Fractions lesson 7.2: What children need come know around fractions in qualities 2 and also 3 (CCSS) exercise problems

1. Look at at this sample answers come a problem around making fractions on a geoboard (from day-to-day Mathematics class 3)

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a. Call what fractions are shown in each diagram

top left: 1/12"s, top right: 1/3"s

bottom left: 1/3"s, bottom right: 1/6"s

b. How can you prove the the parts shown in each diagram space equal?

top left: every is a solitary square, and all of the squares room the same size

bottom left: each is a rectangle, and all of the rectangles are the very same size (each rectangle is 4 squares)

top right: each piece includes 4 squares

bottom right: the bottom 2 rectangles have actually 2 squares each. Every of the triangles have the right to be separation into 2 smaller triangles that have the right to be put together to make a rectangle the covers 2 squares, so every triangle has an area the 2 squares:

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c. In what ways are the 2 diagrams top top the right various from the diagrams ~ above the left?

The people on the left have actually pieces that space the same shape and size. The people on the right have pieces that space the very same size, however not the exact same shape.

You are watching: Square divided into 3 equal parts

2. On her geoboard, or on geoboard dot paper, find several an ext ways of mirroring thirds and fourths top top the very same rectangle displayed in the previous difficulty (4 spaces wide by 3 spaces high)

Many answers space possible, the course. Below are a few of mine:

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3. What is a shape that the is difficult to find different ways to divide it in half? What is a form that the is easy to find different ways to division it in half?

It"s tough to find an ext than one method to division a circle into a particular portion (like a half). Rectangles and squares are much easier

4. If you use a yellow hexagon (from your pattern block set) to stand for a whole, what fountain are easy to represent? What shapes would represent them?

Easy fountain are:

1/2: trapezoid

1/3: blue rhombus

1/6: triangle

5. Explain, making use of the same ideas emphasized in the class 3 fraction standards, what 3/4 means. Draw a number-line chart to assist your explanation.

If you break-up a entirety unit right into 4 same parts, then each of those parts has actually size 1/4. 3/4 way 3 parts, each of which has size 1/4.

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6. Explain, making use of the same principles emphasized in the class 3 fraction standards, what 4/3 means. Draw a number-line diagram to aid your explanation.

If you separation a whole unit right into 3 equal parts, then each the those parts has actually size 1/3. 4/3 means 4 parts, each of which has actually size 1/3.

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7. Tell a fraction that is equivalent to 3/4. Attract a rectangle-diagram to help your explanation.

Split a rectangle right into fourths using only horizontal lines, and shade in to display 3 parts of dimension 1/4. Then divide it v 1 upright line down the middle. Currently you have 6 shaded components out of 8 equal components in the whole. That method 3/4 and also 6/8 present the very same amount:

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8. Call a fraction that is tantamount to 3/4. Attract a number-line diagram to aid your explanation.

Split a unit length into fourths, and also put a dot at wherein 3/4 is ~ above the number line.

Now break-up each the the fourths into 2 equal pieces. It takes 8 the those equal pieces to do 1 whole, so each of those show 1/8. Count up to the dot. That number is 6/8.

3/4 and also 6/8 present the same dot top top the number line, for this reason they are identical fractions:

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9. Call a portion that is identical to 2. Attract a number-line diagram to aid your explanation.

There room many possible right answers. This is just one of them:

6/3 = 2 because when if you break-up each unit into 3 equal components (thirds) and count up, climate there room 6 equal actions to obtain to 2.

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10. Describe three different ways that youngsters might settle the trouble of 6 children sharing 8 brownies.

I"m hoping that everyone obtained these two means of fixing the problem:

very first give each kid 1 brownie. The two staying brownies space each break-up into 6 parts, and also each boy gets among the components from each brownie, therefore each boy gets 1 2/6 brownies an initial give each child 1 brownie. Three youngsters share among the staying brownies, and also 3 youngsters share the various other brownie, so each of those brownies is separation into 3 parts. Each kid gets 1 1/3 brownies

There is one other solution strategy the would apply well to this problem:

divide each brownie into sixths. Give each kid one item from each brownie. Each boy gets 8/6 brownies.

Children will frequently move from giving out totality brownies to cutting every of the brownies in half, but that isn"t as most likely a strategy for this problem because splitting the two continuing to be brownies in fifty percent gives only 4 pieces, i m sorry is not enough for 6 children. The is likely that some youngsters would shot to deal with the difficulty by cutting brownies in half, and then cutting the halves in half, however that strategy isn"t likely to be effective for this problem.

11. Describe how to compare 2 fractions that have the same denominator. (Make sure you incorporate the "why the works" not simply the "how to perform it")

If two fractions have the exact same denominator, that means that they space made out of the exact same size pieces. The one v the larger numerator has more pieces, so it is the larger fraction.

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12. Describe how come compare two fractions that have actually the exact same numerator. (Make certain you encompass the "why the works" not just the "how to do it")

If 2 fractions have actually the same numerator, that way they room made the end of the same variety of pieces. If two fractions have actually a different denominator, climate the one with the larger denominator has actually smaller sized pieces, since you require to reduced the totality into more shares. The portion whose piece are larger will be bigger due to the fact that there are the same variety of pieces in both fractions. The portion with the smaller denominator has actually larger pieces, so the portion with the smaller denominator will certainly be the larger fractional amount.