3rd Grade - Comparing Fractions Using Pictures

Fractions and Probability
Comparing Fractions Using Pictures
Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1 - 2 of a pizza is the same amount as 2 - 4 of another pizza that is the same size; show that 3 - 8 is larger t
Number Sense: comparing fractions The ability to complete basic manipulations of fractions. The ability to determine the least common multiple.

Sample Problems


Help your child to understand that when we write a fraction, we are really drawing a “number picture” to show a number that is less than 1. The bottom number tells us that a whole item was cut into this many pieces. (In other words, if the bottom number is “4” this whole item was cut into 4 pieces.) The top number tells us how many pieces of that size are a part of our number. (In other words, if the top number is “3” then our number includes 3 pieces.) Three-fourths, then, tells us that a whole item was cut into 4 pieces and we are using 3 of them to make this item or number.


Define numerator, denominator and fraction (the numeral above the fraction line that gives us the number of fraction parts that are named below the fraction line, the numeral below the fraction line, a number that represents part of a whole).


What part of the fraction is used to compare two fractions? (the denominators)


How can ½ of a pie be bigger than another ½ of a pie? (the pies are different sizes)


What is one way to help a child find the least common multiple? (make sure the child is familiar with skip counting the multiplication tables 1-10 or 1-12)

Learning Tips


Cut a piece of paper in fourths. Ask the child to fold one square in half. Ask the child to color one of the halves. Have him/her write the part of the fraction that is colored as a fraction (1/2). Remind your child that the number that goes on the bottom tells how many pieces the original item was divided into. The top number tells how many of those pieces are being used (colored, in this case). Have the child fold another square into fourths and color one of the four. Write the fraction (1/4). Strips of paper can be folded and colored in different increments.


Children can use manipulatives to explore fractions. Give the child 12 base ten cubes or other object and have them separate them into various groups and then talk about what fractional part is represented. For example, 10 cubes can be separated in half and 5/10 is the result or 2 cubes can be pulled from a group of 12, which would be 2/12.


Give children blank strips of paper, paper plates or even food items and have them separate them into fractional parts. This is very flexible, but children should come away from the activity understanding that fractions are part of a whole. The top number (numerator) represents the part that is taken away or separated or eaten, etc. and the bottom portion (denominator) represents the total number of pieces. Continue this practice as the child goes about his/her day. Fractions are everywhere and you want to alert the child to their presence.


After children have a basic understanding of fractions, they can explore equivalent fractions. Children can try to match fraction strips. For example, a child can take the strip that represents ½ and match it to the strip that represents 5/10 or 6/12. This should continue until the child has a good understanding of how fractions can be equivalent. This activity can be culminated with a batch of cookies that must be divided amongst a group of friends. How would the cookie be divided if only one friend came over, how about 2 or 3, etc?


Children can learn to make a circle graph to represent a fraction problem/survey. For example, children can ask 10 people what their favorite pet is and then graph the results on a paper plate circle graph. (Take a paper plate and divide it into the number of sections that matches the number of people surveyed. Then choose a color to represent each pet. For example, if you have 5 people that like dogs, then color all five “pie” pieces together and color them red, for instance.)

Extra Help Problems


Which is larger 1/3 or 8/9? Show your answer in a number sentence. (1/3 < 8/9)

Children do not need to know how to find like denominators on their own at this point. Encourage children to use concrete manipulatives and fractional strips/pies to solve the problems.


Circle the numerator: 1/10 (1)


Circle the numerator: 4/9 (4)


Circle the denominator: 1/3 (3)


Circle the denominator: 2/7 (7)


More difficult problems in which students find the like denominator:

What is the least common multiple: 1/3 and 2/9 (9)

(Nine is in the 3’s skip counting)


What is the least common multiple: 1/6 and 5/8 (24)

(Twenty-four is in both the six and 8 skip counting)


Use the fraction tree to encourage students to write equivalents: For example, ½ = 2/4 = 4/8 = 8/16 = 16/32.


Use pieces of pizza or pie to practice equivalency. Children draw pieces of pizza and or pie and write the equivalent fraction next to both pictures. For example, children draw 2 pieces of a 6-piece pizza and write 2/6 and they draw 1 piece of a 3-piece pizza and write 1/3.


Jane eats 3 pieces of a six-piece pizza. Her friend Rob eats 1 piece. How many did they eat all together (show as a fraction)? (4/6) Is there another way to represent that number with a lower denominator (least common multiple)? (2/3) Both 4 and 6 are in the 2’s times table/skip counting.


Complete the pattern: 2, 4, 6, __, 10, 12, _____, 16, 18, 20 (8, 14)


Complete the pattern: ____, _____, 9, ____, 15, 18, 21, 24 (3, 6, 12)


Complete the pattern: 10, 20, 30, ___, _____, ____, 70 (40, 50, 60)


Complete the pattern: ____, 12, _____, 24, _____, 36, _____ (6, 18, 30, 42)


Complete the pattern: 21, 28, _____, ______, 49, 56, ____ (35, 42, 63)


Use fraction pieces of a paper plate cut into 10ths to solve the problems: Jose took 4 pieces of a pie that was cut into 10 pieces. He wanted to give one to his mother, but she wanted two. What fraction of the pie did he have left? His mother felt badly for taking so much pie and she gave one of her pieces to her daughter, Rachel. What fraction of the pie did Rachel get? (4/10, 1/10)


If the family in the above problem cut the whole pizza that is in 10ths pieces in half again how many pieces would there be? Would they be bigger or smaller pieces? (20, smaller)


If the pieces of the pizza were cut into 20ths, how many would a family of five get to eat if they were divided among them equally? (4)


If a large rectangular cake is cut into 8 pieces, what fraction would you eat if you got one piece? (1/8)


If you had two pieces of the cake cut into 8ths, what fraction would you have eaten? What fraction is left? (2/8, 6/8)


A cup is filled ½ full of water. What fraction would there be if I filled the cup ½ more? Is there another way to write that number? (2/2, 1 whole)


Make the number sentence true with <, >, =: ¼ ? 1/8 (>)


1/10 ? 1/16 (>)


1/4 ? 1/3 (<)


½ ? 2/4 (=)



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