I came across this puzzle in a book full of questions that were on 11-plus tests in the 1940s and 1950s under the ‘General Intelligence’ section (couldn’t use that term nowadays!). It’s a great one for getting the children to reason in a non-standard context:

The leader of a Guide patrol is named Mary Jenkins; so her surname is Jenkins, her Christian name is Mary, and her initials are M.J. There are 6 other girls in the patrol; each has 2 initials. Surnames: Brown, Smith, Evans, Clark, Jones. Christian names: Molly, Celia, Gwen, Ruth, Sally. Two girls have surnames and Christian names beginning with the same letter; two others are named Ruth. One of the twins has the same initials as the leader and the other has the same Christian name as Evans. Write down each girl’s full name.

Here’s a typical route for answering the question:
*There are 6 girls but only 5 surnames/Christian names – there are two Ruths and there are twins.
*To have the same initials as the leader, one twin is Molly Jones.
*The other twin must be Ruth Jones (same Christian name as Evans, only repeated name is Ruth). This also gives Ruth Evans.
*Two Surnames/Christian names with same letter, Sally Smith and Celia Clark
*One Christian name and one surname left, Gwen Brown

I then give children this question to show how they can use the same kind of logical reasoning to answer a more ‘standard’ maths question:

Use the following digits once to make the calculations correct: 7, 6, 3, 9, 8

_______ x 3 = 18 + _______

2 < 9 – _______

_______ / 2 < 4

_______ + 8 > 2 x 2 x 2 x 2

Here’s a typical route to solve the problem:
*2 x 2 x 2 x 2 = 16 so 9 is the only number that can go in the last gap.
*There are two combinations that make the top line balance (7&3, 8&6) but the 8 can’t fit in any of the other gaps, so it must be on the top line with the 6.
*You are left with 7 and 3. Either number can go on the 3rd line but the 7 doesn’t fit the second line, therefore 3 is on line 2.
*By process of elimination, 7 must be on line 3. It is Gwen Brown – the leftover number!

These principles could then be applied and extended in a range of other contexts: for example, Ken Ken puzzles rely on very similar logical thought processes. I will be using these two questions at the start of the school year as I look to establish a positive mathematics culture with my new class.

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One thought on “Reasoning tasks to start the school year

  1. I used this activity with my more able y6 mathematicians for our first homework, making a copy for the parents too and asking each to work through it. It was very well-received by parents who enjoyed working through with their children. The very able worked through independently but most needed help to succeed. The following week I asked the children to use the same approach to solve the number problem. This required a bit more stamina than they were used to. Thank you for sharing your ideas.

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