Overview

This module gives students their first opportunity to explore decimal numbers via their relationship to decimal fractions, expressing a given quantity in both fraction and decimal forms. Utilizing the understanding of fractions developed throughout Module 5, students apply the same reasoning to decimal numbers, building a solid foundation for Grade 5 work with decimal operations.

Topic A: Exploration of Tenths

Topic B: Tenths and Hundredths

Topic D: Addition with Tenths and Hundredths

Topic E: Money Amounts as Decimal Numbers

Advanced Preparation:

- 1-liter container with milliliter marks
- Area model
- Centimeter ruler
- Decimal place value disks (tenths and hundredths)
- Digital scale
- Meter stick
- Number line
- Place value chart with decimals to hundredths
- Tape diagram
- Whole number place value disks (hundreds, tens, and ones)

Module 4: Angle Measure and Plane Figures

This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in their work throughout the module, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures

Topic C: Problem Solving with the Addition of Angle Measures

Topic D: Two-Dimensional Figures and Symmetry

Advanced Preparation:

- Folded paper models
- Pattern blocks
- Protractors of various diameters, including a 360° and 180° protractor
- Rectangular and triangular grid paper
- Right angle template (created in Lesson 2), set square
- Ruler (used to measure length), straightedge (used to draw straight lines)

Module 7: Exploring Measurement with Multiplication

In this module, students build their competencies in measurement as they relate multiplication to the conversion of measurement units. Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion.

Topic A: Measurement Conversion Tables

Topic B: Problem Solving with Measurement

Topic C: Investigation of Measurements Expressed as Mixed Numbers

Advanced Preparation:

- Analog clock (with second hand)
- Balance scale with mass weights
- Beaker (marked for mL and L)
- Composite figure
- Digital scale (metric and customary units)
- Gallon, quart, pint, and cup containers
- Meter stick, yard stick, 12-inch ruler, centimeter ruler
- Number bond
- Number line
- Protractor
- Stopwatch
- Tape diagram
- Two-column table

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 (Module 6 guide is unavailable)

Week 1: April 16

Standards Addressed in Lessons

Topic A

4.NF.6

4.NBT.1

4.MD.1

Topic B

4.NF.5

4.NF.6

4.NBT.1

4.NF.1

4.NF.7

4.MD.1

Notes:

OMIT LESSON 1 - This lesson has been omitted due to pacing considerations. The tape diagram model from Lesson 1 of decomposing a whole into tenths can be abbreviated and incorporated into the beginning of Lesson 2's Concept Development.

Lesson 2 - While introducing the area model to show tenths as fractions greater than 1 and as decimal numbers, make sure to show the table diagram and ruler image of how a whole is broken down into tenths from omitted Lesson 1.

Lesson 3 - Consider giving students 15-20 minutes for today's Problem Set because the Exit Ticket mirrors components of the entire Problem Set, indicating all practice is important before moving onto Lesson 4.

Lesson 4 - For the Problem Set, some students may find partitioning hundredths on the meter strip challenging. Alternatively, have students model with an area model (e.g., a 10 by 10 square partitioned into 100 unit squares). Or, enlarge the template (and tape diagrams on the Problem Set) to ease the task.

Week 2: April 23

Assessment:

Biweekly #1: Lesson 5 Exit Ticket

Mid-Module

Standards Addressed in Lessons

Topic B

4.NF.5

4.NF.6

4.NBT.1

4.NF.1

4.NF.7

4.MD.1

Topic C

4.NF.7

4.MD.1

4.MD.2

Standards in Assessment

Mid-Module:

4.NF.5

4.NF.6

Notes:

Lesson 5 - While the general rule is that students should read 0.08 and 8/100 as 8 hundredths, in this lesson students benefit from hearing decimal numbers read in both fraction form and as, for example, “zero point zero eight.” Without the latter, it is hard to verify orally that students have written a decimal correctly.

Lesson 6 - This lesson involves modeling decimal fractions on the number line and with area models. Students working above grade level may present alternative ways of locating 3 46/100 on the number line, such as reasoning that half of 100 is 50 and then counting back to 46. Encourage these representations and emphasize efficiency in helping more advanced students select methods to model the numbers.

Lesson 7 - During Concept Development, note that as learners begin to write numbers with decimal points, some students may need to be explicitly told to write a zero in the ones place as a placeholder, for example, in the number 0.7.

OMIT LESSON 8 - This lesson emphasizes decimal equivalence to decimal fractions. Make sure to assess student understanding from Lesson 7, where students began to write numbers as decimal points and possibly reinforce with an opening exercise before the Mid-Module Assessment.

One day provided to administer Mid-Module Assessment after Lesson 7.

Week 3: April 30

Standards Addressed in Lessons

Topic C

4.NF.7

4.MD.1

4.MD.2

Topic D

4.NF.5

4.NF.6

4.NF.3c

4.MD.1

Notes:

Lesson 9 - Notes on vocabulary for Concept Development: mass is a fundamental measure of the amount of matter in an object. While weight is a measurement that depends upon the force of gravity (one would weigh less on the moon than one does on Earth), mass does not depend upon the force of gravity. Both words are used here, but it is not important for students to recognize the distinction in mathematics at this time.

Lesson 10 - The Application Problem in this lesson reviews comparison of metric measurements from Lesson 9. Students may try to use addition and subtraction, but encourage them to use what they know about completing the whole and benchmark numbers.

Lesson 11 - The three Fluency activities review Lessons 7, 8 and 10 in preparation for students to be able to compare and order mixed numbers in various forms. During the Fluency, mnemonic devices such as imagining the < symbol to be an alligator mouth that eats the larger amount can be effective. To enhance the practice, ask students to read the comparison statements aloud.

Lesson 12 - After the initial use of multiplication to convert tenths to hundredths, many students may be able to do the conversion mentally. This is an important application of students’ work with equivalence from Module 5, which leads to addition and subtraction of fractions with unlike denominators in Grade 5. If some students still struggle with the conversion, directly link the multiplication to the area model and place value chart.

Week 4: May 7

Notes:

Lesson 13 - During the Concept Development, make sure to model converting to fractions before adding decimals. While it may take longer, the practice strengthens student understanding of the fraction and decimal relationship, increases student ability to think flexibly, and prepares students for success in Grade 5 fractions.

OMIT LESSON 14 for pacing considerations because it repeats the procedural work done in Lesson 13 in the context of measurements. Students get in-depth practice working on measurement word problems in Modules 2 and 7.

Lesson 15 - Notes on reading fractions and decimals: To make close connections between decimals, fractions and units, read numbers such as 0.33 meter as “thirty-three hundredths meter” and 1/100 dollar as “one hundredth dollar.” Also, share common ways in which decimals and fractions are read daily, such as “zero point thirty-three meters” or “one hundredth of a dollar.”

Lesson 16 - This lesson follows a format of student presenters. Models shared may include concrete manipulatives, computer software, or other adaptive materials. If the pace of the lesson is a consideration, prepare presenters beforehand. The first problem may be most approachable for students working below grade level.

One day provided to administer End-of-Module Assessment.

Standards Addressed in Lessons

Topic D

4.NF.5

4.NF.6

4.NF.3c

4.MD.1

Topic E

4.MD.2

4.NF.5

4.NF.6

Standards in Assessment

End-of-Module:

4.NF.5

4.NF.6

4.NF.7

4.MD.2

Week 5: May 14

Notes:

Module 4 comes directly after Module 6. Module 4 was moved to the end of the year to reflect the earlier focus on the major work of the grade band.

OMIT LESSON 1 for pacing considerations. A model of #1 in the Problem Set from this lesson should be incorporated into Lesson 2.

Lesson 2 - Instead of the Fluency and Application for this lesson, use time to model #1 from Lesson 1's Problem Set while students copy the example and give students the chance to complete #2 on their own. You will need to provide the language: point, ray, line, line segment, angle. Make an anchor chart for the vocabulary. Do not expect this to be cemented from this short model, but students will gain familiarity with the language given the anchor chart as the unit progresses. Follow the rest of Lesson 2 as written. Note: Print or project with color for this lesson.

COMBINE LESSONS 3/4 -

Lesson 3 addresses parallel lines and Lesson 4 introduces perpendicular lines. If time allows, some teachers may prefer to teach these lessons in isolation. If that is not the case, combine Lessons 3 & 4. In the Concept Development teach #1 and #4 for each lesson. Have students complete the first page of each Problem Set and the Exit Ticket from Lesson 4.

Lesson 5 - Students need the right angle templates from Lesson 2 for the Application Problem in this lesson. In this lesson, students are building on their understanding of fractions from Module 3 to see the degrees in a circle as fractional turns around the circle (1 degree is 1/360 of a whole turn). If possible, print circular protractor template from the lesson on transparencies to create your own circular protractors for the class.

Lesson 6 - This lesson calls for providing students with a variety of protractors (circular and 180 degrees) to distinguish angle measure from length measure. Students can share calculators and do not need to each have their own variety of calculators.

Week 6: May 21

Module

Notes:

Lesson 7 - Suggested scaffolds: 1) As they measure ∠C, guide students working below grade level to adjust the paper rather than the protractor. 2) Challenge students working above grade level to predict the measure of ∠C before measuring.

Lesson 8 - Consider scaffolding the Problem Set by putting a dot in the center of the circle to assist with drawing in Problem 5 and guiding students to count by 90° or fourths up to the desired turn.

One day provided this week to administer the Mid-Module Assessment after Lesson 8.

OMIT LESSON 9 - This lesson has students examine patterns in interior and exterior angles in various polygons. Due to pacing considerations, this lesson has been omitted since it is not a major work of the grade level and is not a necessary building block for upcoming lessons.

Lesson 10 - This lesson shows students that the measure of the whole angle is equal to the sum of the measures of the two parts through an exercise folding paper. Make sure to have your document camera set up so students can clearly see the model for this to make it meaningful.

Assessment:

Bi-Weekly #3: Lesson 10 Exit Ticket

Mid-Module

Standards Addressed in Lessons

Topic B

4.MD.5

4.MD.6

Topic C

4.MD.7

Standards in Assessment

Mid-Module:

4.G.1

4.MD.5

4.MD.6

Week 7: May 28

Module

Notes:

Lesson 15 - Students construct quadrilaterals given conditions (perpendicular vs. parallel sides, side lengths, angle measures). Since we are omitting the next lesson for pacing considerations, consider giving students working above grade level the opportunity to attempt the first page of the Homework or Problem Set from Lesson 16 in addition to the Lesson 15 work.

OMIT LESSON 16 - This lesson was omitted for pacing considerations as it relates to an extension of constructing two-dimensional figures addressed in previous lessons.

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

Combine Lessons 1, 2, 3 - All three lessons have students create conversion tables for length, weight, capacity and time units and use the tables to solve problems. To save time, eliminate the fluency from all three lessons and pre-create conversion tables on anchor charts (consider having handouts for students also ready). Use the structure of the Concept Development to have students create at least one conversion table from each lesson, and then show students the rest of the conversion tables already pre-prepared. Have students complete page 1 of all three Problem Sets. Use Lesson 1's Exit Ticket. Consider assigning the written fluency (multi-digit addition and subtraction) as homework.

Lesson 4 - This lesson leads students to apply the procedural conversion they learned in the previous combined lesson to real-world scenarios. The Concept Development involves solving the Problem Set's word problems using the following sequence: 1) Model 2) Calculate and Write 3) Assess the Solution.

OMIT LESSON 5 - This lesson involves peer critiques of Topic A and has been omitted for pacing considerations. Consider incorporating Lesson 5 into small group time, if possible, as this collaboration leads to high levels of student thinking and discussion.

Standards Addressed in Lessons

Topic C

4.MD.7

Topic D

4.G.1

4.G.2

4.G.3

Week 8: June 4

Notes:

Lesson 15 - Students construct quadrilaterals given conditions (perpendicular vs. parallel sides, side lengths, angle measures). Since we are omitting the next lesson for pacing considerations, consider giving students working above grade level the opportunity to attempt the first page of the Homework or Problem Set from Lesson 16 in addition to the Lesson 15 work.

OMIT LESSON 16 - This lesson was omitted for pacing considerations as it relates to an extension of constructing two-dimensional figures addressed in previous lessons.

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

Combine Lessons 1, 2, 3 - All three lessons have students create conversion tables for length, weight, capacity and time units and use the tables to solve problems. To save time, eliminate the fluency from all three lessons and pre-create conversion tables on anchor charts (consider having handouts for students also ready). Use the structure of the Concept Development to have students create at least one conversion table from each lesson, and then show students the rest of the conversion tables already pre-prepared. Have students complete page 1 of all three Problem Sets. Use Lesson 1's Exit Ticket. Consider assigning the written fluency (multi-digit addition and subtraction) as homework.

Lesson 4 - This lesson leads students to apply the procedural conversion they learned in the previous combined lesson to real-world scenarios. The Concept Development involves solving the Problem Set's word problems using the following sequence: 1) Model 2) Calculate and Write 3) Assess the Solution.

OMIT LESSON 5 - This lesson involves peer critiques of Topic A and has been omitted for pacing considerations. Consider incorporating Lesson 5 into small group time, if possible, as this collaboration leads to high levels of student thinking and discussion.

Assessment:

End-of-Module

Standards Addressed in Lessons

Topic D

4.G.1

4.G.2

4.G.3

Topic A

4.OA.1

4.OA.2

4.MD.1

4.NBT.5

4.MD.2

Standards in Assessment

End-of-Module:

4.MD.5

4.MD.6

4.MD.7

4.G.1

4.G.2

4.G.3

Week 9: June 11

Assessment:

ANet

End-of-Module

Standards Addressed in Lessons

Topic B

4.OA.2

4.OA.3

4.MD.1

4.MD.2

4.NBT.5

4.NBT.6

Topic C

4.OA.3

4.MD.1

4.MD.2

4.NBT.5

4.NBT.6

Standards in Assessment

End-of-Module:

4.OA.1

4.OA.2

4.OA.3

4.MD.1

4.MD.2

ANet

Major

4.NF.5

4.NF.6

4.NF.7

Supporting

4.MD.2

4.MD.5

4.MD.6

4.MD.7

Additional

4.G.1

4.G.2

4.G..3

4.MD.5

4.MD.6

4.MD.7

4.OA.5

Review

4.MD.1

4.NF.1

4.NF.2

Notes:

COMBINE LESSONS 6/7/8/9- All four of these lessons require students to use the conversion tables they created in 1/2/3 to solve addition and subtraction problems with mixed units. Model examples 1 from Lessons 6 and 9 and then have students work in pairs to complete the first page of all four Problem Sets. Set an 8-minute timer for each Problem Set. If some students are finished early, have the second page of the Problem Set (more application work) ready for them during that lesson's allotted 8 minutes. Give first page of homework from Lessons 7 and 9. Use the first problem from Lesson 6 and Lesson 7's Exit Tickets.

Lesson 10 - This lesson gives students an additional day to apply the procedural addition and subtraction problems they completed in the previous combined lesson. Students use tape diagrams to model the word problems they are solving with mixed units. Make sure anchor charts/handouts with conversion tables are accessible for all students.

OMIT LESSON 11 for pacing considerations because this lesson repeats Lesson 10's objective.

COMBINE LESSONS 12 and 14 for pacing considerations to show students how to convert larger units expressed as mixed numbers to smaller units, and then apply the procedural skill to word problems. Model #1 from Lesson 12 Concept Development, and #1 from lesson 14's Problem Set. Then give students the first page of Lesson 12's Problem Set and all of Lesson 14's Problem Set. Allow students to work in partners to solve (use Lesson 12 Exit Ticket).

One day provided to administer End-of-Module Assessment.

OMIT LESSONS 13 for pacing considerations because this lesson repeats Lesson 12's objective.

OMIT LESSONS 15-18 from Topic D. These lessons compose the Year in Review and have been removed for pacing considerations since they have been previously taught.