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Students may also say 2 13 , but if they do not produce 37 ask if there is another way to express the answer. In conjunction with the mixed number answer 2 13 ask students Maths Question Solution Online Youtube why the fractional part is 13 and not This will help to emphasize the different unit amounts being used.
Part a: or 2 One is flipped upside down compared to the other. In other words, one frac- tion is the reciprocal or multiplicative inverse of the other. Class Activity 2D: Relating Fractions to Wholes This activity is an opportunity not only for problem-solving, thereby addressing Stan- dard for Mathematical Practice 1, but also for attention to precision in using the definition of fraction, thereby attending to Standard for Mathematical Practice 6.
We have to specify the whole in order to interpret unambiguously math drawings that represent fractional amounts. Students will see this point in this activity; it is especially important when it comes to improper fractions and mixed numbers. In your class discussions, you might encourage students to draw a separate picture of the whole and to label the whole as such.
The swing area consists of of the park because it is 1 out of 12 equal parts after suitably subdividing the park. Note that the whole for this and for the 31 is the area of the entire neighborhood park.
The whole for 1 is the area of the playground. Ben should use 21 of the oil in the bottle. Note that the whole for this 12 is the amount of oil in the bottle. But the whole for the 13 and the 32 is a cup of oil. If the two plots did have the same area, then her reasoning would be correct. If the two plots were each 1 acre, then the shaded pieces would in fact be two parts, each of which is 51 of an acre, and therefore the two parts together would be 52 of an acre.
As always, attending to the whole is crucial when working with fractions! At this point, you might like to show IMAP video: Felicia interprets the whole of a fraction number 14 on the DVD , in which Felisha divides 2 cookies equally among 5 people.
Is it 10 or 25? The answer depends on what we take the whole to be. Eric has actually divided the interval from 0 to 1 into 5 equal pieces. She may not understand that the interval between 0 and 1 must be divided into 4 equal pieces. Although not incorrect, it probably means she is not attending to the distance from 0. It looks like Tyler has the idea of making 4 equal intervals to plot 43 , but he may not realize that he needs to take the interval between 0 and 1 as the unit amount for the fraction.
Although it looks like Amy attended to the number of intervals between 0 and 1 and not the number of tick marks, for example , Amy probably ignored the fact that the tick marks are not equally spaced, and that some intervals are longer than others. She could ignore the first and last tick marks and realize that the box is at 41 or she could put in more tick marks and recognize that the location of the box can also be described as See text for the idea of circling intervals.
Students may think of other ways of highlighting the intervals. Be sure students talk about dividing the interval between 0 and 1 into 4 equal- length segments, and in particular, focus on length. It will be worth noting that dividing the interval from 0 to 1 does not involve making 4 new tick marks.
See text for full discussion of where to locate fractions on number lines and see the answer to the practice problem in this section. As the tick marks should be 41 apart, draw 3 equally spaced tick marks between the tick marks for 0 and 1 so as to divide the interval between 0 and 1 into 4 equal pieces and then continue on.
As the tick marks should be 21 apart, draw 2 equally spaced tick marks between the tick marks for 0 and 23 , so as to subdivide the interval between 0 and 23 into 3 equal pieces, and then continue on.
Note that students must recognize that 3 1 2 consists of 3 pieces, each of length 2. As the tick marks should be 41 apart, draw 2 equally spaced tick marks between the tick marks for 0 and 43 and then continue on.
As the tick marks should be 51 apart, draw 3 equally spaced tick marks between the tick marks for 0 and 54 and then continue on. Class Activity 2H: Improper Fraction Problem Solving with Pattern Tiles In this activity, students swap out a given tile for other tiles, so you can use this activity to lead into the idea of equivalent fractions. Because 45 means 5 parts, each of which is one fourth of the original design , we need to find how to break Design A into 5 equal parts.
We can do this by making the design with 5 green triangles. Then 4 of those green triangles will have the area of the original design because 4 fourths make the whole.
This area can also be made with a trapezoid and 1 triangle or with 2 blue rhombuses. Because 53 means 5 parts, each of which is one third of the original design , we need to find how to break Design B into 5 equal parts. A design whose area is the same as the area of 3 trapezoids is what we are looking for because 3 thirds make the whole.
Another possibility is to make the area of the design with 15 triangles, which can be considered as 5 groups of 3 triangles each. Then make a design using 3 groups of 3 triangles each. Implicitly, this uses the equivalence of the fractions 5 15 3 and 9 , so could be a springboard to the topic of equivalent fractions. Because 79 means 9 parts, each of which is one seventh of the original design , we need to find how to break Design C into 9 equal parts.
Then a design whose area is the same as the area of 7 blue rhombuses is what we are looking for because 7 sevenths make the whole. This video explains in two ways why we can multiply the numerator and denominator of a fraction by the same number to obtain a new fraction that is equal to the original fraction. One Maths Question Solution Online Year explanation involves multi- plication by 1. Another explanation involves reasoning about math drawings. Common Core State Standards 4.
Before you have students work on the next Class Activity, you might have them work with fraction strips first. Give each student 3 long strips of paper e. Ask students how they could fold the paper to show fourths of the strip fold in half and then in half again while still folded.
Have the students fold each strip to make fourths and then unfold and shade 3 of the fourths to show 43 of each strip. Next have students fold the second strip back into fourths and then fold in half again.
Ask students to predict the size of the parts eighths and ask them to predict how they will be able to describe the shaded part in terms of those new parts as 6 eighths. Have students fold the third strip back up and have them fold and third strips back into fourths, and then fold in half again, and then again. Have students write equations that correspond with what they have found and ask them how the numerators and denominators are related to the numerator and denominator of Class Activity 2I: Explaining Equivalent Fractions You could show or assign the video Equivalent fractions after students complete the activity.
Before you do the activity, you might ask students if they can think of ways to explain why the two fractions are equal. Some students will think of the idea of multiplying by 1 in the form of Although this is a nice way to explain fraction equivalence, it is only suitable for students who have already studied fraction multi- plication. In the Common Core State Standards, students study equivalent fractions in Grade 4 before they complete their study of fraction multiplication.
Also, stan- dard 4. Note that a brief comment is made about explaining fraction equivalence by multiplying by 1 in the text. See text for an explanation using different numbers. You may wish to present an explanation to students first using different numbers. Then have them explain this example to each other. Students will sometimes give an explanation that involves repeating a drawing of the fraction 3 times.
By subdividing parts, we can argue that we have the same overall amount shaded and in all, therefore the two fractions express the same quantity. The issue addressed in this part may already come up in your discussion of part 1. Note that it makes sense that when we divide each piece into 4 equal pieces there will be 4 times as many pieces in all, and shaded.
So the pieces become smaller and to compensate, there are more of them. The pieces themselves are divided, but the number of pieces is multiplied. Both fractions are equal to 1.
Peter may not realize that when the whole is divided into more parts, each part becomes smaller. The two smallest common denominators are 12 and When giving these fractions common denominators we are dividing the strips and number lines into like parts. In solving this problem, 2 also appears as 4. We can make 4 equal parts horizontally or vertically, which 3 6 look different. In solving the problem the fractions appear as equivalent fractions with denominator 6.
You could also ask students to discuss the different wholes that are used in the problem. The whole associated with 12 and 13 is a cup of butter, but the whole associated with 32 is the amount of butter Jean needs, namely the 12 cup of butter. Using a math drawing, we see that Joey should eat 83 of a cup of cereal. In the drawing, we turn 43 into 86 in order to solve the problem. The whole associated with the 34 in the problem is a cup of cereal. The whole associated with the answer, 83 , is also a cup of cereal.
But the whole associated with 21 is a serving of cereal. Class Activity 2M: Problem Solving with Fractions on Num- ber Lines In this activity, students will need to give fractions either common denominators the first 3 parts or common numerators the last two parts to solve the problems and Maths Question Solution Online Design they will need to focus on the meaning of fractions in terms of number lines. If students are stuck, give them the hint that they could try to make equivalent fractions to help them solve the problems.
These are challenging problems! If we extend these tick marks past the tick mark for is the first 12 3 4 2 one past 3. Use the common denominator Draw five equally spaced tick marks between the tick marks for 0 and Please check the sample to exactly know the material that you will download after buying.
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