Overview

Module 3: Multi-Digit Multiplication and Division

Students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers.

Topic D: Multiplication Word Problems

Topic E: Division of Tens and Ones with Successive Remainders

Topic F: Reasoning with Divisibility

Topic G: Division of Thousands, Hundreds, Tens, and Ones

Topic H: Multiplication of Two-Digit by Two-Digit Numbers

Advanced Preparation:

- Personal White boards
- Grid paper
- Number bond
- Place value disks: suggested minimum of 1 set per pair of students (18 ones, 18 tens, 18 hundreds, 18 thousands, 1 ten thousand)

Module 5: Fraction Equivalence, Ordering, and Operations

Students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers

Topic A: Decomposition and Fraction Equivalence

Topic B: Fraction Equivalence Using Multiplication and Division

Advanced Preparation:

- Personal White Boards
- Area model
- Fraction strips (made from paper, folded, and used to model equivalent fractions)
- Line plot
- Number line
- Rulers
- Tape diagram

2016-2017 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: November 7

Notes:

Lesson 12

Consider having students use the Read, Draw, Write approach for each word problem in this lesson. The Problem Set comprises word problems from the Concept Development and is therefore to be used during the lesson itself.

Lesson 13

Application is not a component of this lesson since all of the lesson is comprised of word problems. The Problem Set comprises word problems from the Concept Development and is therefore to be used during the lesson itself.

Week 2: November 14

Assessment

Mid Module Assessment : Administer after lesson 13

Biweekly #1 from lesson 15 Exit Ticket

Standards Addressed in Week's Lessons

Topic E

4.NBT.6

Standards Addressed in Assessments

Mid Module Assessment

4.OA.1

4.OA.2

4.OA.3

4.NBT.5

4.MD.3

Notes:

Two days this week are provided for Mid Module assessment and remediation.

Lesson 14

While multiple solutions are always encouraged, modeling with arrays is a strategic choice for this lesson and should be the model used.

Lesson 15

The exit ticket may be modified to include a graph, as a graph is used for most of the concept development and problem set. It's use does not change the assessment of the standard.

Week 3: November 21

Week 4: November 28

Assessment

Biweekly #2 from lesson 20 Exit Ticket

Standards Addressed in Week's Lessons

Topic E

4.NBT.6

Topic F

4.OA.4

Notes:

Lesson 17

Consider continuing to help students make a connection from division to multiplication and vice versa by digging in on the checking of work.

Lesson 18

Divide Mentally fluency is an activity that leads itself well to being done during transition times to give transitions an academic feel and gain some additional time during the lesson.

Lesson 19 Omit

Omitted for pacing considerations. Consider embedding discussions of interpreting remainders into other division lessons.

Lesson 20

Consider asking students to regularly explain the connection between the area model and the algorithm for division.

Lesson 21 Omit

Omitted for pacing considerations. Students solve similar division problems using area model in lesson 20.

Lesson 22

Consider adding "prime" and "composite" to the class word wall. Consider using manipulatives for students to explore arrays as prime or composite.

Week 5: December 5

Notes:

Lesson 23

Consider letting students work in groups and persevere through the application problem and discuss their reasoning. Circulate during problem to take data on students understanding of prime numbers and place value.

Lesson 24

Problem set question #5 has students find all composite and prime numbers between 1-100. Consider starting class by asking students to guess how many prime numbers there are between 1-100, put them on a post it note and collect. Announce winner at the end of lesson 25. Answer = 25.

Lesson 25

The problem set from lesson 24 will be used in this lessons concept development. Consider having a fresh, empty copy ready as mistakes may have occurred the previous day. Announce winner of the "guess how many prime numbers between 1-100" game.

Lesson 26

If students use whiteboards with inserts, consider having a place value chart template as an insert for this lesson. Even while using models for division, have students ask themselves if models are necessary or if they have mental strategies that help them go model free to answer some problems.

Week 6: December 12

Notes:

Lesson 27

Two days are provided for this lesson. Students who are not as fluent with adding and subtracting within 1,000,000 (the required fluency of the grade) may need more time to work through multiple problems of three digit division.

Lesson 28

Students should be prepared with thousands white board template. Encourage students who are ready to begin to move away from place value disks into abstract model of the division algorithm.

Lesson 29

While the lesson demonstrates the use of a tape diagram for problem 2, allow students to use other models as well, like place value disks, and discuss multiple solutions.

Standards Addressed in Week's Lessons

Topic G

4.OA.3

4.NBT.6

Week 7: December 19

Notes:

Lesson 30

The lesson demonstrates problems with a zero in the dividend and the quotient. The exit ticket focuses on questions with a zero in the dividend only.

Lesson 31 Omit

Omitted for pacing considerations. Instead, consider embedding analysis of division situations throughout later lessons.

Lesson 32

The application problem may be confusing for students who have not done lesson 31. Consider using smaller numbers and focusing on the use of the tape diagram and word problem generating, as that is what connects to today's concept development.

Lesson 33 Omit

Omitted for pacing consideration.

Lesson 34

Students will need personal whiteboards and thousands chart. The application problem links directly to the beginning of the concept development. For problem #1, students may use associative property to join either (4*10) *22 or 4* (10*22) Both are acceptable ways to move through the problem.

Week 8: January 9

Module

Notes:

Lesson 35

Students will need personal white boards. It is OK to model for students 30*25 as a 2x2 area model with a 0 in the ones place for the 30 so students can better recognize why it is drawn as a 1x2 in the lesson.

Lesson 36

For those that need scaffolding, consider drawing 2x2 empty area models next to the probem set problems for support.

Lesson 37

When making an area model, it has been strategic to have the horizontal number to line up with the tens place on the left and then the ones on the right, and the vertical number to line up one place on top and tens place below. This will help make a smoother transition to the multiplication algorithm and therefore should be used in all modeling.

Lesson 38

Two days are provided for this lesson to allow time for differentiation in small groups. Students will need personal white boards for this lesson. Some struggling students may still rely on an area model for assistance with multiplication.

Standards Addressed in Week's Lessons

Topic H

4.NBT.5

Week 9: January 16

Notes:

Lesson 38

Two days are provided for this lesson to allow time for differentiation in small groups. Students will need personal white boards for this lesson. Some struggling students may still rely on an area model for assistance with multiplication.

One day is provided this week for the End of Module Assessment.

We have moved Module 4 (Angles) to Quarter 4. Students should begin working on Module 5 (Fractions) after completing Module 3. This change prioritizes the major work of the grade level and aligns to the standards assessed on ANet.

Lesson 1 & 2 Combine

Lessons 1 and 2 have the same objective and can be combined. Use the concept development from lesson 1 and the problem set and exit ticket from lesson 2. Consider modeling the beginning of the problem set for students.

Assessment

End of Module Assessment: administer after lesson 38

Standards Addressed in Week's Lessons

Topic H

4.NBT.5

Topic A

4.NF.3b

4.NF.4a

Standards Addressed in Assessments

End of Module Assessment

4.OA.1

4.OA.2

4.OA.3

4.OA.4

4.NBT.5

4.NBT.6

4.MD.3

Week 10: January 23

Module

Notes:

Lesson 3

Students should have personal white boards ready to complete concept development questions.

Lesson 4 Omit

Omit lesson for pacing considerations. Instead, in Lesson 5, embed the contrast of the decomposition of a fraction using the tape diagram versus using the area model.

Lesson 5

The application problem is a bridge to today’s lesson where students use the area model as another way to show both decomposition and equivalence. Consider using graph paper inserts in personal white boards.

Lesson 6

In the Problem Set, if a solution method is not specified, students should use the Read, Draw, Write approach to solve.

One day this week is provided for ANet testing.

Assessment

ANet

Standards Addressed in Week's Lessons

Topic A

4.NF.3b

4.NF.4a

Standards Addressed in Assessments

ANET

Major

4.NBT.B

4.NBT.B.6

4.OA.A.1

4.OA.A.2

4.OA.A.3

Supporting

4.MD.A.3

4.MD.B.4

Review

4.NBT.A.1

4.NBT.A.2

4.NBT.A.3

4.NBT.B.4

4.NBT.B.5

Week 11: January 30

Notes:

Lesson 7

Students should have personal white boards ready to complete concept development questions. Consider modeling and asking students to be precise with mathematical language of 'numerator' and 'denominator".

Lesson 8

Students should have personal white boards ready to complete concept development questions. Consider that students are working towards answering the question, "How are we able to show equivalence without having to draw an area model?"

Lesson 9

Consider avoiding the word "simplify" as in future math concepts the word simplify is relative to the type of problem you are trying to solve. Consider instead using the term "equivalent" or "renaming".