Fractions class 7.2: What youngsters need to know about fractions in grades 2 and 3 (CCSS) exercise problems

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

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a. Tell what fountain are displayed in each diagram

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

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

b. How could you prove the the parts presented in each diagram room equal?

top left: each is a single square, and every one of the squares are the very same size

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

top right: each piece consists of 4 squares

bottom right: the bottom two rectangles have actually 2 squares each. Each of the triangles have the right to be split into 2 smaller sized triangles that have the right to be put together to do a rectangle that covers 2 squares, so every triangle has an area of 2 squares:

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

The persons on the left have actually pieces that room the same shape and also size. The ones on the right have pieces that space the very same size, yet not the very same shape.

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2. On her geoboard, or on geoboard period paper, find several more ways of mirroring thirds and fourths top top the same rectangle presented in the previous trouble (4 spaces vast by 3 spaces high)

Many answers room possible, that course. Here are a few of mine:

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3. What is a form that that is tough to find different ways to division it in half? What is a shape that it is simple to find various ways to division it in half?

It"s tough to find much more than one method to division a circle right into a particular fraction (like a half). Rectangles and squares are lot easier

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

Easy fountain are:

1/2: trapezoid

1/3: blue rhombus

1/6: triangle

5. Explain, using the same concepts emphasized in the grade 3 portion standards, what 3/4 means. Draw a number-line diagram to assist your explanation.

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

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6. Explain, using the same concepts emphasized in the grade 3 portion standards, what 4/3 means. Attract a number-line chart to aid your explanation.

If you break-up a totality unit into 3 same parts, climate each of those parts has actually size 1/3. 4/3 method 4 parts, each of which has actually size 1/3.

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7. Phone call a portion that is identical to 3/4. Draw a rectangle-diagram to help your explanation.

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

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8. Phone call a fraction that is equivalent to 3/4. Draw a number-line diagram to aid your explanation.

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

Now split each that the fourths into 2 equal pieces. That takes 8 the those equal piece to do 1 whole, so every of those present 1/8. Count up to the dot. The number is 6/8.

3/4 and 6/8 display the exact same dot ~ above the number line, so they are tantamount fractions:

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9. Phone call a fraction that is identical to 2. Draw a number-line diagram to aid your explanation.

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

6/3 = 2 because when if you separation each unit into 3 equal parts (thirds) and count up, then there space 6 equal procedures to obtain to 2.

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10. Describe three various ways that kids might deal with the trouble of 6 kids sharing 8 brownies.

I"m hoping that everyone obtained these two ways of resolving the problem:

an initial give each kid 1 brownie. The two continuing to be brownies room each split into 6 parts, and each child gets one of the components from every brownie, therefore each child gets 1 2/6 brownies very first give each kid 1 brownie. Three youngsters share among the continuing to be brownies, and 3 kids share the other brownie, so each of those brownies is split into 3 parts. Each kid gets 1 1/3 brownies

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

divide each brownie right into sixths. Provide each child one piece from each brownie. Each boy gets 8/6 brownies.

Children will often move from providing out entirety brownies to cutting each of the brownies in half, yet that isn"t as likely a strategy because that this problem since splitting the two staying brownies in half gives just 4 pieces, which is not enough for 6 children. It is likely that some kids would try to solve the trouble by cut brownies in half, and also then cut the halves in half, however that strategy isn"t most likely to be successful for this problem.

11. Describe how to compare two fractions that have actually the very same denominator. (Make certain you incorporate the "why it works" not simply the "how to execute it")

If 2 fractions have actually the exact same denominator, that method that they are made out of the very same size pieces. The one with the bigger numerator has more pieces, so that is the bigger fraction.

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12. Describe how come compare two fractions that have the very same numerator. (Make sure you include the "why the works" not just the "how to execute it")

If two fractions have actually the exact same numerator, that method they space made the end of the same variety of pieces. If two fractions have a different denominator, then the one v the larger denominator has smaller sized pieces, due to the fact that you need to reduced the totality into much more shares. The portion whose pieces are larger will it is in bigger due to the fact that there are the same number of pieces in both fractions. The fraction with the smaller sized denominator has larger pieces, so the portion with the smaller sized denominator will be the bigger fractional amount.