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  • = Denotes Benchmark Expectation

  • = Includes a Feedback Box

Benchmark Expectations. Several of the Expectations are prioritized as Benchmark Expectations becausethey are particularly important concepts and skills to be learned in this unit. Benchmark Expectations identify the concepts and skills that are central to the unit, are prerequisites for learning content in an upcoming unit, are the last significant opportunity for assessment in the curriculum or grade, or are concepts commonly associated with difficulties or misconceptions. These Expectations are marked with a red circle in the Key Assessment Opportunities Chart.

Feedback Boxes. Feedback Boxes are provided with several activities to report progress toward these Expectations. Look for the box ( ) on the Unit 8 Key Assessment Opportunities Chart. See Figure 2. In this unit, students will also get better acquainted with the Math Practices Expectations by discussing them in the context of a specific problem, receiving feedback, reviewing a peer's work, and revising their work.

Equivalent Fractions Quiz
Feedback Box		 Expectation Check
In		 Comments
Find equivalent fractions using circle pieces. [many questions and Q# 4E] E8
Find equivalent fractions using a Fraction Chart. [many questions and Q# 2B] E8
Find equivalent fractions using multiplication and division methods. [many questions and Q# 4F] E8
Write number sentences to show equivalent fractions from area models. [Q# 4A, B, D] E6

Figure 2: Sample Feedback Box from Lesson 8

Key Assessment Opportunities Chart Print

L1TG Examples from Part 1 discussion
Key Ideas in Unit 8

L1 TG

L1 SG

L1 DPP

L2 TG

L2 SG

L3 SG

L3 SG

L3 DPP

L4 SG

L5 SAB

L6 SG

L6 SG

L6 SG

L6 SG

L7 SAB

L7 SAB

L8 TG

L9 SG

L9 TG

L10 TG

L10 DPP

L11 SG

L11 SG

L11 SAB

L11 DPP

L12 SAB
Unit 8 Expectations

Math Content

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Content Expectations. The Expectations assessed in this unit focus on concepts of number and operations, specifically related to fractions. Because all the Algebra Key Ideas arise from and are closely connected to ideas in the other content strands, Expectations related to algebra will also be listed under a second content strand. For example:

Number 2. Understand the meaning of numerical operations and their application for solving problems.

E11. Multiply fractions by a whole number. (e.g., 1/3 × 3 = 1, 2/3 × 6 = 1/3 × 6 × 2). (Algebra 4)

The Content section of the Unit 8 Key Assessment Opportunities Chart identifies some of the activities in the unit that are appropriate for assessing students' abilities with expectations related to the conceptual understanding of fractions. The Math Facts section of the same chart identifies activities in the unit that are appropriate for assessing students' division facts strategies.

Number 1

Number Sense: Understand the base-ten number system, recognize relationships among quantities and numbers, and represent numbers in multiple ways.

E1

 Represent fractions using area models (circle pieces, fraction strips, drawings) and number lines. [3.NF.2] [MP1, 2, 4, 7]

E2

 Use words and numbers to name fractions. [3.G.2] [MP1, 6]

E3

 Recognize that the same fractional parts of different-sized unit wholes are not equal. [4.NF.2] [MP1, 2, 3, 4]

E4

 Identify the unit whole when given a fractional part of a whole. [4.NF.1, 2] [MP1, 2, 3]

E5

 Name and represent fractions greater than one as mixed numbers and improper fractions using models (fraction strips, circle pieces, number lines). [3.NF.3C] [MP1, 2, 4]

E6

 Write number sentences from area models of fractions (e.g., 1/2 = 3/6, 1/3 + 1/3 = 2/3, 1/3 + 1/3 + 1/3 = 1/3 × 3). (Algebra 3) [4.NF.3] [MP1, 2, 4, 7]

E7

 Make connections among representations of fractions including symbols, words, area models, and number lines. [4.NF.1, 2] [MP1, 2, 4, 5]

E8

 Find equivalent fractions using area models (circle pieces, fraction strips, drawings) and multiplication and division strategies. [4.NF.1, 2; 4.NF.4] [MP1, 3, 5, 7]

E9

 Compare and order fractions using area models, number lines, and one-half as a benchmark. [4.NF.2] [MP1, 2, 3]

Number 2

Operations: Understand the meaning of numerical operations and their application for solving problems.

E10

 Add and subtract fractions with like denominators using area models. [4.NF.3] [MP1, 2, 4, 5]

E11

 Multiply fractions by a whole number (e.g., 1/3 × 3 = 1, 2/3 × 6 = 1/3 × 6 × 2). (Algebra 4) [4.NF.4] [MP1, 2, 4, 5]

Math Facts

Number 3

Computation and Estimation: Use efficient and flexible procedures to compute accurately and make reasonable estimates.

E12

 Demonstrate fluency with the division facts for the 9s. [3.0A.7]

E13

 Determine the unknown number in a multiplication or division sentence relating three whole numbers for the 9s facts. [3.0A.4]

Math Practices

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Math Practices Expectations. Students use the Math Practices Expectations on the Math Practices page to help them focus on practices related to both problem solving and communication. See the page in the Student Guide Reference section. Students become more comfortable with these Expectations by reviewing them before, during, and after solving a problem and by deciding how well they are met in their work and the work of others.

The Math Practices section of the Unit 8 Key Assessment Opportunities Chart identifies activities in the unit that are appropriate for assessing students' use and development of the math practices related to problem-solving habits and communication skills. In this unit, students will focus on finding a strategy [MPE2], checking for reasonableness [MP3], and showing their work [MPE5].
MPE1 Know the problem. I read the problem carefully. I know the questions to answer and what information is important.
MPE2 Find a strategy. I choose good tools and an efficient strategy for solving the problem. [MP4, 5, 7, 8]
MPE3 Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again. [MP6]
MPE4 Check my calculations. If I make mistakes, I correct them.
MPE5 Show my work. I show or tell how I arrived at my answer so that someone else can understand my thinking. [MP3, 4, 6]
MPE6 Use labels. I use labels to show what numbers mean.