Time's up
This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.
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:
- Know multiplication facts.
Time's up
Achievement objectives
NA3-2: Know basic multiplication and division facts.
Required materials
- Figure It Out, Level 2-3, Basic Facts, "Time's up", page 8
See Materials that come with this resource to download:
- Time's up activity (.pdf)
Activity
Activities similar to those suggested for page 7 can be introduced. Shading odd and even answers on a copy of the multiplication array produces a pattern of a few odd numbers surrounded by even numbers. Students should be encouraged to explain why this occurs. This may lead to general rules about the product of numbers:
O x O = O
O x E = E
E x O = E
E x E = E
(where O is any odd number and E is any even number)
Students might look for factors of a given product, say 24 or 18, write the equations, and look for patterns:
3 x 8 = 24
4 x 6 = 24
6 x 4 = 24
8 x 3 = 24
2 x 9 = 18
2 x 6 = 18
6 x 3 = 18
9 x 2 = 18
These equations might be modelled with square tiles to investigate why the patterns occur. For example, 3 x 8 and 8 x 3 can be seen as rotations of each other:
3 x 8 can be mapped onto 4 x 6.
Students might also investigate the numbers along the diagonals of the table, for example: 4, 9, 16, 25, 36, … (square numbers).
2 x 2 squares of numbers can also be looked at for patterns, for example:
Students may need calculators to find the products. Note that the products of the numbers on each diagonal are equal, and the sums of these numbers have a difference of one.
Activity 1
1. |
12 |
2 x 6 = 12 12 ÷ 6 = 2 |
6 x 2 = 12 12 ÷ 2 = 6 |
2. |
21 |
7 x 3 = 21 21 ÷ 7 = 3 |
3 x 7 = 21 21 ÷ 3 = 7 |
3. |
8 |
8 x 7 = 56 56 ÷ 8 = 7 |
3 x 7 = 21 21 ÷ 3 = 7 |
4. |
4 |
9 x 4 = 36 36 ÷ 9 = 4 |
4 x 9 = 36 36 ÷ 4 = 9 |
5. |
6 |
3 x 6 = 18 18 ÷ 6 = 3 |
6 x 3 = 18 18 ÷ 3 = 6 |
6. |
4 |
4 x 6 = 24 24 ÷ 6 = 4 |
6 x 4 = 24 24 ÷ 4 = 6 |
7. |
3 x 3 |
3 x 3 = 9 |
9 ÷ 3 = 3 |
8. |
7 x 7 |
7 x 7 = 49 |
49 ÷ 7 = 7 |
Note: Each family of facts contains either two or four equations.
Activity 2
1.
8 equations (2 x 6 = 12, 6 x 2 = 12, 12 ÷ 6 = 2, 12 ÷ 2 = 6, 4 x 3 = 12, 3 x 4 = 12, 12 ÷ 4 = 3, 12 ÷ 3 = 4)
2.
4 equations (6 x 7 = 42, 7 x 6 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6)
3.
8 equations (6 x 4 = 24, 4 x 6 = 24, 24 ÷ 6 = 4, 24 ÷ 4 = 6, 8 x 3 = 24, 3 x 8 = 24, 24 ÷ 8 = 3, 24 ÷ 3 = 8) Other equations for 24 not shown on this array:
2 x 12 = 24, 12 x 2 = 24, 24 ÷ 2 = 12, 24 ÷ 12 = 2
4.
8 equations (6 x 3 = 18, 3 x 6 = 18, 18 ÷ 6 = 3, 18 ÷ 3 = 6, 2 x 9 = 18, 9 x 2 = 18, 18 ÷ 2 = 9, 18 ÷ 9 = 2)
5.
2 equations (9 x 9 = 81, 81 ÷ 9 = 9)
6.
6 equations (4 x 4 = 16, 16 ÷ 4 = 4, 8 x 2 = 16, 2 x 8 = 16, 16 ÷ 2 = 8, 16 ÷ 8 = 2)
7.
2 equations (5 x 5 = 25, 25 ÷ 5 = 5)
8.
4 equations (9 x 3 = 27, 3 x 9 = 27, 27 ÷ 9 = 3, 27 ÷ 3 = 9)
Note: The full family of facts is not required for this activity but is provided here for reference.
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