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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know multiplication facts
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:
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.
Answers to Activity
Activity One
Note: Each family of facts contains either two or four equations.
Activity Two
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.