Tessa, age 6, solves equations, and subtracts with negatives

Grandpa Don only sees Tessa maybe 4 times a year ;-(. When they are together Grandpa tries to spend some time with her doing math, of course. This sessions lasted about 20 minutes.

First Grandpa checked to see if she could multiply. She did three times three equals 9, and wrote it vertically (as she normally does in school):
3
x3
9

Grandpa immediately went to the horizontal notation. After talking about 3 x 3 tens, she said 9 tens. Then Grandpa read each one below and she gave the correct answers, quickly.

The he gave her an equation to solve. "find a number x, multiply by 2, add 3 and you have to get 17", or  "you have to find a number x to make this sentence true". Tessa figured out the first one easily. Then Grandpa gave her the second equation.

Then Grandpa worked on negative numbers with Tessa. She had seen them before, and Grandpa used a thermometer or vertical number line below right as a "model" for adding and subtracting. First Tessa was able to go below zero, to the negatives. So for 5 - 6 Tessa said 1. Grandpa asked her what 5-5= and of course she said zero. Grandpa asked her what 5-4= and she said 1. For 5 - 6 Grandpa showed her that we start at 5, then count down 6 spaces. Where do we end up?

Once Tessa was able to do problems like that Grandpa asked her to do 24 - 15 above, and she was able to count down to get 9. Then Grandpa showed her how to use negative numbers and see if we get the same answer. He started right to left, but probably better he should have gone left to right. So

4 - 5 = -1 and 2 tens- 1 ten or twoty minus onety  (normally 20 - 10) = 10, and 10 and  -1, ten and take away 1 = 9, the same answer. Tessa found when doing 65 - 28, counting down 28 was much harder than using negatives.  5 - 8 = -3, and  60 - 20 = 40. So 40 -3 = 37.

Fine work, Tessa!

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