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#### Material

A board with 18 horizontal and 12 vertical squares (2 cm^2).
The top squares are numbered 1 to 10 in red, and 11 to 18 in blue.
A vertical red line after the number 10 divides the board.

Two sets of 9 strips from 1 to 9 squares in length.
Blue with numerals 1 to 9 in red.
Red with numerals 1 to 9 in blue, and subdivided into squares by blue lines. The number is written at the right end of each strip.

Pages for combinations, or booklets of 9 pages with the combinations:
From 1 + 1 = … 1 + 9 = , to 9 + 1 = … 9 + 9 = …

Addition Chart 1 (Control Chart 1), listing all possible combinations of single digit addition, and answers in red.

Addition Chart 2 (Control Chart 2), listing addition combinations with answers, but eliminating all the reverse combinations (following the commutative principle).

#### Presentation

##### Introduction to the Material
1. Invite the child to the lesson.
2. Show him the addition strip board and box of strips.
3. Ask the child to bring the material to a table.
4. Lay an underlay under the board so that it doesn’t move.
5. “Can you find something you’re familiar with? Right, those numbers are familiar! One, two and three…”
6. Call attention to the vertical red line, and that 1 to 10 is red, and that 11 to 19 is blue.
7. Show the child the strips.
8. When removing the strips, hold the box in your dominant hand and cover it with your sub dominant hand, tilt the box to the left and place what you get on the table. (you get what you get)
9. Place the blue strip 1 on the left, aligned to the left.
10. Place the blue strip 2 above the blue strip 1, aligned to the left.
11. Make light conversation about the color and that there are numbers on the strips.
12. Ask the child to place the rest of the blue strips.
13. Repeat this process for the red strips.
14. Point out the vertical blue lines that are on the red strips.
15. “Let’s put a 1 here.”
16. Place a blue 1 strip in the first square, top left.
17. “And let’s add a two.”
18. Place a red 2 strip next to the blue 1.
19. “What does that make? One, two three. And look! The answer is right there! Right above the last square!”
20. Put the strips back in their places.
21. Give another two numbers to combines, such as 1 and 5.
22. “It’s six! There’s the answer, right on the board.”
23. Repeat this process once more.
24. Leave the materials on the table and proceed to the presentation.
##### Exercise 1: Presentation
1. Introduce the paper.
2. “We’re going to use this paper to write down problems.”
3. Ask child to bring two pencils, papers, and underlays on a tray to the table.
4. Write a 1 in the blank spot underneath “Addition Table of.”
5. Ask the child to write it as well.
6. “We are going to do the addition table of 1.”
7. Point to the plus signs.
8. “This little symbol means plus, plus means we add.”
9. Write a 1 in the first addend spot of the paper, ask the child to do it as well.
10. “What does this say? Right, one plus one!”
11. “Can you do that?”
12. Wait for child to place blue strip 1 and red strip 1 on the board.
13. “What is it? Yes, it’s two!”
14. Write the answer in the blank spot after the equal sign.
15. “One plus one equals two.”
16. Repeat this process with 1 added to 2 through 9.
17. Once the child does them all through slow and methodical work, introduce the Addition Chart 1 for control of error.
18. Check all the answers with the child by using the chart.
19. Repeat this process for the table of 2, and table of 3, possibly all in the same day.
20. Show the child how to put the strips back in the box by placing the longest blue strip in first, then make a stair with them, longest to shortest, aligned left.
21. Place red strips in, shortest to longest, making a stair, aligned right.
##### Exercise 2: Loose Slips
1. Invite the child to the lesson.
4. At the table, open the box of addition slips.
5. “Can you pick out a random slip? It doesn’t matter where you pick it from!”
6. Write the problem after the child reads it, ask child to write it as well, such as 8 + 8.
7. Ask the child to use the strips to find the answer.
8. Both of you write the answer on your papers: 8 + 8 = 16.
9. Read it “eight plus eights equals sixteen!”
10. Repeat this process until the child loses interest or ties.
11. Show him the addition chart 1 again to check the answers.
13. “You can use this longer paper and do even more problems on just this one paper!”
##### Exercise 3: Ways to Make a Number
1. Invite the child to the lesson.
3. Think of a higher number such as 7, 8, or 9.
4. “I’m going to show you ways to make a number. I’m thinking of 8, let’s find ways to make 8.”
5. Place the blue strip 1 on the board.
6. “Here’s one, what do I need to place with one to make eight?”
7. Child may get it right at first, if not, just say something such as “oh that doesn’t look long enough. I know you can find it, look again!”
8. If child finds it, say “Right, seven!”
9. Ask the child to write it down on the paper: 1 + 7 = 8.
10. Place a 2 on the board.
11. “Two and what make eight?”
12. Repeat the same process.
13. Continue this process until you end at 7 + 1 = 8.
14. If the child chooses to place an 8 on the board, you can say “Eight plus what makes eight? It’s already eight! So eight plus nothing is eight! What’s another way to say nothing? Right, zero! Eight plus zero is eight! Can you write that?”
15. Ask the child to get the addition chart 1 to check.
##### Exercise 4: Eliminating the Duplicates
1. Invite the child to the lesson.
2. Pick a high number just like in exercise three, such as 8, and ask the child to make it in all the different ways.
3. “Can you make eight in all the different ways with the strips? Remember, start with 1. Come get me when you are done!”
4. “Yes, these are all ways to make eight!”
5. “Let’s read this first one. What does it say?”
6. “Right, it says one and seven make eight.”
7. “Do any of these other strips have the same numbers? Let’s see.”
8. “Oh look! Seven and one are the same numbers as one and seven!”
9. “Let’s slide that down here.”
10. Repeat this process for two and six, three and five.
11. “Well, we took away the ones that were there two times. This is all that’s left to know!”
13. Compare the two charts to each other.
14. “See how full the chart was? Now look! These are the only ones we need to know, because we took out the ones that were there twice!”
15. Ask the child to find 1 + 7 and then 7 + 1.
16. “See, we can’t find it because it’s not there! Only 1 + 7 is on there because that’s they are the same thing!”

#### Exercises

Exercise 1: Child works independently.
Exercise 2: Loose Slips.
Exercise 3: Ways to Make a number.
Exercise 4: Eliminating the Duplicates (commutative principle).