Monday Mix and Match

This is a completely open-ended task that can be differentiated by the students themselves to make it as easy or as hard as they like.

The idea is that the numbers in the Mix and Match box can be sorted, combined and manipulated in many ways. It is an – into invitation to play with numbers.

We have played with the Mix and Match given above just to give you some ideas to play with. First question: What do you notice?

  • 1, 2, and 3 are in counting sequence.
  • 1, 3, 5 and 7 are in odd number counting sequence.
  • 2, 3, 5, 7 are all prime numbers.
  • 2 is the only even number.
  • 1 is the only square number.

Second question: How can you combine and manipulate these numbers when you are allowed to use any of the four operations, +, –, × and ÷?

Remember each number can be used once only each time.

  • 1 + 2 = 3, 2 + 1 = 3, 3 – 2 = 1, 3 – 1 = 2 (the fact family for 3)
  • 2 + 3 = 5, 3 + 2 = 5, 5 – 2 = 3, 5 – 3 = 2 (the fact family for 5)
  • 2 + 5 = 7, 5 + 2 = 7, 7 – 2 = 5, 7 – 5 = 2 (the fact family for 7)
  • 7 + 1 – 3 = 5, 1 × 2 + 3 = 5, 7 + 3 ÷ 2 = 5, 1 × 7 – 2 = 5
    (mixed operations – students need lots of opportunities to create, read and solve such number sentences.)
  • 3 + 2 = 5 × 1, 7 – 2 = 5 × 1
    (moving towards algebra and the concept of balance, the expressions on each side of the equals sign must balance, i.e., have the same value).

No, we have not exhausted the possibilities but surely that will be enough to get you started.

But wait, there’s more!

Here’s another mix and match for you to play with:

Too easy? Try this one:

Note: In this one, you can also put two numerals together to make a 2-digit number.

Fun? The real fun and a lot of learning happens when you experiment with making your own Mix and Match. We would love to see what you all come up with so post them on our Facebook page or send them to john@naturalmaths.com.au  so we can post a few of yours.

Happy, healthy Monday!