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What's the Difference?

Number and Operations
Location: Unknown

During this lesson, students use reasoning to find differences from numbers up to 10, using real and virtual calculators and an addition chart as tools. They also play a concentration game.

Give the students calculators. Explain that they are to use the calculator to find pairs of numbers that have a sum of six, and then model each addend pair with their pasta. As they find the addend pairs, ask them to record them on the Addends and Sums Activity Sheet.

pdficonAddends and Sums Activity Sheet 

When they have finished, ask them to write addition and subtraction sentences for one of the rows of the chart. Remind them to use zero as one of the addends for each sum. Repeat with other numbers if you wish. At an appropriate time, ask the students to share the sentences they wrote.

691 mac math5 

Next, demonstrate how they can use an addition chart to find differences. Choose a number in the interior of the chart, and the number at the top of the column it appears in. The addends for the number that will be the number at the top of the same column and the number at the far left of the same row. You may wish to distribute the Addition Chart to students.

pdficonAddition Chart 

Call on volunteers to show how to find other differences.

691 numbers 

Now put the students in pairs and display the Calculators and Hundred Boards: Displaying Number Patterns tool. Assign two pairs at a time to take turns finding and recording differences using the online calculator.

appicon Calculators and Hundred Boards 

Ask those pairs of students not at the computer to play a concentration game in pairs. Using their Addends and Sums Activity Sheets from earlier in the lesson, have them write one subtraction sentence without the answer on each of four index cards, and the answers on four other cards. Next, have one student in each pair collect and shuffle the 16 cards and place them upside down in a 4 × 4 array. The other student should go first in turning over two cards. If the differences match, he or she keeps the cards and takes another turn. If the differences do not match, the cards are returned to the array and the other student takes a turn. Tell the students to continue playing until all the cards have been removed from the array. Then have the pairs of students exchange the card decks that they made and play the game again.

Assessment Options

  1. Put the students in pairs, and give each pair of number cubes and a supply of pasta shapes. Tell them to make a set of 25 pasta shapes each, then to take turns rolling the die and removing that many pasta shapes from their set. Ask them to record each subtraction sentence as they remove the pieces of pasta. The Heading to Zero Activity Sheet is available for the students to use to record their number sentences. The student whose set disappears last will be the winner for each round.
    pdficon  Heading to Zero Activity Sheet 

    After the students have completed several rounds, challenge those who you think are ready to play without the pasta shapes. For example, students might select a target number, roll the number cube, and subtract the number rolled from the target number.

  2. You may wish to document your observations about student understandings and skills on the Teacher Resource Sheet, Class Notes, begun earlier in this unit plan. These comments may be useful when you are planning additional learning experiences for individual students.

Questions for Students 

1. What number pairs have differences of five? Of seven? Of four?

[9-4, 8-3, 7-2, 6-1, 5-0; 9-2, 8-1, 7-0; 9-5, 8-4, 7-3, 6-2, 5-1, 4-0.]

2. When you found addends that had differences of one, did you find any doubles? Why not? How about when there was a difference of 0?

[No; The difference of doubles is zero.]

3. What happens when you add zero to a number? When you subtract zero?

[The sum is the original number; The difference is the original number.]

Teacher Reflection 

  • Which students have some of the facts memorized?
  • Did most students remember the effects of adding zero?
  • Which students have memorized all the subtraction facts? What extension activities are appropriate for those students?
  • Which students still have many facts to memorize? What additional instructional experiences do they need?
Number and Operations

Recording Two Ways

The students make sets of pasta shapes and count some away, then record the subtraction in vertical and horizontal formats. They draw a set and cross out some shapes, then write in both formats the subtraction that the drawing represents.
Number and Operations

How Many Left?

This lesson encourages the students to explore the familiar set model of subtraction. The students write story problems and find differences using sets, including subtracting all and subtracting zero. They record the differences in a chart.
Number and Operations

Where Will I Land?

In this lesson, the students find differences using the number line, a continuous model for subtraction. [Number can be considered in two ways: discrete and continuous. The counting and set models use the discrete form of number.] Students are encouraged to predict differences and to compose puzzles involving subtraction.
Number and Operations

What Balances?

This lesson encourages students to explore another meaning of subtraction, the balance. They use subtraction facts to generate related addition facts and explore at the concrete level the idea of subtraction as the inverse of addition.
Number and Operations

Who's in the Fact Family?

In this lesson, the exploration of the relation of addition to subtraction is continued as the students use problem-solving skills to find fact families, including those in which one addend is zero or in which the addends are alike.

Learning Objectives

Students will:

  • Use calculators and addition charts to find differences.
  • Practice subtraction facts from 10.

NCTM Standards and Expectations

  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.