This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.
A PDF of the student activity is included.
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use basic facts and mental strategies to solve problems
A classmate
This activity is a great way of encouraging the students to solve problems by combining number operations.
Before the students attempt to answer the questions, encourage them to explore the problem to get a feeling for what is happening and show them how they could record their attempts. For example, follow the path along the top route. One way to record this route would be:
Use problem-solving groups of four students and have them discuss starting strategies for question 1. “Trial and error” will be a common strategy, so make sure that this develops into “trial and learn” (from the result). It will also be useful to emphasise the need to be systematic in choosing and recording which pathways have been followed because it is easy to get confused or waste time repeating a rule that didn’t work.
A good strategy for this type of problem is simply to try out and keep a record of different pathways and their answers and then see which part of question 1 matches the path followed.
The students may also get a feeling for the pathways by looking at the last two steps along each pathway. They may notice that two of the possible three ways use division, which will reduce the aggregated totals, while the other way (+ 45 + 15) will increase the total at the end.
Answers to Activity
1. Possible pathways include:
a. 20 x 5 ÷ 10 x 15 + 36 + 45 + 15
b. 20 – 15 + 25 ÷ 6 x 9 + 45 + 15
c. 20 x 5 – 70 + 36 ÷ 11 – 6
d. 20 ÷ 4 x 7 + 3 ÷ 2 – 6
e. 20 ÷ 4 x 15 + 36 + 45 + 15
f. 20 – 15 x 3 x 7 + 3 ÷ 2 – 6
g. 20 x 5 ÷ 10 x 7 + 11 + 45 + 15
(Note that the order of operations does not apply in this step-by-step process.)
2. Totals and pathways will vary.
3. Pathway diagrams will vary.