Grade 3Math
Estimating the AnswerCalculate with rough numbers, and notice mistakes
You can check whether the answer from the column method is right by estimating with rough numbers. Let's see how to estimate with examples of addition and multiplication.
The narration and the pictures are in Japanese. You can hear the same words that are used in class at a Japanese school.
- Video
- 1:49（6 scenes）
- Problems
- 3 problems
Open this lesson in Japanese（答えの 見当を つけよう）
Let's try
Write the math sentence in your notebook first, then open the answer.
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1Which is a good estimate for the answer to 498 + 2996: "about 3500," "about 8000," or "about 100"?
Hint
498 is close to 500, and 2996 is close to 3000.
Answer
"about 3500." If you think of 498 as about 500 and 2996 as about 3000, 500 + 3000 = 3500. When you calculate, it is 3494, which is close to the estimate.
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2When you got 8787 as the answer to 389 + 4897, what can you do to notice the mistake?
Hint
Compare the estimate with the answer from the column method.
Answer
Think of 389 as about 400 and 4897 as about 5000, and make the estimate 5400. 5400 and 8787 are very different, so you can notice the mistake. The right answer is 5286.
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3Will the answer to 19 × 6 be bigger or smaller than 120?
Hint
If you think of 19 as about 20, 20 × 6 = 120.
Answer
It will be smaller, because 19 is smaller than 20. When you calculate, it is 114.
Words in this lesson
- estimate 見当
- A guess of about how much something will be.
- about およそ
- Roughly. Used when you think of a number as a close number, not the exact one.
- lining up the places 位を そろえる
- In the column method, writing the ones place, the tens place, and so on lined up in columns.
For parents and guardians
- Japan's national curriculum guidelines (the Course of Study) state that in 3rd grade, "estimating the results of calculations should also be touched on." The official commentary gives as examples a situation where, in calculating 389 + 4897, a child did not line up the places and answered 8787, and "by thinking of 389 as about 400 and 4897 as about 5000, the answer would be 5400, so the child can notice that the answer 8787 is wrong"; and that "for the product of 19 × 6, since 20 × 6 is 120, one can estimate that it will be smaller than 120." The two situations in this unit are based on these examples.
- At this grade, deciding on "about 400" is treated as "because it is a number close to 400"; the word "rounding" and its procedure are not used. Rounding and approximate numbers are explained in the 4th grade unit "Estimating with Approximate Numbers."
- Asking "About how much do you think the answer will be?" before using the column method helps your child build the habit of estimating. At home, too, try talking about things like a shopping total: "About how many hundred yen is it?"