Lesson 9 Different Ways to Decompose

    • Let’s compare different ways to subtract.

Warm-up Number Talk: Multiples of 10

Find the value of each expression mentally.

Activity 1 Aren’t You Missing Something?

Lin and Clare made base-ten diagrams to find the value of .

Lin

Base ten diagram. 6 tens, 11 ones. 5 tens and 6 ones crossed out.

Clare

Base ten diagram. 2 tens and 1 one.  1 ten crossed out with arrow pointing to a circle with 10 ones inside.  The 1 one is crossed out and 6 ones inside the circle are crossed out.

  1. What do you notice about their work? What do you wonder?

  2. Lin and Clare each wrote equations to show their thinking. Explain how you know which group of equations matches Lin’s work and which matches Clare’s work.

    A:




    B:




  3. How are Lin and Clare’s methods the same? How are they different?

Activity 2 Different Ways to Decompose

Problem 1

Andre found the value of . He made a base-ten diagram and wrote equations to show his thinking.

Base ten diagram. 6 tens and 5 ones. 3 tens crossed out, one ten has an arrow pointing to a circle with 10 ones. 5 ones and 3 ones inside the circle are crossed out.



Do you think Andre’s method is more like Clare’s or Lin’s method? Explain.

Problem 2

Find the value of each difference. Show your thinking.

Practice Problem

Problem 1

Here is how Clare found the value of .

Here is how Han found the value of .

Base ten diagram. 4 tens and 6 ones. 3 tens towers are crossed out. Arrow is pointing from one tower to a circle with 10 ones inside. The 6 ones are crossed out and 3 ones inside the circle are crossed out.

How are Han’s and Clare’s calculations the same?

How are they different?