Standard Met: CCSS.Math.Content.3.NF.A.1
Objective: Visualize fractional parts of a whole
What You Need: Large-grid paper, scissors, colored pencils or crayons, yarn or string, tape, construction paper
What to Do: Los Angeles third-grade teacher Toluca Rivers started using fraction kites to make “concepts of fractions more concrete and relatable.”
Begin by reviewing fractions as parts of a whole. Explain that students will make their own visual representation of fractions. Then, cut out diamond-shape “kites” of 7-by-8 grid blocks (56 squares in total) from grid paper. Students should color kites in a pattern of their choosing, using five different colors, and attach string or yarn to one corner. Rivers, who blogs at Markers and Minions, says Minecraft patterns are always a hit!
Next, have students cut five ribbon shapes out of construction paper. They will shade in each ribbon with a color that corresponds to the grid colors and write the fractional part of the whole that each color represents on its ribbon. So, if a kite has 13 red squares out of 56, the student would write the fraction 13/56 on a red ribbon.
Once students create all five ribbons, have them order the fractions from least to greatest and tape their ribbons to the kite in this order.
“This craftivity is a hit year after year,” says Rivers. “The students get to be creative while learning, and they see their work proudly displayed.”
Standards Met: CCSS.Math.Content .2.G.A.3; 3.NF.A.1
Objective: Create visual representations of fractions
What You Need: LEGO bricks and base plates, index cards, grid paper
What to Do: K–5 teacher Deirdre Smith from Greenville, South Carolina, uses LEGO bricks to review math skills. Smith, who blogs at JDaniel4’s Mom, says the bricks are perfect for this.
Prepare by writing fractions on index cards; keep them small to start, using denominators of 2, 3, 4, and 8. Each student will need at least six different fraction cards.
Explain that they will be creating visuals for the fractions they are given using LEGO bricks. For each fraction, students will build a model out of bricks on their base plates. Show an example, as follows: 4/5 could be displayed by laying out four bricks in one color (say, red) with a fifth brick of the same size in another color, such as blue. Explain that four of the five bricks are red, so 4/5 are red (and 1/5 is blue).
Allow kids to gather materials and decide how they will display the fractions—vertically, horizontally, with dark or light colors as the numerator and denominator, etc. You may also have them draw their fractions on grid paper after creating them.
Once they’ve made models for each of their fractions, have them create fraction cards and form these on their base plates. Then, they will turn their cards facedown and switch seats to name the fractions on classmates’ boards. They can check their work by looking at the cards.
For an added challenge, provide students with cards featuring fractions with larger digits. For these, students will need to reduce the fraction to display it on their board. So, if the fraction is 8/12, they will reduce it to 2/3 to fit the LEGO board. Smith loves that “the LEGO fraction display makes it easier to see the relationship” between two equivalent fractions.
It’s in the Cards
Standard Met: CCSS.Math.Content .3.NF.A.3
Objective: Compare and order fractions
What You Need: Decks of playing cards, paper and pencils (two for each pair), Fractions reproducible
What to Do: Justin Holladay, a grades 1–8 teacher in Alberta, came up with Fraction War as a way for students to practice comparing and ordering fractions. Holladay, who blogs at MathFileFolderGames, believes that “students learn math best while playing math games.”
Review how to compare and order fractions. This may start as a conversation about fractions that share the same denominator; for more advanced students, you may discuss how to compare fractions with unlike denominators. Ask students to think about ways to use estimation to make a comparison. For example, if they are given the fractions 2/7 and 3/4, students may recognize that 3 is very close to 4, making 3/4 a larger fraction. If they have difficulty reaching this conclusion, guide them to use a visual. Provide a printout of the Fractions reproducible and encourage students to use this as a reference.
Next, give each pair of students a deck of cards and two pencils. The digits on the cards represent the numerator or denominator in a fraction and the pencils are used for the fraction bar. Each student takes half the deck. They then simultaneously turn over two cards each and place them over and under their fraction bar to create a proper fraction. For example, if one player turned over a 4 and a 10, he or she would make the fraction 4/10. The player who creates the largest fraction wins all four cards. If both students lay down equivalent fractions, there will be a “war,” and each will flip two cards again. The player with the largest fraction from that round will win all eight of the cards.
For students just beginning to grasp fractions, you may consider limiting the possible denominators (for example, only include 2, 3, 4, 5, and 8 as possibilities). If students are more comfortable with ordering, you may leave all cards in the deck and allow face cards to take on higher values (jack = 11, queen = 12, etc.).
Hopscotch and a Half
Standards Met: CCSS.Math.Content .2.G.A.3; 3.NF.A.1
Objective: Understand and represent fractions as parts of a whole
What You Need: Chart paper, chalk
What to Do: Take learning outside while challenging kids to think deeply about fractions.
First, review what fractions look like as parts of a whole. Then, talk through the game of hopscotch. Draw a simple hopscotch board (1 to 10) on chart paper and review the rules as follows: The first player tosses a marker (beanbag, twig, etc.) to land inside a square with a number on it. If player one misses, the next player takes a turn. If not, player one hops into each empty square, then back to the start, picking up the marker on the way. On the next turn, he or she moves the marker to the next number up. The first player to hit 10 wins.
Explain that students will add a fractional twist to the game. Instead of creating squares with whole numbers, they will be creating fractional parts of shapes. Show them an example using a hopscotch board that goes from 1/8 to 1 rather than 1 to 10. It would have blocks going up by eighths. If students are advanced, reinforce the concept of equivalency by showing that 2/8 can share a square with ¼, as they are equivalent (the same is true of 4/8, 1/2, and 2/4, as well as 6/8 and 3/4).
Then, head outside! Beginners may start by recreating the board made in class with eighths. Encourage others to work with different or more complicated fractions. For example, if counting by sixteenths, you will want to have them show equivalence with halves, quarters, and eighths. Have students play hopscotch in pairs or groups of three on the boards they have drawn in chalk, or encourage them to try others’ boards.
As a challenge, they may create more complicated boards using different shapes. Instead of using square blocks, students may try segmenting circles or triangles on their boards, requiring different kinds of jumps. And if it’s a rainy day outside, don’t worry—a long hallway and plenty of masking or painter’s tape works just as well!
Photo: Courtesy of Toluca Rivers