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

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

Our plan was that I would teach a lesson, she would observe sầu, and then we’d revisit it. I’d focus on talking with students about naming fractional parts, the standard symbolism of fractions, & equivalence.

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My first real-world context: a six-pachồng of water


I showed the class the six-paông xã I had brought to class & talked about one bottle being 1/6 of the six-pachồng, two bottles being 2/6, three bottles being 3/6, and so on up to 6/6 being the same as the whole six-pachồng. The students seemed comfortable with this, and 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-paông chồng, & that 3/6 và 1/2 were equivalent fractions because they both described the same amount of the six pachồng. 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 & 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-pachồng would be left after I drank four bottles, và 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


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 talk about another equivalent fraction for 50%, 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 each of five students, what fraction of the pencils would I have sầu given away?” They answered easily and 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, and 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, & I next called the students’ attention lớn 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.


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


Addison’s hvà shot up. “Can I come up & 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 and denominators to lớn add fractions và think that adding 1/3 và 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.

They were all pleased. I was a wreông xã.

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So much for buying some time.

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

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

After thinking some more, I returned khổng lồ the context of the two tables of students. I said to lớn 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 xã, Margaux, Robbie, & Max, are each 1/6 of that group, just as each bottle of water is 1/6 of the whole six-paông chồng.” Another nod. And because 1/6 + 1/6 equals 2/6, it makes sense to 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 into lớn a sweat.

I tried again lớn explain“Let’s look at just one of the tables,” I suggested. “There are three students—Brad, Samantha, and Jack. 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

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