Overview

Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction.

In Module 1, students extend their work with whole numbers and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart.

Topic A: Place Value of Multi-Digit Whole Numbers

Topic B: Comparing Multi-Digit Whole Numbers

Topic C: Rounding Multi-Digit Whole Numbers

Topic D: Multi-Digit Whole Number Addition

Topic E: Multi-Digit Whole Number Subtraction

Topic F: Addition and Subtraction Word Problems

Advanced Preparation:

- Number lines
- Personal white boards
- Place value cards
- Place value chart
- Place value disks

Module 2: Unit Conversions and Problem Solving with Metric Measurement

In Module 2, student uses length, mass and capacity in the metric system to convert between units using place value knowledge.

Topic A: Metric Unit Conversions

Topic B: Application of Metric Conversions

Advanced Preparation:

- Balance scale, weights (masses)
- Centimeter ruler, meter stick
- Liter containers with millimeter scale
- Number line
- Tape diagram

Module 3: Multi-Digit Multiplication and Division

In this module, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers.

Topic A: Multiplicative Comparison Word Problems

Topic B: Multiplication by 10's, 100's and 1,000's.

Topic C: Multiplication up to 4 Digits by Single-Digit Numbers

Advanced Preparation:

- Area model
- Grid paper
- Number bond
- Place value disks
- Tape diagram
- Ten thousands place value chart (Lesson 7 Template)
- Thousands place value chart (Lesson 4 Template)

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: September 5

Standards Addressed in Week's Lessons

Topic A:

4.NBT.1

4.NBT.2

4.OA.1

Notes:

Lesson 1

Students need to recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. This lesson is conceptual and requires students to use place value charts and disks to understand the comparison of the value of digits.

Lesson 2

The Application Problem builds on the concept from the previous lesson of 10 times as many. Students continue to build on their conceptual understanding of place value

Week 2: September 10

Assessment

Biweekly #1

Exit ticket from Lesson 3*

Standards Addressed in Week's Lessons

Topic A:

3.OA.1

3.OA.3

Topic B:

3.OA.2

3.OA.3

3.OA.4

3.OA.6

Notes:

Lesson 3

In this lesson, the place value chart is extended to the millions place. At this point, continue to push student understanding until they are able to fluently read numbers. *The Exit Ticket from this lesson will be used for the biweekly because it has a balance of the procedural and conceptual levels of rigor from this standard.

Lesson 4

Consider scaffolding reading number words by providing individual cards with number words that can be easily copied and allowing students to abbreviate number words.

Lesson 5

Provide students with sentence frames to refer to when using comparative statements. For students who have difficulty converting numbers from expanded form into standard form, demonstrate using a place value chart to show how each number can be represented and then how the numbers can be added together.

Lesson 6

This is the last lesson that directly addresses this standard. Consider moving to more abstract levels of rigor if students understand the conceptual breakdown of multiplication.

Week 3: September 18

Assessment

Mid Module Assessment

Module 1

Standards Addressed in Week's Lessons

Topic C:

4.NBT.3

Standards in Mid or End of Module Assessment

Mid Module Assessment:

4.NBT.1

4.NBT.2

4. NBT.3

Notes:

Lesson 7 & 8 Combine

The objective in these lessons are the same but value of the digits increase. Continue to build on students’ conceptual understanding of rounding by using the vertical number line even as value of the numbers get bigger.

Lesson 9

Students begin to move away from using the vertical number line to round numbers. Instead they are moving to applying their understanding of place value to round numbers. This would a good opportunity to revisit the place value chart and have students work procedurally on understanding rounding.

Lesson 10

Much like the previous lesson, students are using their place value knowledge to round numbers. Throughout this lesson, they are applying their understanding of rounding in real world problems.

There are only 3 lessons this week, therefore there is a day built in to administer the Mid-Module assessment, and a second day for remediation and reteaching.

Week 4: September 25

Notes:

Lesson 11

It's important to make sure that students are able to represent addition using a tape diagram and their understanding of place value. Even though students may feel comfortable jumping into the algorithm and reasoning abstractly, the emphasis of the lesson is around bundling in the different place values, which will be important when they move into subtraction and borrowing.

Lesson 12

Students working below grade level may have difficulty conceptualizing word problems. Use smaller numbers or familiar contexts for problems. Have students make sense of the problem, and direct them through the process of creating a tape diagram. Emphasize reasonability of an answer in the lesson, which will allow students to revisit rounding. *The biweekly this week is the exit ticket which allows students to revisit their knowledge of rounding while practicing addition and subtraction.

Lesson 13

The standard is a very procedural standard, and at this point in the instruction, it may be advisable to have students begin using a standard addition and subtraction algorithm to solve problems.

Lesson 14 & 15 Combine

In Lessons 14 and 15, the objectives are the same except that in lesson 15, there are more opportunities for practice and developing fluency.

Week 5: October 2

Notes:

Lesson 16

Students may not consider whether their answer makes sense. Guide students to choose the sensible operation and check their answers. Encourage students to reread the problem after solving and to ask themselves, “Does my answer make sense?” If not, ask, “What else can I try?”

Lesson 17 Omit

Multi-step problems are taught in lesson 18, so embed problems from Lesson 17 throughout Module 2 and 3 lessons to give students more recurring practice.

Lesson 18

To culminate the module, students are given tape diagrams or equations and are encouraged to use creativity and the mathematics learned during this module to write their own word problems to solve using place value understanding and the algorithms for addition and subtraction.

Lesson 19 Omit

Because multi-step problems are taught in lesson 18, add problems from lesson 19 to problem set 18 in order to give students more practice.

The End of Module students should be administered after lesson 18 during one of the instructional days, with a day for remediation before beginning Module 2 Lesson1.

Lesson 1

Throughout this module students will be learning how to convert metric units in the context of addition and subtraction problems using mixed units. This will set the foundation for future modules, as well as work in future grades. When possible, emphasize how to convert between units, emphasizing number bonds and other templates within the unit. Within this lesson, consider prioritizing fluency exercise #2 to support this work.

Week 6: October 10

Module

Notes:

Lesson 2

This lesson requires a lot of manipulatives that are necessary to help student have a conceptual understanding of units of measurement. You will need to gather many of the materials including 1000 paper clips, a balance scale, and weights. In addition, consider assigning each unit of measurement a color and using that consistently when teaching each lesson so that students can conceptualize the units as different when working with mixed units. Emphasize the use of tape diagrams when solving problems, as this will continue to be used throughout this year and beyond. *This biweekly is the exit ticket from the lesson and covers the breadth of the standard.

Lesson 3

Students continue to build off of their measurement work from previous grade levels. They solidify their understanding of the relationship between metric units and the place value chart and apply unit conversions to solve and reason about multi-step word problems (4.MD.2). Applying the skills learned in Module 1, students discover and explore the relationship between place value and conversions.

Lesson 4

Lesson 4 connects metric measurement conversions and place value by comparing mixed units of measure and verifying statements such as 1 kilometer is 1,000 times as much as 1 meter.

Week 7: October 16

Notes:

Lesson 5

In Lesson 5, as students solve two- and three-step word problems by adding and subtracting metric units, their ability to reason in parts and wholes is taken to the next level. This is important preparation for multi-digit operations and manipulating fractional units in future modules.

Lesson 1

Connect students’ conceptual and procedural understanding around area and perimeter by presenting mathematical calculations using both graph paper as well as the formula. This will help student understand how the formula relates back to the visual representation of perimeter and area.

Lesson 2

Have base ten cubes available for students during this lesson. During concept development, ease the task of drawing by offering students the choice of tracing the concrete tiles. Alternatively, reduce the small motor demands by providing a template, grid paper, or computer software for drawing.

Lesson 3

Multiplicative comparison is foundational for understanding multiplication as scaling in Grade 5 and sets the stage for proportional reasoning in Grade 6. Students determine, using times as much as, the length of one side of a rectangle as compared to its width. Beginning this Grade 4 module with area and perimeter allows students to review their multiplication facts, apply them to new and interesting word problems, and develop a deeper understanding of the area model as a method for calculating with larger numbers.

Due to pacing there is only one day given for this End of Module assessment.

Week 8: October 23

Module

Notes:

Lesson 4

When modeling patterns of multiplying by 10’s by using the place value chart and disc also display numerical representations (i.e. numbers in each disc circle or x10 on arrows) alongside these visual models. This will ensure that students are able to connect their conceptual to procedural understanding in future lessons.

Lesson 5

Some students with organizational difficulties may struggle with drawing place value disc. It may be beneficial to allow students to use manipulatives to allow them to physically move place value disc. This would serve as a way to scaffold students from concrete understanding to pictorial.

Lesson 6

This lesson builds a foundation for two-digit by two-digit multiplication. Students practice the new complexity of multiplying two two-digit multiples of 10. For example, students have multiplied 20 by 10 on the place value chart and know that it shifts the value one place to the left, 10 × 20 = 200. To multiply 20 by 30, the associative property allows for simply tripling the product, 3 × (10 × 20), or multiplying the units, 3 tens × 2 tens = 6 hundreds (alternatively, (3 × 10) × (2 × 10) = (3 × 2) × (10 × 10)). Introducing this early in the module allows students to practice during fluency so that, by the time it is embedded within the two-digit by two-digit multiplication in Topic H, understanding and skill are in place.

Lesson 7

Make sure to emphasis the language of the “value” of numbers represented in the place value chart. This will help students make connection to the renaming of numbers.

Week 9: October 30

Standards Addressed in Week's Lessons

Topic C:

4.NBT.5

4.OA.2

4.NBT.1

Notes:

Lesson 8

Continue to clarify math language such as expression, value, vertically, partial products, equation, and sum, and emphasize the use of correct mathematical terminology throughout the lesson

Lesson 9

Have students use and compare the two methods: partial products and the standard algorithm. Encourage learners to analyze their proficiency and efficiency using each method. Guide students to ask, “What mistakes do I make? When? Which method is easier for me? When? Why?”

Lesson 10 Omit

Omit Lesson 10 as the objectives for lesson 10 are the same as for lesson 9.

Lesson 11

By lesson 11 learners may differ in the strategies they use to solve a problem. Use this as an opportunity to begin to cultivate a classroom culture of acceptance of multiple methods to solve. Encourage students to share and innovate efficient strategies for this and other math topics.