## Virtual Pattern Blocks

3-5
1

Students use virtual pattern blocks to problem solve and reason with fractions. They investigate relationships between parts and wholes using another representation of a region model, virtual fractions. Students use conversation to explain their understandings in order to extend and clarify their mathematical content knowledge.

Explain to students that they will the Patch Tool to model part-whole relationships. The directions for using the tool should be reviewed prior to this lesson. The students may need to be guided in how to drag the pattern blocks to the work area. When making comparisons, the students can drag one pattern block on top of another one to compare the area of the region. If your technological resources are limited, you can also create and print pattern block activity sheets using the Dynamic Paper Tool. Pattern blocks can be found under the Shapes tab.

Have students work in pairs using the Web-based pattern blocks to explore relationships among the four shapes. Use the same Guiding Questions found in Lesson One. This will facilitate exploration with a new tool, help the students focus on the mathematical concepts demonstrated with this region model, and reinforce the content of the previous lesson, Investigating with Pattern Blocks.

The students should use the virtual pattern blocks to answer the questions. Provide students with a new, blank copy of the Region Relationships 1 Activity Sheet and ask them to complete it.

Encourage students to discuss various options with their partner. This allows students to articulate their understandings, making them available for discussion, clarification, and extension.

Assessment Option

At this stage of the unit, it is important to know whether the students can do the following:
• Understand that a fraction is part of a whole
• State the relationship between the pattern block shapes [e.g., that there are three triangles in one red trapezoid]
The students' recordings can be used to make instructional decisions about their understanding of fraction relationships. Because this entire unit deals with relationships, areas needing additional work can be developed during subsequent lessons. You may choose to use the Class Notes recording sheet to make anecdotal notes about the students' understanding and use those notes to guide your instructional planning.
Extension
Move on to the next lesson, Pattern Block Fractions.

Questions for Students

1. Is there a way to represent the red trapezoid using blue and green pattern blocks? Can you cover the red trapezoid using only one color? What does this tell us about the relationship between the blue rhombus and the green triangle?

[The trapezoid can be covered with one green triangle and one blue rhombus, or it can be covered with three green triangles. Consequently, there are two green triangles in one blue rhombus.]

2. Are there other ways to represent various pattern blocks (for example, the yellow hexagon) using more than one color pattern block?

[The students should be lead in a discussion of the relationships inherent in these representations.]

Teacher Reflection

• Which students understand that a fraction is part of a whole? What activities are appropriate for those students who have not yet developed this understanding?
• Which students/groups can articulate the relationship between the pattern block shapes? What activities are appropriate for those students who have not yet developed this understanding?
• What parts of the lesson went smoothly? What parts should be modified for the future?

### Investigating Fractions with Pattern Blocks

3-5
This lesson promotes problem solving and reasoning with fractions as students investigate the relationships between various parts and wholes. It also focuses on representation because students are given multiple opportunities to investigate the relative value of fractions. Students use communication skills as they work in pairs to articulate and clarify their understanding of fraction relationships.

### Pattern Block Fractions

3-5
This lesson builds on the previous two lessons by focusing on the identification of fractional parts of a region and by recording them in standard form. Students continue to develop communication skills by working together to express their understanding of fraction relationships and to record fractions in written form.

### Expanding Our Pattern Block Fraction Repertoire

3-5
In this lesson, the students expand the number of fractions they can represent with pattern blocks by increasing the whole. Instead of representing the whole with one yellow hexagon, the students explore fractional relationships when two, three, and four yellow hexagons constitute the whole.

### Exploring the Value of the Whole

3-5
This lesson focuses on the relationship between parts and the whole. These relationships were developed earlier and require the students to consider the size or value of the same fraction when different "wholes" are compared (i.e., the value of x is relative to the whole; x of a small pie is not equivalent to x of a large pie). This lesson promotes problem solving and reasoning as the students compare similar fractions with different "wholes." Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole.

### Learning Objectives

Students will:

• Demonstrate understanding that a fraction is part of a whole.
• Identify fraction relationships.

### NCTM Standards and Expectations

• Use models, benchmarks, and equivalent forms to judge the size of fractions.
• Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
• Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

### Common Core State Standards – Mathematics

Grade 3, Num & Ops Fractions

• CCSS.Math.Content.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• CCSS.Math.Content.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Grade 4, Num & Ops Fractions

• CCSS.Math.Content.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Grade 4, Num & Ops Fractions

• CCSS.Math.Content.4.NF.A.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Grade 5, Num & Ops Fractions

• CCSS.Math.Content.5.NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.