4th Grade Unit 1

MAXIMIZING MATH MENTALITY

SARASOTA COUNTY SCHOOLS

Guide to Plan for Success

Unit 1: Multiplicative Comparison, Factors/Multiples, Area and Perimeter

Grade 4: Unit 1

Operations and Algebraic Thinking & Measurement and Data Geometry

MAFS.4.OA.2.4 MAFS.4.MD.1.1

15 days

MAFS.4.G.1.1

3-5 days MAFS.4.OA.1.1 MAFS.4.MD.1.3

MAFS.4.OA.1.2

Unit 1 Assessment

Instructional Routines for the 4th Grade Math Block

Number Talk: 5-15 Minutes Every Day Overarching Goals:

• Develop computational fluency (flexibility, accuracy, and efficiency) with numbers. • Developing number sense. • Preview and review skills throughout the year using mental math.

*Number talks do not always align with the instructional skills sequence used for problem of the day. Teaching Format:

• Teacher: poses problem • Students: mentally solve the problem and uses hand signals to communicate the message • Teacher: calls on students to get answers and records them on the board (for questions with one

answer only) • Students: Justify their answers and strategies with purposefully picked partners. • Teacher: Calls on students, records students’ strategies, and connects strategies with the learning

goal. • Class agrees on the answer.

Problem of the Day (Instructional Sequence): 20-45 Minutes Every Day

*Overarching Goals:

• Making sense of problems and persevering • Promote student discourse and reasoning. • Collaborating and constructing mathematical ideas with peers.

*It is important to understand that mathematics is to be taught through problem solving. Problem-based tasks or activities are the vehicle through which the standards are taught. (Van de Walle and Lovin, Teaching Student-Centered Mathematics: 3-5 pg. 11 and 12) *For additional support, reference “The 5 Practices In Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom” book (Margaret Peg S. Smith, Victoria bill, and Miriam Gamoran Sherin) for best practices in facilitating productive mathematical conversations in your classroom.

**Teaching Format (Upside-Down Teaching): Whole group or partners: Problem is posed and “Three Reads Method” is utilized

You Do: • Students grapple independently and record their thinking. • Teacher monitors: circulates, listens to student thinking, encourage,

ask questions, observe, and assess. We Do:

• Students work in partners or teams to share answers, justify thinking, clarify understanding, explain their thinking, question each other. Teacher continues to monitor and mentally selects students who s/he would like to share with whole group.

I Do: • Teacher purposefully selects and sequences students to share

strategies with the whole class. • Teacher poses questions for students to make connections across

strategies, and with the learning intentions and success criteria for that day.

Similar question is posed for students to work together while teacher works with a small group or students go to centers while teacher works with a small group.

The next section within this guide, Instructional Sequence, will support the Problem of the Day by connecting standards, Success Criteria, and aligned resources.

Unit 1 Number Talk Goals (after the “First 10 Days of Math”)

• Setting Up Expectations • Review of 3rd Grade Concepts • Making 10s • Landmark Numbers

Resources:

• Unit 1 Number Talks Digital • Unit 1 Number Talks PDF

4th Grade Unit 1

Unpacking the Standards: Operations and Algebraic Thinking & Measurement and Data MAFS.4.OA.2.4: DOK 2 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Notes: Students investigate whether numbers are prime or composite by:

→ Building rectangles (arrays) with the given area and finding which numbers have more than two rectangles (e.g., 7 can be made into only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number).

→ Finding factors of the number.

→ Students should understand the process of finding factor pairs so they can do this for any number 1-100.

o Example: Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12.

4th Grade Unit 1

MAFS.4.MD.1.1: DOK 1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft. is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36)

Notes:

Foundational understandings to help with measure concepts:

→ Understand that larger units can be subdivided into equivalent units (partition).

→ Understand that the same unit can be repeated to determine the measure (iteration).

→ Understand the relationship between the size of a unit and the number of units needed (compensatory principle).

4th Grade Unit 1

MAFS.4.OA.1.1: MAJOR STANDARD DOK 1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Watch this video explaining this standard.

Notes: → A multiplicative comparison is a situation in which one

quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

→ Students should be given opportunities to write and identify equations and statements for multiplicative comparisons.

→ Examples:

o 5 x 8 = 40: Sally is five years old. Her mom is

eight times older. How old is Sally’s Mom?

o 5 x 5 = 25: Sally has five times as many pencils as Mary. If Sally has 5 pencils, how many does Mary have? (Mary’s pencils x 5 = Sally’s pencils)

4th Grade Unit 1

MAFS.4.OA.1.2: MAJOR STANDARD DOK 2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Sample Test Item: Johnny has 17 marbles. Mitchell has 3 times as many marbles as Johnny. How many marbles does Mitchell have?

Notes: → Unknown Product: A blue scarf costs $3. A red scarf costs 6

times as much. How much does the red scarf cost? (3 6 = p)

→ Group Size Unknown: A book costs $18. That is 3 times more than a DVD. How much does a DVD cost? (18 ÷ p = 3 or 3 p = 18)

→ Number of Groups Unknown: A red scarf costs $18. A blue scarf costs $6. How many times as much does the red scarf cost compared to the blue scarf? (18 ÷ 6 = p or 6 x p = 18)

→ When distinguishing multiplicative comparison from additive comparison, students should note the following. o Additive comparisons focus on the difference between two

quantities. For example, Deb has 3 apples and Karen has 5

apples. How many more apples does Karen have? A simple way to remember this is, “How many

more?” o Multiplicative comparisons focus on comparing two

quantities by showing that one quantity is a specified number of times larger or smaller than the other. For example, Deb ran 3 miles. Karen ran 5 times as

many miles as Deb. How many miles did Karen run? A simple way to remember this is “How many times

as much?” or “How many times as many?”

4th Grade Unit 1

MAFS.4.MD.1.3: MAJOR STANDARD DOK 2 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Sample Test Item: A rectangle has a length of 11 feet and a perimeter of 38 feet. What is the width, in feet, of the rectangle?

Notes:

→ Students developed understanding of area and perimeter in 3rd grade by using visual models.

→ While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work.

→ The formula for area is l x w and the answer will always be in square units.

→ The formula for perimeter can be 2 l + 2 w or 2 (l + w) and the answer will be in linear units.

→ This standard calls for students to generalize their

understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization.

4th Grade Unit 1

Click here for the Hot Math Minute Video…Coming Soon! Prerequisite Instruction: Operations and Algebraic Thinking & Measurement and Data

Preassessment- 3rd Grade Teacher Toolbox Lesson 1 Quiz: Understand Multiplication &

3rd Grade Teacher Toolbox Lesson 27 Quiz: Understand Area

Skill: 3rd Grade Review Understand the meaning of multiplication and division

Pacing: 2 days

Success Criteria:

• I can use the words “factors, product, times, and groups of” to describe the multiplication model, picture, and equation.

• I can represent a multiplication equation with models and pictures. • When given a multiplication expression, I can create a scenario to

represent it. • I can explain what division means. • I can represent a division equation with models and pictures. • I can determine the unknown number in a multiplication or division

equation by showing the relationship between multiplication and division with pictures, models, or words.

• I can explain the relationship between division and multiplication (factor x factor = product and product factor = missing factor).

Resources: Teacher Toolbox:

• Grade 3-Lesson 1 Understand the Meaning of Multiplication

• Grade 3- Lesson 4 Understand the Meaning of Division

Videos: Related Multiplication and Division

Skill: 3rd grade review: Understanding area and perimeter These concepts will be reviewed in current grade level standards.

Pacing: 2 days

Success Criteria: • I can explain the difference between the area and perimeter of a

rectangle. • I can describe real-world situations where I would need to find area. • I can describe real-world situations where I would need to find

perimeter. • When given a problem involving area or perimeter, I can identify

and explain what the problem is asking me to find. • When given a problem involving area or perimeter, I can choose a

strategy to solve the problem (drawing on grid paper, using square tiles, equations, etc.)

• When given a problem involving area or perimeter, I can draw a picture to represent the problem, label the dimensions, and write the equation to solve for the unknown.

• I can create real-world area and perimeter scenarios and explain how to solve them.

Resources: Teacher Toolbox:

• Grade 3- Lesson 28 Multiply to Find Area

o Slides

FSA Reference Sheet Other Resources: What’s the same? What’s different image Open Middle: Biggest Rectangle Open Middle: Rectangle Area and Perimeter Open Middle: Perimeter Open Middle: Squares: Perimeter v. Area Open Middle: Rectangles: Perimeter V. Area

4th Grade Unit 1

Instructional Skill Sequence: Operations and Algebraic Thinking & Measurement and Data Skill: Solve word problems involving multiplicative comparisons and additive comparisons

Pacing: 3 days

Success Criteria: • When given a multiplicative comparison situation, I can identify

which factor is being multiplied and which factor is telling how many times.

• When given an expression, I can write a multiplicative comparison scenario.

• I can write an equation that represents a multiplicative comparison situation.

• I can draw a bar model and label it to describe a multiplicative comparison problem.

• I can write an equation to solve a multiplicative comparison problem using a symbol for the unknown.

• I can write an equation to solve an additive comparison problem using a symbol for the unknown.

• I can explain what is similar and what is different between multiplicative and additive comparison problems.

• I can create a multiplicative and additive comparison word problem and explain how to solve it.

Resources: Ready MAFS Teacher Resource Book

• Lesson 6 Teacher Toolbox:

• Lesson 6-Multiplication and Division in Word Problems

o Slides o Formative Assessment

Lesson 6 Quiz Other Resources: August Flipchart Formative Assessment: Multiplicative Comparison Formative Assessments

Skill: Solve multiplicative comparison word problems involving measurement using a two-column table

Pacing: 2 days

Success Criteria: • I can convert measurements from a larger unit to a smaller unit

(minutes to seconds, yards to inches, etc.) • I can create a two-column table to show my measurement

conversions.

Resources: FSA Reference Sheet Other Resources: August Flipchart Formative Assessment: Multiplicative Comparison Formative Assessments

Skill: Solve multiplicative comparison word problems by the applying area and perimeter formulas

Pacing: 3 days

Success Criteria: • When given the area of a rectangle and the amount of times greater

one side is than the other, I can determine the missing side lengths.

Resources: FSA Reference Sheet Other Resources: August Flipchart

4th Grade Unit 1

**Include problems using “times as many”, “double”, and “half”

• When given a problem involving area or perimeter, I can draw a picture to represent the problem, label the dimensions, and write the equation to solve for the unknown.

Formative Assessment: Multiplicative Comparison Formative Assessments

Skill: Factors, Multiples, and Prime and Composite

Pacing: 2 days

Success Criteria: • I can create arrays to find all the factor pairs of a given whole

number. • I can identify whether a number is prime or composite. • I can explain the difference between a prime number and a

composite number. • I can describe a process to finding factor pairs. • I can show and explain the difference between a factor and a

multiple. • I can explain the relationship between skip counting and finding

multiples.

Resources: Ready MAFS Teacher Resource Book • Lesson 7

Teacher Toolbox: • Lesson 7-Multiples and Factors

o Slides o Formative Assessment-

Lesson 7 Quiz Other Resources: Factors and Multiples Flipchart Videos: Multiplication Factors Open Middle: Rectangles: Maximizing Area Open Middle: Rectangles: Maximizing Perimeter Esti-Mysteries: “Not Carrot Sticks” “String Beads” “Triangular Prisms” “Advanced Bingo” Printouts: Number Puzzles

Optional Review:

Pacing:

As needed

Success Criteria:

• Select aligned criteria from above for review lesson.

Resources: Teacher Toolbox

• Unit 2: Math in Action: Multiplication in Word Problem

4th Grade Unit 1

Unpacking the Standard: Geometry Vocabulary MAFS.4.G.1.1: DOK 1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Notes: → The focus for Measurement and

Geometry within this unit is reviewing 3rd grade vocabulary and introducing new vocabulary words through exploration.

Prerequisite Skill: Geometry Vocabulary Skill: 3rd Grade Review: Understand Properties of Shapes

Pacing: 2 days

Success Criteria: • Identify two-dimensional shapes and their attributes. • Draw two-dimensional shapes, given attributes. • Compare and contrast attributes of two-dimensional shapes. • Categorize two-dimensional shapes according to attributes. • Identify and draw two-dimensional shapes that do not

belong to a given category.

Resources: Teacher Toolbox:

• Grade 3 -Lesson 31 Understand Properties of Shapes pp. 338-339

Formative Assessment: “Reflect” question p. 339 OR Which Two Shapes Are Most Alike and Why?

4th Grade Unit 1

Instructional Skill Sequence: Geometry Vocabulary

Skill: Points, Lines, Line Segments, Rays, and Angles

Pacing: 1 day

Success Criteria:

• I can explain what the terms point, line, line segment, ray, and angles mean.

Resources: Ready MAFS Teacher Resource Book

• Lesson 31 Teacher Toolbox:

• Lesson 31-Points, Lines, Rays, and Angles

o Slides 8– 14 o Formative Assessment: “Try

It” questions on slide 14 or p. 341

Play Geometry “Simon Says” Other Resources:

• Geometry Flipchart • Same, But Different Image: Ray,

Angle, Line Segment • WODB Image Points, Lines, Segments • Angles on the Geoboards • Right Triangles on the Geoboard • What’s The Point

Skill: Perpendicular and Parallel Lines

Pacing: 1 day

Success Criteria:

• I can identify the number of line segments, parallel lines, perpendicular lines, and types of angles when given shapes.

• I can describe how polygons are created using terms like line segments, parallel and perpendicular lines, acute, obtuse and right angles.

Resources: Ready MAFS Teacher Resource Book pp. 344-345 Teacher Toolbox:

• Lesson 31-Points, Lines, Rays, and Angles

o Slides 22– 28 • Formative Assessment: “Try It” p.

345 or slide 28

4th Grade Unit 1

Other Resources: Geometry Flipchart • Same, But Different Image: Parallel vs

Perpendicular • Same, But Different Image: 2

Quadrilaterals • Same, But Different Image: Two Polygons

Skill: Identify Points, Lines, Rays, and Angles

Pacing: 1 day

Success Criteria:

• I can draw given shapes using a ruler when given information such as number of line segments, parallel lines, perpendicular lines, or type of angles. (obtuse, right, or acute)

• I can describe how polygons are created using terms like line segments, parallel and perpendicular lines, acute, obtuse and right angles.

Resources: Ready MAFS Teacher Resource Book

• Lesson 31: pp. 342-343 Teacher Toolbox:

• Lesson 31-Points, Lines, Rays, and Angles

o Slides 15– 21 o Formative Assessment: “Try

It” p. 343 or slide 21 Activity: Use pipe cleaners, paper, tape, or glue to represent different angles. Other Resources:

• Geometry Flipchart • Alphabet Lines • Same,But Different Image: Acute vs

Right • Same, But Different Image: Obtuse

vs Right • WODB Image Shapes • Which Two Angles are Most Alike

& Why?

Formative Assessment Check: Teacher Toolbox Lesson 31 Quiz

Grade 4 Unit 1 Assessment