Overview

Module 4: Multiplication and Area

Students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication.

Topic C: Arithmetic Properties Using Area Models

Topic D: Applications of Area Using Side Lengths of Figures

Advanced Preparation, Module 4:

- Grid paper (inch and centimeter)
- Rulers (both centimeter and inch measurements)
- Unit squares in both inch and centimeter lengths (e.g., square tiles used for measuring area—can be made out of paper if plastic or wood tiles are not available)

Module 5: Fractions as Numbers on the Number Line

Students extend and deepen Grade 2 practice with equal shares to understanding fractions as equal partitions of a whole.

Topic A: Partition a Whole into Equal Parts

Topic B: Unit Fractions and Their Relation to Whole

Topic C: Comparing Unit Fractions and Specifying the Whole

Topic D: Fractions on the Number Line

Topic F: Comparison, Order, and Size of Fractions

Advanced Preparation: Module 5:

- 1-liter beaker (optional)
- 1 m length of yarn
- 12″ × 1″ strips of yellow construction paper
- 2″ × 6″ strips of brown construction paper
- 200 g ball of clay or play dough
- 4″ × 4″ orange squares
- 4 1/4″ × 1″ paper strips
- Clear plastic cups
- Concrete fraction models (e.g., water, string, clay)
- Food coloring (to color water)
- Fraction strips (made from paper, used to fold and model parts of a whole; see the example to the right.)
- Pictorial fraction model (e.g., drawing of a circle or square)
- Rectangular- and circular-shaped paper
- Rulers
- Sets of <, >, = cards
- Shapes partitioned into fractional parts

Module 6: Collecting and Displaying Data

This 10-day module builds on Grade 2 concepts about data, graphing, and line plots.

Topic A: Generate and Analyze Categorical Data

2017-2018 Math Schedule of Assessed Standards (SAS)

Module Tip Sheet for Parents

These documents provide parents an opportunity to see what their children are learning in the current module including:

- Standards
- Key vocabulary
- Example Problems
- Pictorial Models
- Ideas for how to can help children at home
- Coherence of learning with past and future modules

For guides in Spanish, go here

Week 1: February 5

Standards Addressed in Week's Lessons

Topic C:

3.MD.5

3.MD.7a

3.MD.7b

3.MD.7c

3.MD.7d

Topic D:

3.MD.6

3.MD.7a

3.MD.7b

3.MD.7c

3.MD.7d

3.MD.5

Notes:

Lesson 9 Omit

This lesson reviews previously learned skills and has been omitted for pacing considerations.

Lesson 10

This lesson builds on previous knowledge of the distributive property (which students have been working on throughout Q2) and focuses on applying it to area models. Students determine unknown side length of an array and decompose area into two separate rectangles with one common factor. Students discover that the sum of the side lengths gives the length of the unknown side. Materials needed for each student: square centimeter tiles, tiling (template).

Lesson 11

Students use a given number of square units to determine all possible whole number side lengths of rectangles with that area. MP.3: Students are required to justify that they have found ALL possible solutions for each given area using the associative property. Note: Areas of 24, 36, 48 and 72 are chosen to reinforce multiplication facts that are often more difficult.

Lesson 12

This lesson emphasizes real-world application: students apply understanding of area to solving word problems. These word problems provide a stepping-stone for the real-world, project-based application of area to composite shapes and the area floor plan in this topic. Students need their Multiply by 7 pattern sheet for the Fluency.

Lesson 13

Students find the area of composite shapes in this lesson and the next lesson (#14). Students find the unknown measurements using the given side lengths and make decisions about whether to decompose the tiled region and add areas that are easier to calculate, or complete the whole area and then subtract the missing portion. Students materials: large grid (template) for the Concept Development.

Week 2: February 12

Assessment:

Module 4: End-of-Module Assessment

Biweekly #1: Lesson 2 Exit Ticket

Standards Addressed in Week's Lessons

Topic D:

3.MD.5

3.MD.6

3.MD.7a

3.MD.7b

3.MD.7c

3.MD.7d

Topic A:

3.G.2

3.NF.1

Standards Assessed in Assessments

End of Module

3.MD.5

3.MD.6

3.MD.7a

3.MD.7b

3.MD.7c

3.MD.7d

Notes:

Lesson 14

This lesson is a continuation of Lesson 13. Students continue to work on finding missing side lengths and choosing the most accessible method to find the area of composite shapes. The Problem Set is used for the Concept Development. During the Concept Development, consider adjusting the numbers in Problem 2 to challenge students working above grade level.

Lesson 15 & 16 Omit

These lessons guide students through a project involving floor plans.. We suggest skipping the application of area that these lessons provide for pacing considerations.

One day provided for End of Module Assessment after Lesson 14.

Lesson 1

This lesson requires liquids/cups to demonstrate partitioning liquids to demonstrate the concept of fractions. Teachers could use images instead of actual liquids, but would need this prepared beforehand. In both Lesson 1 and Lesson 2 in this topic, students are dividing a given whole into equal parts to create fractional units (halves, thirds, fourths). In the next topic, they will associate each of these units with a number called a unit fraction (1/2, 1/3, 1/4). Teacher materials:: 1 clear plastic cup full of colored water, 2 other identical clear plastic cups (empty), 2 12" × 1" strips of construction paper. Student materials: 2—12" × 1" strips of construction paper, 12-inch ruler.

Lesson 2

This lesson involves students counting unit fractions by folding fraction strips- these need to be prepared beforehand and are a very helpful tool for fraction concept development. Student materials: 8 paper strips sized 4 1/4” × 1” (vertically cut an 8 1/2" × 11” paper down the middle), pencil, crayon.

Week 3: February 19

Notes:

Lesson 3 & 4 Omit

Lesson 3’s objective is similar to Lesson 2’s. The difference is a shift from concrete to pictorial. Students will have exposure to extensive pictorial practice throughout the module. Although Lesson 4 is an exploratory lesson that affords students the opportunity to synthesize their learning, no new material is presented.

Lesson 5

In this lesson, students partition a whole into equal parts and learn to label each part as a unit fraction numerically. This builds on understanding from the previous unit. During the Concept Development, students working above grade level may enjoy identifying fractions with an added challenge of each shape representing a fraction rather than the whole.

Lesson 6

Students build non-unit fractions from the unit fractions they learned about in the previous lesson. In the Concept Development, be ready to ask the same question in multiple ways, for example, by changing the question, “What’s happening to my parts?” to “How are my parts changing?” or “Do you notice an increase or decrease?” or “Is the amount growing or shrinking?”

Lesson 7

Students write shaded/non-shaded parts of one whole as fractions (shift from pictorial to abstract). Suggestion for Application Problem for students below grade level: give explicit steps for problem solving to students organized as a checklist such as, “Underline important words, draw a model, label your model.” (instead of just saying RDW) Teacher materials: 1-liter beaker, water. Student materials: paper, scissors, crayons, math journal. You also need a clock for the Fluency..

Week 4: February 26

Notes:

Lesson 8

Students represent parts of one whole as fractions with number bonds. Students need Sprint B for the Concept Development.

Lesson 9

Students build and write fractions greater than one whole using unit fractions. For students working above grade level, extend the Application Problem with an open-ended prompt such as, “If Julianne adds another bead of the same size and shape to her bracelet, what fraction would the new bead represent? Why do you think so?” Student materials: fraction strips.

Lesson 10 & 11 Combine

In these combined lessons, students use fraction strips to recognize that, when the same whole is folded into more equal parts, each part is smaller. In Lesson 10, only use the "Greater or Less Than 1 Whole" Fluency, skip the Application Problem, present the Concept Development and give students 20 minutes to work on the Problem Sets from Lessons 10 and 11. Student materials: folded fraction strips (halves, thirds, fourths, sixths, and eighths) from Lesson 9, 1 set of <, >, = cards per pair.

Lesson 12

In this lesson, students are creating corresponding wholes based on a given unit fraction. This lesson requires a lot of pre-planned materials on the teacher's part (Concept Development and Problem Set). If teacher chooses to change the materials, they will also need to change the student's work product. Student materials: 10-centimeter length of yarn, 4” × 1” rectangular piece of yellow construction paper, 3” × 1” brown paper, 1” × 1” orange square, water, small plastic cups, clay.

Standards Addressed in Week's Lessons

Topic B:

3.NF.1

3.NF.3c

3.G.2

Topic C:

3.NF.3d

3.NF.1

3.NF.3a–c

3.G.2

Standards Assessed in Assessment

3.NF.3d

3.NF.1

3.NF.3a–c

3.G.2

Standards from Week's Lessons not Assessed before ANet

3.NF.1

3.NF.3c

3.G.2

Week 5: March 5

Notes:

Lesson 13 Omit

Lesson 13 provides practice with concepts and skills taught in the three preceding lessons. Although this lesson deepens practice, no new material is presented.

One day provided for Mid-Module assessment.

Lesson 14

Students place fractions on a number line with endpoints 0 and 1. In this topic, number bonds and fraction strips serve as bridges into this work from comparing unit fractions in Topic C. Students learn to see intervals on the number line as wholes. Student materials: fraction strips.

Lesson 15

Students place any fraction on a number line with endpoints 0 and 1. Fluency suggestion: during "Place Unit Fractions on a Number Line Between 0 and 1," as students estimate to equally partition fourths and eighths on the number line, guide them to begin by finding the midpoint—first by drawing 2 equal parts and then continue halving until the desired unit fraction is created.

Lesson 16 & 17 Combine

Choose one Fluency, skip the Application Problem and use the Concept Development from Lesson 16 .Then, give students extra time do work on the Problem Sets from Lessons 16 and 17. Use Exit Ticket from Lesson 16. Students place whole number fractions and fractions between whole numbers on the number line. Then students practice placing various fractions on the number line. If gauging that students working below grade level need it, build understanding with pictures or concrete materials. Extend the number line back to 0. Have students shade in fourths as they count. Use fraction strips as in Lesson 14, if needed.

Standards Addressed in Week's Lessons

Topic D:

3.NF.2ab

3.NF.3cd

Standards Assessed in Assessment

Mid-Module

3.G.2

3.NF.1

3.NF.3cd

Standards from Week's Lessons not Assessed before ANet

3.NF.2ab

Week 6: March 12

Module

Notes:

Lesson 18

Compare fractions and whole numbers on the number line by reasoning about their distance from 0. Teacher materials: large-scale number line partitioned into thirds (described in lesson), 4 containers, 4 beanbags (or balled-up pieces of paper), sticky notes.

Lesson 19 Omit

Lesson 19, designated as an optional lesson in the teaching sequence, provides practice with concepts and skills taught in the five preceding lessons.

Lesson 20 Omit

The seven subsequent lessons in Topic E provide practice that is more targeted toward specific understandings about equivalent fractions.

Lesson 21

Students recognize and show that equivalent fractions refer to the same point on the number line. This builds on the work students did in Topic D, placing and comparing fractions on the number line. In this lesson, they see that 1/2 and 2/4 (1 half = 2 fourths) are represented by the same point on the number line, as long as both fractions are in reference to the same length unit. Student materials: 4 1/4-inch × 1-inch fraction strips (5 per student), math journal, crayons, glue, personal white board

Lesson 22

Part 1 of 2-Part Sequence. This lesson involves students generating simple equivalent fractions by using visual fraction models on the number line.

Useful scaffolds: students working below grade level may alternatively use two fraction strips—one partitioned into sixths, the other partitioned into fourths—to compare 3 sixths and 2 fourths. Or, have students draw number lines on personal white boards so that they may erase partitioned sixths before partitioning fourths. Student materials: math journal or fraction strips made in Lesson 21, new 4 1/4-inch × 1-inch fraction strips (3 per student), crayons, personal white board, glue.

Lesson 23

Part 2 of 2-Part Sequence. Students continue to generate simple equivalent fractions on the number line. Student materials: Index card (1 per pair, described below), sentence strip (1 per pair), chart paper (1 per group), markers, glue, math journal.

Assessment:

Biweekly #3 - Lesson 18 Exit Ticket

Standards Addressed in Week's Lessons

Topic D:

3.NF.2ab

3.NF.3cd

Topic E:

3.NF.3a–c

Standards Assessed in Assessment

3.NF.3cd

Standards from Week's Lessons not Assessed before ANet

3.NF.2ab

3.NF.3a–c

Week 7: March 19

Module

Topic

Notes:

*Only two lessons due to consideration of PARCC Administration

Lesson 24

Express whole number fractions on the number line when the unit interval is 1. Consider differentiating the Application Problem. Partitioning the interval into two different fractional units is a stimulating challenge for students working above grade level. Students working below grade level can draw two separate number lines or use fraction strips to solve.

Student materials: fraction pieces (template provided), scissors, envelope, personal white board, sentence strip, and crayons.

Lesson 25 Omit

Consider omitting Lesson 25 for pacing considerations since its content is embedded into the work of prior lessons. Ensure that students have practiced counting and labeling whole number fractions as part of their work with fractions on the number line.

Lesson 26

Decompose whole number fractions greater than 1 using whole number equivalence with various models. Note: number bonds and number lines are used to model this for students. As an alternative to the Problem Set, offer students working above grade level the option of drawing their own number lines with larger intervals (e.g., 6, 7, and 8) and their choice of fractional unit for partitioning (e.g., fifths).

Assessment:

PARCC

Standards Addressed in Week's Lessons

Topic E:

3.NF.3a–c

Week 8: April 2

Module

Notes:

One day provided this week for ANet testing.

Lesson 27

Explain equivalence by manipulating units and reasoning about their size. This lesson is the end of Topic E (explaining equivalence). For students below grade level, revisit discussion of doubling, tripling, halving, and cutting unit fractions as presented in Lesson 22.

Student materials: 3 wholes (Lesson 25 Template 1), personal white board, fraction strips (3 per student), and math journal.

Lesson 28

This is the first lesson of Topic F. Fraction strips and the number line continue in this topic as students compare fractions with the same numerator, but those materials do not need to be printed out for students during this lesson. In this lesson, students compare fractions with the same numerator pictorially and pictorial supports are provided on the problem set. Students need their work from the Application Problem for the Concept Development. Give students working below grade level the option of rectangular pizzas (rather than circles) to ease the task of partitioning.

Lesson 29

Students compare fractions with the same numerator using <, >, or =, and use a model to reason about their size. Prioritize questions 1 and 3 in the Student Debrief to emphasize the importance of an equal whole when comparing fractions. Student materials: 3 wholes (Lesson 25 Template 1)

Assessment:

ANet

Standards Addressed in Week's Lessons

Topic E:

3.NF.3a–c

Topic F:

3.NF.3d

Standards Assessed in Assessment

ANet Major

3.MD.C.6

3.MD.C.7

3.NF.A.1

3.NF.A.2

Supporting

3.G.A.2

Review

3.NBT.A.2

3.OA.A.3

3.OA.A.4

3.OA.C.7

3.OA.D.8

Week 9: April 9

Standards Addressed in Week's Lessons

Topic F:

3.NF.3d

Topic A:

3.MD.3

Standards Assessed in Assessment

3.NF.2ab

3.NF.3a-d

Standards from Week's Lessons not Assessed before ANet

3.MD.3

Notes:

Lesson 30

Students partition various wholes precisely into equal parts using a number line method. Students working below grade level may benefit from naming the fractional unit (e.g., eighths) before naming the shaded fraction. Student materials: 9-inch × 1-inch strips of red construction paper (at least 5 per student), lined paper (Template) or wide-ruled notebook paper (several pieces per student), 12-inch ruler. It is highly recommended to try the activity with the prepared materials before presenting it to students.

One day this week provided for End-of-Module Assessment after lesson 30.

Lesson 1

This is the beginning of Module 6 (Generate and Analyze Categorical Data). In this lesson, students organize the data and then represent them in a variety of ways (tally marks, graphs with one-to-one correspondence, or tables). By the end of the lesson, students show data as picture graphs where each picture has a value greater than 1. Students need the Problem Set for the Concept Development, as well as a class list in alphabetical order.