## Lesson: Modeling Addition Developing the Concept

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Once children have had practice joining groups with sums to 6, you can introduce the Zero Property and the Commutative Property, and writing addition sentences vertically. Finally, introduce sums to 7 and 8 and then focus on different ways to make a number, up to 8.

Materials: overhead projector, 8 overhead counters, blank overhead transparency; Workmat 2 (Two-Part Mat in the student book), 8 counters, and Ways to Make (PDF file) worksheets for each child; Race to the Sum (PDF file) game board, spinner (0–3), number cubes (1–5) for every 2 children

Preparation: Be prepared to give each child 8 counters and a copy of Workmat 2 during the lesson. Prepare Ways to Make (PDF file) worksheets for each child. Make copies of Race to the Sum (PDF file) game boards and spinners with the numbers from 0 to 3 for each pair of children.

Prerequisite Skills and Concepts: Children should be proficient in counting and recognizing numbers to 10. They should also demonstrate a good understanding of joining groups with sums to 6.

• Say: We have learned how to add two groups and how to write addition sentences.
Place 1 red counter on the left side of the overhead and 4 yellow counters on the right side.
• Ask: Who can tell me what addition sentence we can write?
Elicit from children the sentence 1 + 4 = 5.
• Ask: Which number is the total, or tells us how many in all?
Children should say “five.”
• Say: Another word for total is sum. The sum of 1 + 4 is 5.
Move one counter from the right side of the overhead to the left.
• Ask: How many counters are on this side?
(Point to the left side.)
Children should say “two.”
• Ask: Now how many counters are on this side?
(Point to the right side.)
Children should say “three.”
• Say: Now let's count to find the sum.
Children should count aloud to 5.
• Ask: How do we write this number sentence?
Elicit 2 + 3 = 5.
• Say: Two plus three equals five.
Write 2 + 3 = 5 under 1 + 4 = 5. Make sure the numbers and symbols are lined up. Move all 5 counters to the right side of the overhead.
Elicit “zero.”
• Say: When you add zero to a number, the sum is that number.
Write 0 + 5 = 5 above 1 + 4 = 5. Make sure the numbers and symbols are lined up.
• Say: Let's look at 2 + 3 = 5 again.
Put the blank overhead transparency on the overhead and place counters on top of it to show 2 + 3.
• Ask: Can anyone tell a story for this fact?
Select a child to tell a story illustrating 2 + 3.
• Say: Now I'm going to tell that story a different way.
Turn the transparency around so that it now illustrates 3 + 2. Retell the story, reversing the order of the addends.
• Ask: Is the sum the same in the two stories? (yes) What was different about the two stories?
Children should say the order of the addends was different.
• Say: So if I change the order of the addends, the sum stays the same.
• Ask: Are there still the same number of counters on the overhead? (yes) What addition sentence does this show now?
Elicit 3 + 2 = 5. Write 3 + 2 = 5 under 2 + 3 = 5. Make sure the numbers and symbols are lined up.
• Ask: Look at our list of ways to make 5. What other facts can we add to our list?
Elicit 4 + 1 = 5 and 5 + 0 = 5. Write these on the overhead below the previous sentences.
• Say: There is another way that we can write these addition facts.
Turn the transparency so that the group of 2 counters is above the groups of 3 counters.
• Ask: Do we still have the same number of counters on the overhead? (yes) If I wanted to write 2 + 3 = 5 the way it is shown here, how would I do it?
Elicit from the children that you could write the 2 above the 3. Then, on the board, write this problem vertically.
• Say: When you add down like this, you are adding vertically.
On the board, have children rewrite in vertical form the other number sentences from the overhead.
• Say: So far we have added up to 6. Now let's use the counters to find ways to make 7.
Give children time to work with their counters. Eventually, children should say that 6 + 1, 1 + 6, 5 + 2, 2 + 5, 4 + 3, 3 + 4, 0 + 7 and 7 + 0 all equal 7.
Write these sentences on the overhead.

### 7 + 0 = 7

• Say: Let's look at all the different ways we have found to make seven. Say the numbers as I point to them.
Have children count down each column from top to bottom.
• Ask: Do you see a pattern?
Children should say that each number in the first column is 1 more than the number above it. Children should say that each number in the second column is 1 less than the number above it.

Distribute Ways to Make (PDF file) worksheets. Have children use the counters to find all the ways to make 8 and then write them on their worksheets.

Wrap-Up and Assessment Hints:
You can assign to each child or pair of children a number or set of numbers and have them model and write all the ways to make that number. You can assess children's understanding of addition by observing them as they play Race to the Sum. This game will assess their ability to add numbers to 8. You may wish to have children record their addition sentences as they play.