A Balancing Act

Using Materials

Problem: “Maggie and John are given a bag of sweets each. Both bags have the same number of sweets in them. Maggie shares her bag of sweets with her friend Jan. Maggie gets four sweets, and Jan gets five. John shares his bag with Anne. John gives Anne six sweets. How many sweets does John have left?”

Discuss why this problem is 4 + 5 = ? + 6 and record it on the board or modelling

book. In pairs, nominate one person to be Maggie and the other to be John. Maggie

creates piles of four and five while John has to work out that a pile of six leaves three for the other pile. Common wrong answers are nine and 15. Discuss why they occur and why they are wrong. (Nine comes from adding the left side of the equation and 15 from adding all the numbers on both sides. In both cases, the student views “equals” as meaning “get the answer” rather than “balance each side”.)

Examples: Word stories and recording for: 2 + 4 = ? + 3

5 + 5 = ? + 6

5 + ? = 4 + 3

? + 6 = 6 + 3

? + 6 = 8 + 2

1 + 7 = 4 + ? ...

Using Imaging

Problem: “Solve: 9 + 3 = ? + 7.”

Record the problem on the board or modelling book and discuss how to build piles of counters. Show 9 + 3 in two piles of counters. In separate piles, place five under a container and seven in sight beside it. Encourage the students to think about the equality of the two sides of the equation.

9 + 3 is 12, so switch attention to the other two piles. Record the answer on the board or modelling book.

Examples: Word stories and recording for: 5 + 4 = ? + 3

6 + 5 = ? + 3

5 + ? = 4 + 6

? + 2 = 5 + 3

? + 6 = 8 + 3

3 + 8 = 4 + ? ...

Using Number Properties

Problem: “Solve 67 + ? = 66 + 44”

Discuss why the answer is one less than 44 (because 67 is one more than 66 and “balance” has to be maintained). Record 43 in the square.

Examples: Word stories and recording for: 42 + 38 = ? + 39

55 + 35 = ? + 34

105 + ? = 103 + 43

? + 65 = 67 + 33

? + 180 = 190 + 38

1 020 + ? = 1 010 + 67

Challenging examples: 442 – 38 = ? – 39

585 – 35 = ? – 34

105 – 56 = 103 – ?

? – 65 = 667 – 62

? – 280 = 790 – 29 ...