This is a level 2 number and algebra activity from the Figure It Out theme series.
A PDF of the student activity is included.
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solve number sentences involving unknowns
solve addition and subtraction problems using mental strategies
A classmate
Activity One
In this activity, the students should have fun being detectives and attempting to find the mystery numbers. At the same time, they will be further enhancing their understanding of balance or equality in the structure of equations. The students will also apply their knowledge of the nature of addition, subtraction, multiplication, and division. Remind the students that they need to identify the inverse of those operations (backtracking). You may have to work through a puzzle to highlight this and to help the students to follow what is happening.
Some students may have had some previous experience with input and output machines, for example, pages 10–11 of Algebra, Figure It Out, Level 3.
Example
In this activity, the output is given and the original input number has to be found. The students will need to think of the inverse operation to help find the input number that will balance the equation. For example, in question 1, some students may be able to process this operation mentally by thinking “7 added to a number is equal to 12. 12 minus 7 gives 5. The number must have been 5 before 7 was added.”
The input number before the 7 was added to give the output number of 12 must be 5: 5 + 7 = 12.
The students should find that writing down problems to chart their course will be easier than doing them mentally. This will help the students to understand the need to retain balance when working with true equations and to think about how to backtrack the equations.
If the students are having trouble calculating the answers mentally or on paper, you could work through the first question with them:
+ 7 = 12
+ 7 – 7 = 12 – 7 Subtract 7 from each side so the equation is still balanced.
= 12 – 7
= 5
Here are some ways the students might chart or write number statements to solve the puzzles:
1. + 7 = 12 = 12 – 7
2. ÷ 2 = 15 = 15 x 2
3. – 6 = 10 = 10 + 6
4. 29 + = 36 = 36 – 29
5. – 2 = 20 ÷ 2 = 10 + 2
6. ( + 3) x 2 = 18 3 + = 18 ÷ 2 = 9 – 3
7. + 12/4 = 30 + 3 = 30 = 30 – 3
There are other ways to think out or chart these puzzles, including guess and check. Ask the students to share all the strategies they used in solving these puzzles.
Activity Two
The students can create their own number puzzles. Writing the equation first could be helpful.
For example:
5 x 6 + 4 = 34 x 6 + 4 = 34
This could become: Multiply me by 6 and add 4 to me to make 34.
As an extension, you could challenge the students to include context problems. For example:
If you multiply the number of pairs of shoes in my wardrobe by 6 and add 4, there will be 34 pairs of shoes altogether.
Answers to Activity
Activity One
1. Suzie threw the gumboot 8 m, 8 m, and 5 m.
Mere threw the gumboot 6 m, 9 m, and 5 m.
Theo threw the gumboot 8 m, 7 m, and 9 m.
Duncan threw the gumboot 9 m, 4 m, and 4 m.
2. Suzie: 16 m
Mere: 15 m
Theo: 17 m
Duncan: 13 m
3. Theo, Suzie, Mere, Duncan
4. Theo, with a total of 17 m for his top two throws
Activity Two
Practical activity