## What's the Difference?

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.

Addends 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.

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.

Call on volunteers to show how to find other differences.

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.

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.

- Index cards
- Calculators
- Paper
- Pasta shapes
- Crayons
- Number cubes
- Addends and Sums Activity Sheet
- Addition Chart
- Calculators and Hundred Boards: Displaying Number Patterns
- Heading to Zero Activity Sheet (assessment option)

**Assessment Options**

- 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.
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.

- 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?

### Recording Two Ways

### How Many Left?

### Where Will I Land?

### What Balances?

### Who's in the Fact Family?

### 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.