# Place Value: Counting Involving Base-10 Units

#### Learning Goal

Develop knowledge and skills for counting flexibly by 1s, 10s, and 100s to support base-ten thinking

#### Learning Goal Description

Counting with base-10 units involves quantitatively incrementing (increasing) and decrementing (decreasing) by units of 1, 10, or 100. This topic builds knowledge relating to the relative magnitude of numbers and the organization of numbers in terms of base-ten units. The learning progression includes counting units of the same rank, switching between different units, multiple units, and mixed units, both in the context of base-10 materials and without materials. This knowledge creates a strong foundation for place value, mental computation, and more formal operational thinking for addition and subtraction.

#### Pre-Requisite Knowledge

Students should have facility with the number words and numerals to at least 100. Students should be able to solve addition and subtraction tasks using count-up-from and count-down-from strategies and possibly some non-count-by-one strategies.  (see Ready Set Math modules Early Numeracy: Words, Symbols, and Quantity and Addition & Subtraction: Counting-based Strategies

#### Sub-goal A : Form 10s and count by 10s

Developing knowledge of 10 as a unit and working with units of 10 is fundamental to operating in our base-10 system of numeration. Initial learning includes developing fluency with verbal sequences by 10 on the decuple (e.g., 10, 20, 30, 40, ...) and off the decuple (e.g., 4, 14, 24, 34, ...), both forwards and backwards. The instructional resources involve using individual items to form groups of 10 and connecting the verbal sequences by 10 to quantity, counting collections of 10s and incrementing or decrementing a collection by units of 10, on and off the decuple.
1. Ask students to count by 10s: starting at 10, starting from different multiples of 10, forwards and backwards (e.g., Start at 70 and count backwards by 10.).
2. Ask students to count by tens from a number other than a multiple of 10 (e.g., Start at 6 and count by 10s.), forwards and backwards.
3. Ask students to say the number that is 10 more, or 10 less, than a given number (e.g., What is 10 more than 30?; What is 10 more than 73?; What is 10 less than 67?; What is 10 less that 104?)

If students are not successful or need to count by ones, the resources for this sub-goal can provide support in designing instruction for counting by 10s.

#### Sub-goal B

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#### Sub-goal C

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#### Sub-goal D

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Wright, R. J., Ellemor-Collins, D., & Tabor, P. D. (2012). Developing number knowledge: Assessment, teaching & intervention. London: Sage Publications, Ltd. (Chapter 5)

The knowledge developed in this module can support the development of mental strategies for addition and subtraction in the range to 100. (see Ready Set Math module Addition & Subtraction to 100: Mental Strategies)  Consideration should also be given to early learning for multiplication and division. (see Ready Set Math module Multiplication & Division: Counting-based Strategies)

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