Lesson 4

Addition Review

Est. Class Sessions: 2–3

Developing the Lesson

Part 1. Adding with Base-Ten Pieces

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If your students worked with base-ten pieces extensively in second grade, you may move quickly through the addition practice problems. However, it is important to thoroughly cover the meaning of the places and trading in Parts 1 and 2. Students also need experience with both paper-and-pencil methods presented in this lesson.

Connect Place Value Representations. Distribute base-ten pieces to student pairs. Tell students to pretend they are helping Eric and Maya at the TIMS Candy Company. The candy company likes to keep track of all the Chocos made.

Present the following problem:

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  • Eric made 23 Chocos and Maya made 34 Chocos. How many Chocos did they make altogether? Write a number sentence to show your total. (23 + 34 = 57)

Have students show the Chocos that Eric and Maya made using base-ten pieces and use the pieces to find the total number of Chocos. See Figure 1.

As students work, ask questions similar to the following to make connections between the base-ten pieces and the symbols in the written number sentence:

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  • What is the value of the 2 in 23? (Possible responses: 20 Chocos, 2 skinnies, or 20 bits)
  • Which of your pieces represent 20 Chocos? (2 skinnies)
  • How many Chocos did Eric and Maya make altogether? (They made 57 Chocos.)
  • What is the value of the 5 in 57 Chocos? (50 Chocos)
  • What do these 7 bits stand for? (The seven ones. The 7 Chocos in the total number.)

When students have completed the problem, ask a student to share his or her thinking using a display of the base-ten pieces and to write a number sentence. A student's solution is shown in Figure 1. As students explain their thinking throughout the lesson, encourage them to refer to the digits in the problem based on their value according to their place. For example, students can describe totaling the tens as “2 skinnies (tens) and 3 skinnies (tens) are 5 skinnies (tens)” or “20 + 30 equals 50.” If students name only the digits in the tens place by saying, “2 + 3 = 5,” ask them to tell you the value of each digit.

Start Collection of Addition Strategies. Tell students you want to make a collection of addition strategies. Start by listing your class's method of using base-ten pieces to add. Record the solution to 23 + 34 on chart paper. Post the solution for later use in the lesson.

Use the Base-Ten Recording Sheet. Distribute four copies to each student and display a copy of the Base-Ten Recording Sheets 2 Master. Show students how to record 23 + 34 on the display. See Figure 2. To the left of the chart, show each addend with base-ten shorthand. Then record the number of bits and skinnies in the chart on the right side of the page. Then show the total. Help students make connections among the representations of the problem: the base-ten pieces, the base-ten shorthand, and the numbers in the columns on the recording sheet.

For example, ask:

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  • What is the value of 3 in 23? (Possible responses: 3 bits or 3 Chocos.)
  • What is the value of the 5 in 57? (Possible responses: 5 skinnies, 50 bits, or 50 Chocos.)
  • How is the 50 bits shown in the base-ten recording sheet? (A 5 is recorded in the skinnies column to show 5 groups of ten or 50 bits or 50 Chocos.)
  • How many Chocos would there be if Eric showed his work as 23 bits and Maya showed hers as 34 bits? (There would be 57 bits—the same amount of Chocos just packaged differently.)
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Mental Math. Mental math strategies are not necessarily strategies completely done in your head. Mental math strategies are those that ask students to think about the numbers they are using and find partitions that can be worked with easily. For example:

53 + 22 = 50 + 20 + 3 + 2 = 70 + 5 = 5.

Mental math strategies also help students develop number sense and place value concepts and help build estimation skills. These strategies help students determine the reasonableness of a solution to a problem. Proficiency and flexibility take time to develop.

If your students need more review, ask them to complete other addition problems that do not require any trades. Each time, students should solve the problem with base-ten pieces. Then they record the addends on the Base-Ten Recording Sheets 2 page in base-ten shorthand and record the number of each piece in the appropriate columns on the right, along with the totals.

Add to Collection of Addition Strategies. Tell students that you are going to add to your collection of addition strategies using the Base-Ten Recording Sheet. Attach the base-ten recording sheet showing your solution to 23 + 34 to the chart you prepared earlier. Label this strategy “Using the Base-Ten Recording Sheet.”

Student Guide:
Student Activity Book:
Master:
23 Chocos plus 34 Chocos is 57 Chocos
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Base-Ten Recording Sheet for 23 + 34 = 57
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