Lesson 19 Compose and Decompose to Add and Subtract

    • Let’s compose and decompose units to add and subtract.

Warm-up Number Talk: Subtract Fractions

Find the value of each expression mentally.

Activity 1 Find and Check Sums

Problem 1

Find the value of each sum.

  1. add. eight thousand, two hundred ninety nine, plus, one
  2. add. eight thousand, two hundred ninety nine, plus, eleven.
  3. add. eight thousand, two hundred ninety nine, plus, one hundred eleven.
  4. add. eight thousand, two hundred ninety nine, plus, one thousand, one hundred eleven.

Problem 2

Use the expanded form of both 8,299 and 1,111 to check the value you found for the last sum.

Problem 3

Each computation shown has at least one error. Find the errors and show the correct calculation.

  1. add. twelve thousand, three hundred nine, plus, four thousand, five hundred sixty seven, equals, sixteen thousand, eight hundred sixty six.
  2. add. thirty two thousand, two hundred sixteen, plus, seven hundred eighty nine, equal, thirty three thousand, nine hundred, ninety five.
  3. Add. Six hundred forty two thousand, nine hundred ninety nine, plus, forty eight thousand, one hundred eleven, equals, six hundred ninety thousand.  
  4. add. eighteen thousand, nine hundred ninety nine, plus, nine thousand, nine hundred ninety nine, equals, twenty seven thousand, nine hundred ninety eight.

Activity 2 Priya’s Family Heirlooms

image of women dressed in sarees

Problem 1

Priya’s mom wore an heirloom bracelet at her wedding in 1996. The bracelet was made in 1947.

Priya subtracted to find out how old the bracelet was when her parents were married.

subtract. one thousand, nine hundred ninety six, minus, one thousand, nine hundred forty seven, equals, forty nine.

Priya learned that her grandmother had also worn the bracelet at her wedding 24 years earlier.

Priya subtracted to find out when her grandparents were married.​​​​​

Subtract. one thousand, nine hundred, ninety six, minus twenty four, equals, one thousand, nine hundred seventy two.

Are both calculations correct? Why does one calculation have some numbers crossed out and some new numbers, but the other one does not? Explain your reasoning.

Problem 2

image of necklace

Priya’s grandmother wore an heirloom necklace and earring set that was 63 years old when she was married in 1972.

  1. If Priya uses the standard algorithm to subtract will she need to decompose a unit? Explain your reasoning.

  2. Use the standard algorithm to subtract and find the year the necklace was made.

Problem 3

Create a subtraction problem that would not require decomposing a unit to subtract. Then solve the problem.

algorithm template. four blank boxes on top of three blank boxes.

Practice Problem

Problem 1

  1. Find the value of the sum. Explain your calculations.

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  2. Find the value of the difference. Explain your calculations.