3rd Grade - Add And Subtract Fractions

 
     
 
     
 
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3rd
Fractions and Probability
Add and Subtract Fractions
Add and subtract simple fractions (e.g., determine that 1 - 8 + 3 - 8 is the same as 1 - 2).
Number Sense: Add and subtract fractions The ability to add and subtract fractions with like denominators. The ability to reduce simple fractions to the lowest form.
 

Sample Problems

(1)

Define simplest form. (the only common factor (what can be multiplied to get the number) in the numerator and denominator is 1).

(2)

What part of the fraction is added or subtracted? (the top/numerator)

(3)

The higher the number under the fraction line, the (bigger or smaller) the piece? (smaller)

(4)

What does the fraction line mean? (divided by)

(5)

Reminder: the bottom number names how many pieces a unit has been divided into and the top number names how many of those pieces are being used, or are involved.

Learning Tips

(1)

Bring out an apple and tell your child that you would like to share it with him/her. Cut the apple in two. Before it is eaten, ask the child to pretend that some friends are coming over and snacks must be served. Ask your child, “two friends are expected, so how many snack pieces will we need?” Cut the apple pieces in half (now you have four). Next, four more friends walk in. Cut the apple pieces in half again (now you have eight). Lastly, 8 more friends walk in (cut the pieces in half again to have sixteen). Point out that the pieces are so small that four friends decided that they didn’t want to eat such a small piece and they gave all four pieces away to the host. (4/16 + 1/16 = 5/16). Three more friends handed over their apple pieces because it wasn’t their favorite fruit. ((5/16 + 3/16 = 8/16). As you perform these manipulations, ask you r child/children what they notice about these numbers. It may be easier to talk about them if you write the fractions on paper so the child can see how the fraction “looks” on paper. In this way your child will experience that as the denominator numbers get bigger the fraction actually represents smaller and smaller pieces of the whole. They also experience ideas such as 8/16 is the same as ½. This is one example of many different equations that can be created from the apple story.

(2)

Bring out the fraction strips (from lesson 13: strips of paper that are folded and colored in different increments.) and guide students through simple addition and subtraction. For example, 5/10 can be put on the table next to 1/10 and the child can see that together they make 6/10. If subtracted, 4/10. Repeat this activity using multiple strips. Encourage students to write the number sentences as they figure out the problems (5/10 + 1/10 = 6/10). Children can compare the fraction strips and see that 6/12 or 4/8 is the same as ½. A fraction in its simplest form when the only common factor in the numerator and denominator is 1.

(3)

Use stories to help children picture adding and subtracting.

Here’s one idea to teach the adding of fractions: The cherries were ripe and two friends went cherry picking. They each carried a 2-pound can. Unfortunately, they ate more than they collected because at the end of the afternoon, Randy had 1/3 of a pound in his can and Melinda had only 1/3 of a pound in hers. How many thirds did they have all together? (1/3 + 1/3 = 2/3)

What part of the fraction was added together? (numerator) Give practice problems at the point to reinforce that concept.

(4)

Subtracting Fractions: The same two friends went apple picking with Melinda’s mother in late Autumn. Melinda’s mother picked 1 bushel of apples, while the two kids only filled 2/3 of a bushel. How much less did the kids pick than Melinda’s mother? (3/3 – 2/3 = 1/3)

How can 1 whole be written in thirds? (3/3)

What part of the fraction was subtracted? (the numerator)

Have children complete practice problems.

(5)

Draw a fraction tree. Draw the trunk and label it 1. Draw two branches coming off of the trunk and label each one ½. Draw two branches coming off of each of those ½ branches and label them ¼. Draw two branches coming off each of the four ¼ branches and label them 1/8. Help children to see that the two ½ branches together = 1 whole. The two ¼ branches = ½. Children can begin to see how fractions are represented, added together and subtracted. They can also see how 2/4 = ½.

Extra Help Problems

(1)

Color 1/4 red and 2/4 blue. What fraction did you color in all?

(2)

Color 2/8 purple and 2/8 green. What fraction did you color in all?

(3)

Shaded fractional circles. Child determines which is greater or lesser than.

(4)

2/7 + 3/7 = (5/7)

(5)

5/16 + 5/16 = (10/16)

(6)

1/8 + 3/8 = (4/8)

(7)

3/9 + 2/9 = (5/9)

(8)

7/10 + _____= 9/10

(9)

10/10 – 1/10 = (9/10)

(10)

4/5 – 2/5 = (2/5)

(11)

6/8 – 3/8 = (3/8)

(12)

7/9 - ______= 5/9

(13)

The lower the number under the fraction line, the (bigger or smaller) the piece? (bigger)

(14)

Find ¼ of 16. (4)

(15)

Find ½ of 10 (5) What is ¼ of 16 + ½ of 10? (9)

(16)

Find 1/6 of 18 (3)

(17)

Find 1/10 of 100 (10)

(18)

Find 1/8 of 56 (7)

(19)

Find 1/3 of 21 (7)

(20)

Find 1/9 of 54 (6)

(21)

Find 1/7 of 49 (7)

(22)

What is ½ a day? (If ½ of 24 is 12, then half a day is 12 hours)

(23)

What is ½ a year? (If ½ of 12 is 6, then half a year is 6 months)

(24)

What is ½ a minute? (If ½ of 60 is 30, then ½ a minute is 30 seconds)

(25)

What is ½ a minute and ¼ of a minute? (30 + 15 = 45 seconds)

(26)

What is 1/7 of a week + 2/7 of a week? (3 days)

(27)

What fraction is 7/10 – 2/10? (5/10) 5/10 is the same as what other fraction? (1/2)

 

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