31 or none
This is a level 3 number and algebra strand activity from the Figure It Out series. It relates to stage 6 of the number framework. 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:
- Use basic facts to solve equations.
31 or none
Achievement objectives
NA3-2: Know basic multiplication and division facts.
Required materials
- Figure It Out, Level 2–3, Basic Facts, "31 or none", page 4
- digit cards (0–9) for each player
- at least 2 classmates to play with
See Materials that come with this resource to download:
- 31 or none activity (.pdf)
- 31 or none digit cards (.pdf)
Activity
Game
This activity is based on an ancient Chinese game in which players had to make given totals by using four single-digit numbers and the four operations. Thirty-one is a good target, as there are many ways in which students can reach this score. Students could use a tally sheet to record who has the highest score in each round.
After students have played the game several times, the target number can be changed. Students may wish to describe why it is easier to get a target of 31 than a target of 13. Similarly, they can be given a target total, such as 27, and asked to write as many four-digit combinations for it as they can.
For example:
- (4 x 5) + 3 + 4 = 27
- (7 x 6) - 9 - 6 = 27
- 9 + 6 + 5 + 4 + 8 = 27
- (8 x 5) ÷ 2 + 7 = 27
Where students use different types of calculators, particularly scientific and four-function, the issue of order for operations may arise. For example, given 4 + 6 x 3 – 5 = ?, a scientific calculator will get 17 whereas a four-function calculator will get 25. Four-function calculators perform calculations in the order of keying, that is, 4 + 6 = 10, then 10 x 3 = 30, and then 30 – 5 = 25.
A scientific calculator uses the convention for operations; that is, multiplication and division are calculated before addition and subtraction. With 4 + 6 x 3 – 5 = ?, the 6 x 3 = 18 is performed first, and then 4 is added and 5 subtracted: 18 + 4 – 5 = 17.
Activity
Students will need to approach this systematically. A table would be useful.
Mon |
4 |
|---|---|
Tue |
8 |
Wed |
16 |
… |
… |
Game
Game of addition, subtraction, multiplication, and division.
Activity
64 plums
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