Topic E

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Math Past

Topic E Addition of Two-Digit Numbers

Now that students have experienced adding two-digit numbers to one-digit numbers and adding a multiple of 10 to a two-digit number, they are ready to add 2 two-digit numbers. Students leverage place value understanding to make problems easier. They use a variety of concrete, pictorial, and abstract tools to model addends as tens and ones. Students record their reasoning by using a written method and then explain their strategy. The goal of topic E is to build number sense that allows students to flexibly manipulate two-digit addends. At first, students self-select ways to combine groups of cubes that represent 2 two-digit numbers. They share how they decomposed each group and combined the resulting parts. Subsequent lessons present the three following ways to add 2 two-digit numbers: • Add like units: Decompose both addends into tens and ones, combine tens with tens and ones with ones, and then put tens and ones together. • Add tens first: Decompose one addend into tens and ones, combine the tens with the other addend, and then add the ones. • Make the next ten: Decompose one addend into tens and ones, combine some (or all) of the ones with the other addend (in many cases to make the next ten), and then add the remaining parts.

Add Like Units Add Tens First Make the Next Ten (Add Ones First)

These three strategies present different ways to add 2 two-digit numbers, primarily to promote flexible thinking; mastering each of the strategies is less important than attaining flexible thinking. When students compare their various recordings, it helps them to identify equivalent expressions that make a problem easier. For example, 35 + 15 is equivalent to 30 + 5 + 10 + 5, but the second expression makes it easy to add 3 tens + 1 ten and 5 + 5. This type of discussion leads students to the general understanding that different ways of thinking about a problem result in the same total.

Using Level 3 strategies, such as those presented in this topic, takes time and practice. Students may self-select the strategies and tools they use to solve the problems, as long as they are able to record and explain their solution pathways.

Progression of Lessons

Lesson 21

Use varied strategies to add 2 twodigit addends. Lesson 22

Decompose both addends and add like units.

I can break up the addends into tens and ones. Then I can combine the tens with tens and ones with ones.

Lesson 23

Decompose an addend and add tens first.

I can break up an addend into tens and ones. Then I can add the tens first to the first addend.

I can break up the tens and ones and combine them in different ways.

Lesson 24

Decompose an addend to make the next ten.

40 is the next ten. 35 needs 5 more. I can break up 25 into 5 and 20 to make 40.

Lesson 25

Compare equivalent expressions used to solve two-digit addition equations.

The number sentence is true because both sides equal 40. We can make easier problems by combining the parts in different ways.