Overview

Module 5 : Addition and Multiplication with Volume and Area

Volume is introduced to students through concrete exploration of cubic units and culminates with the development of the volume formula for right rectangular prisms. The second half of the module turns to extending students’ understanding of two-dimensional figures. Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area of rectangular figures with fractional side lengths.

Topic B: Volume and the Operations of Multiplication and Addition

Topic C: Area of Rectangular Figures with Fractional Side Lengths

Topic D: Drawing, Analysis, and Classification of Two-Dimensional Shapes

Advanced Preparation:

- Area model
- Centimeter cubes
- Centimeter grid paper
- Isometric dot paper
- Patty paper (measuring 5.5 in × 5.5 in)
- Protractor
- Ruler
- Set square or right angle template
- Tape diagram

Module 6: Problem Solving with the Coordinate Plane

Students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiar number line as an introduction to the idea of a coordinate, and they construct two perpendicular number lines to create a coordinate system on the plane. Students see that just as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates.

Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

Topic C: Drawing Figures in the Coordinate Plane

Topic D: Problem Solving in the Coordinate Plane

Topic E: Multi-Step Word Problems

Topic F: The Years In Review: A Reflection on A Story of Units

Advanced Preparation:

- Protractor
- Ruler
- Set square
- Tape diagrams

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: April 17

Notes:

Lesson 1

In this lesson, having students transfer from using cubes to drawing on the isometric dot paper is key to building understanding of volume; if at all possible, do not modify this lesson. Be prepared with materials required for Concept Development: centimeter cubes, rulers, grid paper, and isometric dot paper. Note: the Application Problem comes after the Concept Development.

Lesson 2

Like in Lesson 1, the hands-on component of building the nets is critical for the unit and should not be modified. During the Concept Development, breaking down a tissue or cereal box to show how the sides form a flat shape and then building it back into a box may be helpful for students to understand the figures used in the lesson to make the boxes.

Lesson 3

This lesson builds the understanding of the formula for area, which will be taught in Topic B. Use the template at the end of the lesson to support models for finding the volume with layers.

Week 2: April 24

Assessment:

Biweekly #1: Exit Ticket Lesson 7

Standards Addressed in Lessons

Topic B:

5.MD.3

5.MD.5

Notes:

Lesson 4

Students will benefit from the template used in lesson 3 when drawing their multilayer rectangular prisms in the Concept Development of this lesson.

Lesson 5

Remove the Application Problem to give more time for Concept Development. This lesson has students use beakers and water to show equivalency of cubic centimeters and milliliter. Consider doing this as a demonstration instead of in groups. In addition, the cubic centimeter used for the second part of the lesson will need to be weighted to sink to the bottom of the beaker or the demonstration will not work as effectively

Lesson 6

Students will need 15 centimeter squares each. If supplies are a concern, consider one set per group. If at all possible, try to give students an opportunity to manipulate the cubes to build the concrete understanding necessary for this lesson and Lesson 7.

Lesson 7

Remove the Application Problem to give more time for Concept Development. This is the last lesson taught in Topic B, so assess understanding before moving on, and use this lesson to address misconceptions before Topic C, which introduces fractions.

OMIT LESSONS 8-9 for pacing considerations. These lesson ask students to make sculptures of rectangular prisms. Instead, push this activity into small group time, or ask the art teacher if they are able to do this with students.

Week 3: May 1

Assessment:

Mid-Module Assessment

Standards Addressed in Lessons

Topic C:

5.NF.4b

5.NF.6

Standards in Assessment

Mid-Module

5.MD.3

5.MD.4

5.MD.5

Notes:

Lesson 10

This lessons use patty paper for tiling, as a means to have concrete modeling of area when one of the side lengths is a fraction. If short on time or materials, consider modeling this instead by cutting equal sized square units. If you choose to model, consider making the fractional pieces a different color to show the contrast.

Lesson 11

In the Concept Development, the standard algorithm is provided so that students are exposed to a more formal representation of the

distribution. However, students should not be required to be as formal in their own calculations. Using an area model to keep track of students’ thinking is sufficient.

Lesson 12

Each student will need a ruler for this lesson. If short on time, omit problem 3 and 4 from the Problem Set to allow for more time for measurement with rulers.

One day provided to administer Mid-Module Assessment after Lesson 12.

Week 4: May 8

Notes:

Lesson 13

During the Concept Development, some students may need a quick refresher on changing mixed numbers to improper fractions or vice versa. Students should be reminded that a mixed number is an addition sentence. So, when converting to an improper fraction, the whole number can be expressed in the unit of the fractional part and then both like fractions added.

COMBINE Lesson 14/Lesson 15

These lessons share the same objective: SWBAT solve real-world problems involving area of figures with

fractional side lengths using visual models and/or equations. Both lessons have the Problem Set incorporated into the Concept Development. Combine these lessons by doing problems 1 and 2 from each lesson. Do problem 3 from lesson 15 as an extension for early finishers. Use the Exit Ticket from Lesson 14.

Lessons 16

Problem 1 in the Concept Development provides an opportunity for a quick formative assessment. If students have difficulty sorting and articulating attributes, consider a review of concepts from Grade 4 Module 4.

Lesson 17

In the Concept Development, the discussion of parallelograms as special trapezoids is based on the inclusive definition of a trapezoid as a quadrilateral with at least one set of parallel sides. That is, trapezoids may have more than one set of parallel sides. This teacher scripting assumes recall of Grade 4 geometric concepts. Consider scripting your own scaffolded questions to guide students to verbalize the conditions necessary to classify a trapezoid as a parallelogram.

Standards Addressed in Lessons

Topic C:

5.NF.4b

5.NF.6

Topic D:

5.G.3

5.G.4

Week 5: May 15

Notes:

Lesson 18

During the Student Debrief, if students are confused about the segments of a quadrilateral lying in the same plane or intersecting only at their endpoints, use the straws from Lesson 16 to demonstrate counter examples.

Lesson 19

In this lesson students draw kites and squares and clarify their attributes. To support students in retaining the new vocabulary and attributes, give students a graphic organizer where they can record observations of shape attributes and definitions. Print this on colored paper as an anchor students can reference in future lessons (could also be used for previous lessons 16, 17, 18 in this sequence on shape attributes).

Lesson 20

Consider posting the properties of shapes for students to refer to during the discussion of this lesson. If you did create an anchor graphic organizer for your students to keep as they completed Lessons 16-19, encourage students to independently reference the resource as necessary.

OMIT LESSON 21

This lesson has been omitted for pacing considerations. You may use the content in centers or small groups to reinforce the attributes of two-dimensional shapes.

One day provided this week to administer End-of-Module Assessment after Lesson 20.

Standards Addressed in Lessons

Topic D:

5.G.3

5.G.4

Standards in Assessment

End-of-Module

5.NF.4

5.NF.6

5.MD.3

5.MD.4

5.MD.5

5.G.3

5.G.4

Week 6: May 22

Module

Topic

Notes:

Lesson 1

This lesson references the use of parallel lines to create equidistant intervals outlined in Grade 3 Module 5 Lesson 30. Please see that lesson for more detail.

Lesson 2

In the Concept Development, please note that in this lesson, the axes are drawn with arrows that show the increasing direction of the numbers only. Students should be reminded that although the arrows are not visible on both ends of the axes, they still represent lines that continue in both directions infinitely.

Lesson 3

Emphasize the use of vocabulary such as origin, axis, etc to build understanding throughout this module. To build this vocabulary, consider: having students tap and whisper a new word three times, having students continue to add to their collection of math words on 3″ × 5″ cards held together by a metal ring, have students continue building an illustrated glossary (the last two options assume you've been using some kind of vocabulary tool all year).

Lesson 4

This lesson teaches battleship with coordinate grids. To make this a meaningful activity, consider two kids per team, to help each other with the coordinates, and monitor closely to check that students are finding coordinates. Push students to evaluate their strategic thinking, rather than randomly random guessing, when choosing coordinates.

Assessment:

Biweekly #3: Lesson 3 Exit Ticket

Standards Addressed in Lessons

Topic A:

5.G.1

Week 7: May 29

Module

Notes:

COMBINE Lesson 5/Lesson 6

Combine these lessons due to pacing considerations, since both share the same objective: SWBAT investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes. Do Concept Development #1 and #2 from lesson 5, and #2 from Lesson 6. Give the Problem Set and Exit Ticket from Lesson 6.

Lesson 7

Emphasize SMP 6, attending to precision, as students make observations about the graphs and learn to make tables. Use precise language when describing the location of points in the line.

Lesson 8

Consider having students put the coordinate plane template in a sheet protector and using dry erase markers to do the Concept Development. This will conserve supplies and allow students to increase the number at-bats using the template. Clarify for students the definition of "range of values" on the axes during the Concept Development.

Standards Addressed in Lessons

Topic A:

5.G.1

Topic B:

5.G.1

5.OA.3

Week 8: June 5

Module

Notes:

Lesson 9

If students struggled with Lesson 8, make sure to do fluency activity "Plot Points on Coordinate Grid" for additional review before starting Lesson 10. Continue to use math terms (steepness of slope, intersect, coordinate pair, etc) to help build fluency for students, consider making a word bank for the unit to house vocabulary. Emphasize SMP 7, helping students see patterns to what happens when you graph lines.

Lesson 10

Pay attention to student mastery of determining the rules for each line, starting to give additional practice and support to students who still struggle to find connections between lines, or struggle to graph or make tables. In student debrief, emphasize patterns students see (SMP 7) to help students more easily determine rules. (ex. "What happens when I add a positive constant to x? How is that different than a negative constant? How is that different from multiplying by a constant, etc.)

OMIT Lesson 11

This lesson is not part of 5th grade CCSS, and therefore is omitted for pacing considerations.

OMIT Lesson 12

This lesson is not part of 5th grade CCSS, and therefore is omitted for pacing considerations.

One day provided this week to administer the Mid-Module Assessment after Lesson 10.

Lesson 13

Emphasize questioning around patterns that students are noticing between lines that are parallel and lines that are not. If you have time, asking the final question for student debrief "How does drawing these parallel segments relate to our fluency activity with angles?" Start to help students see the connection between parallel lines and angle measurement, as this will set them up for future lessons.

Assessment:

Mid-Module Assessment

Standards Addressed in Lessons

Topic B:

5.OA.2

5.OA.3

5.G.1

Topic C:

5.G.1

5.G.2

Standards in Assessment

Mid-Module

5.OA.2

5.OA.3

5.G.1

Week 9: June 12

Assessment:

End-of-Module Assessment

Standards Addressed in Lessons

Topic C:

5.G.1

5.G.2

Standards in Assessment

End-of-Module:

5.G.1

5.OA.1

5.OA.2

ANet:

Major:

5.MD.4

5.MD.5a

5.MD.5b

5.MD.5c

5.NF.4

5.NF.4b

Additional:

5.G.1

5.G.2

5.G.3

5.G.4

5.OA.3

Review:

5.MD.1

5.NF.6

5.NF.7a

5.NF.7b

Notes:

Lesson 14

It might be helpful to chart the pairs of points that are parallel, to help students see patterns between several examples. Consider charting examples of parallel lines on one side of the chart, examples of intersecting lines on the other

Lesson 15

If possible, teach this lesson without modification, and make sure to model each step on a projector or whiteboard so students are able to visually see how the angle measurements add up to 90 degrees. Emphasize the angles made both inside and outside of the triangle, as this will help prepare students for future learning about angles

One day provided this week to administer the End-of-Module Assessment after Lesson 15.

OMIT Lessons 16-20

Topics C and D of Module 6 is optional and has been omitted for pacing considerations. These topics do not provide new content, but extend the coordinate plane skills taught in Topics A and B. We decided to include Lessons 13, 14, and 15 from Topic C to give students the opportunity to practice constructing parallel and perpendicular lines where there time was available.

OMIT Lessons 21-34

These lessons are end-of-year review and have been omitted for pacing considerations. Review the summer materials to give to students for additional practice of the major work of fifth grade.