Hãy cho biết có tất cả bao nhiêu số có 3 chữ số lớn hơn 868

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Several years ago, I was working with a class of fourth và fifth graders. Their teacher had begun a unit on fractions & was interested in connecting fractions lớn real-world contexts. “No problem,” I told her.Quý khách hàng đã xem: Combine 2 1/3

Our plan was that I would teach a lesson, she would observe, và then we’d revisit it. I’d focus on talking with students about naming fractional parts, the standard symbolism of fractions, và equivalence.Quý Khách đã xem: Hãy cho thấy tất cả toàn bộ bao nhiêu số gồm 3 chữ số lớn hơn 868

My first real-world context: a six-paông chồng of water


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I showed the class the six-pachồng I had brought khổng lồ class và talked about one bottle being 1/6 of the six-paông chồng, two bottles being 2/6, three bottles being 3/6, & so on up khổng lồ 6/6 being the same as the whole six-pack. The students seemed comfortable with this, & I wrote the fractions on the board:1/6 2/6 3/6 4/6 5/6 6/6

We also talked about three bottles being one-half of the six-pachồng, & that 3/6 & một nửa were equivalent fractions because they both described the same amount of the six paông chồng. I recorded this:3/6 = 1/2

I asked what fraction of the six-pachồng would be gone after I drank four of the bottles and they answered 4/6 easily. I represented this numerically:1/6 + 1/6 + 1/6 + 1/6 = 4/6

I asked what fraction of the six-paông xã would be left after I drank four bottles, & they answered 2/6 easily. I represented this numerically with two equations:6/6 – 4/6 = 2/61 – 4/6 = 2/6

My second real-world context: a box of 12 pencils


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I continued with a different context—a box of 12 pencils. We talked about one pencil being 1/12 of the box, two pencils being 2/12, three pencils being 3/12, và so on. I wrote these fractions on the board:1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 12/12

The pencil box gave sầu us a way to lớn talk about another equivalent fraction for một nửa, this time 6/12. And I talked about 12/12 representing the pencils in the whole box:6/12 = 1/212/12 = 1

I asked, “If I give sầu a pencil to lớn each of five sầu students, what fraction of the pencils would I have given away?” They answered easily và I recorded numerically:1/12 + 1/12 + 1/12 + 1/12 + 1/12 = 5/12

I asked if 5/12 represented more or less than half the box, và they agreed that it was less than half. I recorded again:5/12 Then I hit a snagThe students in this class sat in small groups, and I next called the students’ attention khổng lồ a table where two boys và one girl were seated. I asked them what fractional part of the students at the table were girls. Hands shot up và I had them say the fraction in unison in a whisper voice—one-third. I wrote 1/3 on the board.

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Brad noticed that the table next lớn his also had two boys and one girl sitting at it. Claudia commented, “So if you put the two tables together, then 2/6 would be girls.”


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Addison’s hvà shot up. “Can I come up and write that in fractions?” he asked. I agreed. Addison came up & wrote on the board:1/3 + 1/3 = 2/6

I was stunned. Addison was correct that 2/6 of the students at the two tables were girls. But the addition equation that Addison wrote wasn’t correct. It’s every teacher’s nightmare when students combine the numerators & denominators to add fractions and think that adding 1/3 and 1/3, for example, gives an answer 2/6. But I didn’t think that Addison had applied that incorrect procedure. I wasn’t sure exactly what he was thinking.

So much for buying some time.

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It’s hard lớn think and teach at the same time!I stood quietly & thought for a moment about what khổng lồ vị next.

To fill the quiet, I said to lớn the class, “When thinking about fractions, it’s important to lớn keep your attention on what the whole is.”

After thinking some more, I returned lớn the context of the two tables of students. I said to Addison, “I see that you’re thinking about the two tables together.” He nodded. “So, the group of students at the two tables together has six students.” He nodded again. “Then Brad, Samantha, Jaông chồng, Margaux, Robbie, and Max, are each 1/6 of that group, just as each bottle of water is 1/6 of the whole six-pachồng.” Another nod. And because 1/6 + 1/6 equals 2/6, it makes sense lớn me that 2/6 of that group of six are girls.” I wrote on the board:1/6 + 1/6 = 2/6

None of the students seemed concerned that 1/3 + 1/3, as Addison had written, seemed to produce the same answer as 1/6 + 1/6, as I had written. Now I was breaking out inlớn a sweat.

I tried again to lớn explain“Let’s look at just one of the tables,” I suggested. “There are three students—Brad, Samantha, và Jaông xã. What fraction of the table does Brad represent?” The students answered 1/3 easily. “And what fraction does Jaông xã represent?” They answered 1/3 again. “And what fraction of the table are boys?” They answered 2/3. I wrote on the board, underneath what Addison had written:1/3 + 1/3 = 2/61/3 + 1/3 = 2/3