Crunch machine
This is a level 2 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers notes' and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Solve the basic facts.
- Select the operation symbols (+, -, x, ÷) to complete an equation.
Crunch machine
Achievement objectives
NA2-2: Know forward and backwards counting sequences with whole numbers to at least 1000.
NA2-6: Communicate and interpret simple additive strategies using words, diagrams (pictures), and symbols.
Required materials
- Figure It Out, Levels 2–3, Algebra, "Crunch machine", page 17
- calculator
- classmate
See Materials that come with this resource to download:
- Crunch machine activity (.pdf)
Activity
Organising the results in an in/out table may help students recognise patterns:
Some students may need a calculator to help them, although processing the problems mentally is more efficient.
Realising that the = sign must go in one of the vacant squares is a clue to how the problems can be solved in an organised way.
For example, question 3 offers three possibilities:
- 15 = 21 ? 4 ? 40 [This looks unlikely.]
- 15 ? 21 = 4 ? 40 [More likely, although + and – are the only likely operators.]
- 15 ? 21 ? 4 = 40 [Using addition signs gives the correct solution.]
Students may enjoy making up their own problems, although this is another case where creating problems is much easier than solving them.
Activity 1
+ 5
2 + 5 = 7
4 + 5 = 9
6 + 5 = 11
8 + 5 = 13
10 + 5 = 15
- 8
8 – 8 = 0
12 – 8 = 4
16 – 8 = 8
20 – 8 = 12
x 3
7 x 3 = 21
8 x 3 = 24
9 x 3 = 27
10 x 3 = 30
÷ 5
5 ÷ 5 = 1
10 ÷ 5 = 2
15 ÷ 5 = 3
20 ÷ 5 = 4
Activity 2
1.
6 ÷ 3 = 2 or 6 = 3 x 2
2.
50 = 10 + 10 + 30, 50 – 10 = 10 + 30, or 50 – 10 – 10 = 30
3.
15 + 21 + 4 = 40
4.
24 = 6 x 4 or 24 ÷ 6 = 4
5.
16 + 17 = 3 x 11
6.
10 = 2 x 3 + 4 or 10 + 2 = 3 x 4
7.
12 = 3 x 2 x 2 or 12 ÷ 3 = 2 x 2
8.
40 + 3 + 7 = 50
Activity 3
Answers will vary.
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