.S. and/or other countries, of the Commission on Teacher Credentialing and Pearson Education, Inc. or its affiliate(s). NES and its logo are trademarks in the U.S. and/or other countries of Pearson Education, Inc. or its affiliate(s).
This document may not be reproduced for commercial use but may be copied for educational purposes