Guided Lessons

# Building Squares

In this hands on lesson, students create squares with different fraction pieces while building their knowledge of adding fractions with different denominators.

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students will be able to add fractions with different denominators and justify their thinking with a model.

(10 minutes)
• Gather students together and define equivalent as meaning objects that have the same value and whole as something in its entirety, or all of something.
• Show students a large square on the board. Explain to the students how there are several ways we could divide this square equally. Take student suggestions of ways to divide the square. Draw lines to model their suggestions. Make sure to emphasize that fractions must be made of equal parts.
• Tell students that no matter the way the square is divided it still remains one whole square. All divided parts of the square added together must equal 1.
(15 minutes)
• Show students several whole squares. Model cutting the square into halves, quarters, sixths, and eighths.
• Explain that each of the pieces can be mixed and matched to create a whole square. Model mixing and matching the different slices of square to build a whole square. Try building a square with two quarters and one half, three sixths and four eights or any other combination you would like.
• Explain to students that they will be building squares today. As they build the squares, tell students to find as many different combinations as they can. Model writing an addition sentence to show the fractions equal 1 whole.
• Show the students the Building Squares worksheet. Explain the example. Distribute the Fraction Pieces worksheet. Have students cut out the pieces to use on the Building Squares worksheet.
(10 minutes)
• Have students work as pairs to complete and record the first two squares.
• Ask students to discuss which pieces can be used together to build squares and which cannot. For example, the square cannot be completed with thirds and halves.
(15 minutes)
• Have students complete the rest of the worksheet independently.
• Circulate while students are working.
• Enrichment: Have students in need of a challenge cut a square into pieces greater than 8. These students can build new squares using these pieces and record new addition sentences.
• Support: For students in need of support, label the fraction pieces with the corresponding fraction. Have students place pieces with different denominators on top of each other to visualize which equivalent fractions may be used to build different combinations.
(10 minutes)
• Collect the students’ Building Squares worksheets and check for understanding.
• Circulate and discuss progress with students as they work.
(10 minutes)
• Gather students together. Have students share the different combinations they used to build the squares.
• Ask students if they noticed any equivalent pieces. Ask students to describe the methods they used when deciding which pieces to use.