When students learn math, they also learn how to think through and explain their ideas. This is called “reasoning and proving”. They use what they know about math to explain why they think their answer is right. They do this by showing proof or evidence. Mathematicians do something similar when they make “conjectures”. A conjecture is like a guess that you make when you don’t have all the information. Mathematicians test these guesses by looking for evidence. Then, they use this evidence to see whether their guess was right.
Sometimes, when students talk about their math work with their classmates, they might not agree on the answers. That’s okay! It’s important for each student to be able to explain their own thinking. We don’t want them to just believe they’re right because the teacher says so. We want them to understand why their answer works.
At home, you can encourage your child to engage in reasoning and proving by asking them:
- What’s your prediction? Why?
- Do you have a conjecture?
- Can you explain the reasoning behind your predictions?
- Is this always true?
- Why does this work?
- Have you convinced yourself?
- Can you convince a skeptic?
Which One Doesn’t Belong shows a square split into four smaller squares. Each small square has a different picture, number, or graph. Students look at these, pick the one they think is different from the others, and say, “I think ______ does not belong because ______.” The best part is that any of the four can be the right answer, as long as they can give a good reason. You can even try to find a good reason why each of the four doesn’t belong. It’s a fun way to practice reasoning and proving.
Here are some possible responses for the example below:
I think the 4 and 4 doesn’t belong because it is the only double
I think 6 and 5 doesn’t belong because it is the only one that adds to more than 10
I think the 3 and 0 doesn’t belong because it is the only one with a blank space
I think the 2 and 3 does not belong because it is the only one with 2 prime numbers
Try it Yourself
Primary
Why does it make sense that 2 + 2 is the same as 2 x 2, but 3 x 3 is not the same as 3 + 3?
Would you rather have 5 packs of cards with 2 cards in each pack or 3 packs of cards with 5 cards in each pack?
Junior
Without giving the answer, can you prove that these two addition sentences have (or don’t have) the same sum?
33 + 9 and 35 + 7
Intermediate
Someone said that 2x can be more than 3y. Does this make sense?
Would you rather receive 10 cents each day for one year or 15 cents every weekday for a year?