Core K-5 – Number and Operations in Base Ten – Progression Overview

 

 Review – focussing on the completed thought in this leftmost column.   Test your recall by hiding this column.
1     Students’ work in the ____ ____ is intertwined with their work on counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. base-ten system
2     Work in the base-ten system relies on these meanings and ____ , but also contributes to deepening students’ understanding of them. properties
3     Position
4    The base-ten system is a remarkably efficient and uniform system for systematically representing ____ ____. all numbers
5    Using only the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, every number can be represented as a ____ ____ ____, where each digit represents a value that depends on its place in the string. string of digits
6    The relationship between ____ ____ by the places in the base-ten system is the same for whole numbers and decimals: the value represented by each place is always 10 times the value represented by the place to its immediate right. values represented
6a   The relationship between values represented by the places in the base-ten system is the same for ____ ____ and decimals: the value represented by each place is always 10 times the value represented by the place to its immediate right. whole numbers
6b   The relationship between values represented by the places in the base-ten system is the same for whole numbers and ____: the value represented by each place is always 10 times the value represented by the place to its immediate right. decimals
6c   The relationship between values represented by the places in the base-ten system is the same for whole numbers and decimals: the value represented by each place is always ____ times the value represented by the place to its immediate right. 10
7    In other words, moving one place to the ____, the value of the place is multiplied by 10. left,
8    In other words, moving one place to the left, the value of the place is ____ by 10. multiplied
9    Because of this uniformity, ____ ____ for computations within the base-ten system for whole numbers extend to decimals standard algorithms
10   Base-ten units 

11    Each ____ of a base-ten numeral represents a base-ten unit: ones, tens, tenths, hundreds, hundredths, etc.

place
12    The ____ in the place represents 0 to 9 of those units. digit
13    Because ____ ____ ____ make a unit of the next highest value, only ten digits are needed to represent any quantity in base ten. ten like units
14    The basic unit is a ____ (represented by the right-most place for whole numbers). one
15    In learning about whole numbers, children learn that ten ones compose a new kind of unit called a ____ . ten
16    They understand ____ ____ numbers as composed of tens and ones, and use this understanding in computations, decomposing 1 ten into 10 ones and composing a ten from 10 ones. two-digit
17    The power of the base-ten system is in repeated bundling by ____: 10 tens make a unit called a “____”. ten, hundred
18    Repeating this process of creating new units by bundling in ____ ____ ____ creates units called thousand, ten thousand, hundred thousand groups of ten
19    In learning about decimals, children ____ a one into 10 equal-sized smaller units, each of which is a tenth. partition
18    Each base-ten unit can be understood in terms of any other ____ ____. base-ten unit
20    For example, ____ ____ can be viewed as a tenth of a thousand, 10 tens, 100 ones, or 1.000 tenths. one hundred
21    ____  for operations in base ten draw on such relationships among the base ten units. Algorithms
22    Computations
23    Standard algorithms for base-ten computations with the four operations rely on ____ numbers written in base-ten notation into base-ten units. decomposing
24    The properties of operations then allow any multi-digit computation to be reduced to a collection of ____  computations. single-digit
25    These single-digit computations sometimes require the ____ ____ ____ of a base-ten unit. composition or decomposition
31    Strategies and algorithms
32    In learning about ____, children partition a one into ____  equal-sized smaller units, each of which is a ____. decimals, 10, tenth
33    Each base-ten unit can be understood in terms of any other ____ ____. base-ten unit
34    For example, ____ hundred can be viewed as a tenth of a thousand,10 tens, 100 ones, or1000 tenths. one
35    Algorithms for operations in base ten draw on such ____  among the base-ten units. relationships
36    Standard algorithms for base-ten computations with the ____ ____  rely on decomposing numbers written in base-ten notation into base-ten units. four operations
37    The properties of operations then allow any ____  computation to be reduced to a collection of single-digit computations. multi-digit
38    These single-digit computations sometimes require the ____ or decomposition of a base-ten unit. composition
39    Beginning in ____, the requisite [computation] abilities develop gradually over the grades. Kindergarten
40    Experience with addition and subtraction made within ____ is a Grade 1 standardand fluency is a Grade 2 standard. 20
41    Computations within 20 that “____ ____,” such as 9 + 8 or 13 – 7 , are especially relevant to NBT because they afford the development of the Level 3 make-a-ten strategies for addition and subtraction described in the OA Progression. cross 10

42    From the NBT perspective, _____ strategies are (implicitly) the first instances of composing or decomposing a base-ten unit.

make-a-ten
43    Such strategies are a  foundation for understanding in Grade 1 that addition may require ____  a tenand in Grade 2 that subtraction may require ____ a ten. composing, decomposing
44    The Standards distinguish ____ from algorithms. strategies
45    For example, students use strategies for addition and subtraction in Grades K-3, but are expected to fluently ____ ____ ____  whole numbers using standard algorithms by the end of Grade 4. add and subtract
46    Use of the ____ ____ can be viewed as the culmination of a long progression of reasoning about quantities, the base-ten system, and the properties of operations. standard algorithms
47    This progression distinguishes between two types of computational strategies: ____ strategies and ____ methods. special, general
48    For ample, a special strategy for computing 398 + 17 is to ____ 17 as 2 + 15 and evaluate (398 + 2) + 15. decompose
49    Special strategies either cannot be ____  to all numbers represented in the base-ten system or require considerable modification in to do so. extended
51    A more readily generalizable method of computing 398 + 17 is to ____ like base-ten units. combine
50    General methods extend to all numbers represented in the base-ten system. A ____ method is not necessarily efficient. general
51    For example, ____ on by ones is a general method that can be easily modified for use with finite decimals. counting
52    General methods based on ____ ____, however, are more efficient and can be viewed as closely connected with standard algorithms. place value
53    Mathematical Practices
51    Both general methods and special strategies are opportunities to ____ competencies relevant to the NBT standards. develop
52    Use and discussion of both types of strategies offer opportunities for developing ____ with place value and properties of operations, and to use these in justifying the correctness of computations (MP 3) fluency
53    Special strategies may be advantageous in situations that require ____ computation, but less so when uniformity is useful. quick
54    Thus, they offer opportunities to raise the topic of ____  appropriate tools strategically (MP 5) using
55    Standard algorithms can be viewed as expressions of regularity in ____ ____ (MP.8) used in general methods based on place value. repeated reasoning
56    ____ ____ and recordings of computations, whether with strategies or standard algorithms, afford opportunities for students to contextualize, probing into the referents for the symbols involved (MP.2). Numerical expressions
57    Representations such as bundled objects or math drawings (e.g., drawings of hundreds, tens, and ones) and diagrams (e.g., simplified renderings of arrays or area models) afford the mathematical practice of explaining ____ among different representations (MP.1). correspondences
58    Drawings, diagrams, and numerical recordings may raise questions related to ____ (MP.6), e.g., does that 1represent 1 one or 1 ten? precision
59    This progression gives examples of ____ that can be used to connect _____ with quantities and to connect numerical representations with combination, composition ,and decomposition of base-ten units as students work towards computational fluency. representations, numerals