This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework.
A PDF of the student activity is included.
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find factors of numbers
FIO, Levels 3-4, Basic Facts, Matrix, page 10
Photocopy of the grids
This game gives students practice in quickly identifying common multiples of a single-digit number.
The students will need to have good recall of basic multiplication facts. They can find the common multiples, and therefore find the best position for the thrown factor, by mentally dividing each number in a column or row to see if there is a remainder.
Activity One
You could introduce the students to this page by asking what numbers on the dice are factors of 48 and 54.
This activity will help the students to understand how to play the game that follows. Review the scoring system carefully.
Discuss other possible outcomes. For example, “What might have been the outcome if Gina had put the 7 in the box at the top of the right-hand column?”
Game
Whether or not the students beat Gina’s score depends on what they throw on the dice. It is possible to beat Gina’s score. The highest possible score is 15.
For example:
Top boxes 4 6 9
Side boxes 9 9 4
Points: 2 + 3 + 3 + 2 + 2 + 3 = 15
Activity Two
The students can play the game with these two grids several times. Ask them: “Where is the best place to put the first factor?”
When they have placed the first factor, they can work systematically to work out the highest possible score. For example, for the box above the left column in a, they need to find a number on the dice that is a factor of as many of the numbers in that column (18, 25, and 40) as possible:
6 x 3 = 18
9 x 2 = 18
5 x 5 = 25
4 x 10 = 40
5 x 8 = 40
None of the numbers on the dice is a factor of all three numbers in the column. Five is a factor of two of the numbers, 25 and 40. So the highest score that they can get for that box is two points if they put 5 in it.
As an extension, the students could try to design a matrix that will produce a result of more than 15 points or extend the size of the grid to a 4 x 4 matrix for further games.
To create a matrix that produces a score of more than 15 points means that the numbers used in the grid must have more common factors. In grid b, the bottom left-hand corner has 41. But 41 is a prime number, so no score can be generated from this entry in the grid. An easy way to improve the possible top score for this grid would be to replace 41 with a number that has a factor shown on the dice. A profitable replacement would be 48 because this has 4, 6, and 8 as factors. On the
other hand, 84 is a bonus since it has 4, 6, 7, and 8 as factors!
The highest possible score that can be gained from a well-planned 3 x 3 grid is 18. You can achieve this by being able to score three points on every row and every column of the matrix.
Answers to Activities
Activity One
1. With the 6, 9, and 4 in their best boxes, the final grid should look like this:
2. Her total score is: 2 + 2 + 1 + 3 + 3 + 1 = 12.
(Gina gets 3 points from the 6, 3 from the 9, and 1 from the 4.)
Game
A game of factors
Activity Two
a. The highest possible score for a is 13. There are only four ways to get this:
b. There are 72 ways to get the highest possible score of 11 points. Two of these are: