Making numbers
This is a level 3 number activity from the Figure It Out series. It focuses on writing equations using combinations of operations. 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:
- Write equations using combinations of operations.
Making numbers
Achievement objectives
NA3-6: Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
Required materials
- Figure It Out, Level 3, Basic Facts, "Making numbers", page 24
- numeral cards
- a set of cards showing brackets ( )
- a set of operation cards (addition, subtraction, multiplication, division)
See Materials that come with this resource to download:
- Making numbers activity (.pdf)
- Numeral cards (.pdf)
Activity
Activities 1 and 2
On this page, students are required to use various combinations of numbers and operations to make a target value. Encourage them to use more than one operation in their equations. Have them keep a record of their equations so that they can compare with others and challenge each other as to how many operations they can think of.
Students have the opportunity to use brackets. You may need to explain that this is an important symbol used by mathematicians to designate the order of operations. Students may decide to use their calculators as they try out different combinations, so this may be a good time to discuss the results that different calculators give. For example, if
is keyed into a scientific calculator, it will give 25, that is, 5 + (8 x 3) – 4, whereas some four-function calculators may give 35, that is, (5 + 8) x 3 – 4. A scientific calculator automatically follows the conventions for operations, that is, multiplication and division are calculated before addition and subtraction.
Activity 1
Answers will vary.
Activity 2
1.
Answers will vary. Possible equations include:
- 1 = 3 – 2, 1 = 5 – 4, 1 = 4 – 3, 1 = 2 x 3 – 5
- 2 = 4 – 2, 2 = 5 – 3, 2 = 4 ÷ 2, 2 = 2 x 3 – 4,
- 2 = 3 + 4 – 5
- 3 = 5 – 2, 3 = 2 x 4 – 5, 3 = 2 x 5 – (3 + 4), 3 = 5 – (4 ÷ 2), 3 = (5 + 4) ÷ 3
- 4 = 3 + 5 – 4, 4 = 5 + 2 – 3, 4 = (3 + 5) ÷ 2,
- 4 = (5 – 3) x 2
- 5 = 3 + 2, 5 = 2 x 4 – 3, 5 = 3 + 4 – 2
- 6 = 2 x 3, 6 = (4 x 3) ÷ 2, 6 = 2 x 5 – 4, 6 = 3 + 5 – 2, 6 = (5 – 3) + 4, 6 = (5 + 4) – 3
- 7 = 3 + 4, 7 = 3 x 4 – 5, 7 = 2 x 3 + (5 – 4), 7 = 5 + 2
- 8 = 2 x 4, 8 = 32 ÷ 4, 8 = 24 ÷ 3, 8 = 5 + 3, 8 = (5 – 3) x 4
- 9 = 4 + 5, 9 = 54 ÷ (2 x 3), 9 = 52 – 43, 9 = (5 – 2) x 3
- 10 = 2 x 5, 10 = 2 x 3 + 4, 10 = (4 x 5) ÷ 2, 10 = 5 x 4 ÷ 2
- 11 = 3 x 5 – 4, 11 = 2 x 5 + (4 – 3), 11 = 35 – 24, 11 = 53 – 42
- 12 = 3 x 4, 12 = (5 – 2) x 4
- 13 = 3 x 5 – 2, 13 = 52 ÷ 4, 13 = 45 – 32, 13 = 2 x 5 + 3, 13 = 2 x 4 + 5
- 14 = 3 x 4 + 2, 14 = 42 ÷ 3, 14 = 2 x 5 + 4
- 15 = 3 x 5
- 16 = (3 + 5) x 2
- 17 = 4 x 5 – 3, 17 = 34 ÷ 2, 17 = 3 x 4 + 5, 17 = 3 x 5 + 2
- 18 = 4 x 5 – 2, 18 = 54 ÷ 3
- 19 = 3 x 5 + 4, 19 = 24 – 5, 19 = 23 – 4, 19 = 5 x 4 – 3 + 2
- 20 = 4 x 5
2.
Answers will vary. It could be argued that the easiest numbers to make are the ones with the most possible equations.
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