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Equal Partitioning

Equal Partitioning. Unit of Study 10: Geometry and Fractions Global Concept Guide: 3 of 3. Content Development.

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Equal Partitioning

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  1. Equal Partitioning Unit of Study 10: Geometry and Fractions Global Concept Guide: 3 of 3

  2. Content Development • Children seem to understand the idea of separating a quantity into two or more parts to be shared fairly among friends. They eventually make connections between the ideas of fair shares and fractional parts (Van de Walle, 2006). Students partition rectangles into rows and columns. Students frequently mix up rows and columns. Rows are horizontal, Columns are vertical.

  3. Content Development • Learn Zillion video ~ • 3500- Partition a Rectangle into Rows • 3553 Partitioning a Rectangle into Columns • 3516 Find the Number of same-Sized Squares in a Rectangle • 2440 - Describe Fractions of Rectangles • 2491 - Partition Rectangles into Equal Shares Multiple Ways • 2441 - Describe Fractions of Rectangles by Counting Equal Shares • 2604 - Count Fractions of a Whole Using Fraction Strips • 2658 - Compare Equal Shares from Different Wholes • This GCG will help students build conceptual foundation for fractions in later grades.

  4. Day 1 • Essential Question: How do you find the total of same-size squares that will cover a rectangle? • Possible Engage: • Provide each student with a regular size Post-it note (3 x 3). • Give each student one color tile. • Have students predict how many color tiles it will take the cover the entire Post-it without overlapping. • Have students place and trace the color tile on the post-it. Students can count the squares to determine how many squares will cover the post-it.

  5. Once students complete the Post-it task, engage them in the following task: Day 1 continued • Day 1 should be spent using manipulatives to determine how many squares will fit within different rectangles. Students struggle with correctly identifying rows and columns. Encourage them to describe their rectangles as having certain amount of rows and columns. To extend the learning, provide students with a rectangle that is similar to the one on the right. Have students look at the square tile and determine how many it would take to cover the rectangle. Elements of Go Math Lesson 11.6 can be used to help students solidify their understanding of partitioning rectangles into equal-sized squares. By the end of Day 1, students will be able to partition rectangles into equal-sized squares.

  6. Day 2 • Essential Question: What are halves, thirds and fourths of a whole? • Possible Engage: • Group students in pairs. • Provide each pair of students 3 post-it notes. • Have students discover how they can split the post-it note into two equal parts. • Facilitate a discussion on how students determined the post-it note was split into two equal parts. Some questions you might ask: • How can you prove your post-it note is split into two equal parts? • Is there another way you could have split your post-it into two equal parts? • What do we call something when it is split into two equal parts? (This is a great place to introduce the vocabulary term “halves”) • Repeat the task and have students split their post-it into thirds. • Repeat the task and have students split their post-it into fourths. • Additional ideas: • To build students conceptual understanding give them opportunities to use pattern blocks and folding paper to partition shapes into halves, thirds, and fourths. It is important to model precise vocabulary and insist students use precise vocabulary to ensure they develop an understanding of halves, thirds, and fourths.

  7. Day 2 continued Elements of Go Math lesson 11.7 may be used on this dayto build understanding of halves, thirds, and fourths. By the end of Day 2, students will understand the difference between halves, thirds, and fourths.

  8. Day 3 • Essential Question: How do you find a half of, a third of, and a fourth of a whole? • The focus of this day is for students to partition shapes into halves, thirds, and fourths. Students should also recognize that, when partitioned, they represent equal parts of the whole. • Exposing students to examples and non-examples of halves, thirds, and fourths will build their understanding that it has to be equal parts. • Example: Non-example Example • Possible Engage:

  9. Day 3 • CPALMS: Problem Solving Tasks - Which show One Half • Dividing Circles into halves, thirds, and fourths • Elements of Go Math lesson 11.8 may be used on this day. Refer to GCG for the essential components of this lesson. • By the end of Day 3, students will be able to partition various shapes into halves, thirds, and fourths.

  10. Day 4 • Essential Question: How can drawing a diagram help when solving problems about equal shares? • This day is focused on using a diagram to solve word problems involving partitioning shapes. • Possible Engage Idea: • The Shape Puzzle listed on the GCGs under lesson ideas may be used on this day. • Go Math lesson 11.10 should be used on this day. It has several appropriate word problems to give to students. • Elements of Go Math lesson 11.9 may be used on this day. • By the end of Day 4, students will understand that equal parts and how to partition a shape in halves, thirds, and fourths.

  11. Enrich/Reteach/Intervention Reteach • Reteach p. R104 • Reteach R105 or E105 • Reteach R106 • Reteach R107 • Reteach R108 • ELL Language Support TE p. 537B, 541B • Mega Math: Equal and Unequal Parts • Mega Math: Halves and Fourths Enrich • Enrich TE p. 533B • Enrich p.E104 • Enrich p.E106 • Enrich p.E107 • Enrich p. E108

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