Developed by

# Carrie E. Johnson

Understanding by Design

Unit Design Worksheet

Unit Title: Developing an Understanding of Operations & Rational

Numbers

Topic: Operations and Rational Numbers Grade: 6 th

Stage 1 - Desired Results

Subject/Course: Mathematics

Staff Name: Carrie Johnson

Established Goals:

1.

6. NS. 2 Fluently divide multi-digit numbers using the standard algorithm.

2.

6. NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation

3.

6. NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a.

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. b.

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c.

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

4.

6. NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Understandings:

Students will understand

Essential Questions:

1.

how to use a standard algorithm in order to divide multi-digit numbers

2.

how to add, subtract, multiply, and divide multidigit decimals.

3.

how to extend a number lines and coordinates axes to represent points on a number line and a coordinate plane using negative number coordinates. a.

how to recognize and indicate numbers and its opposite located on opposite sides of zero on a number line. b.

how to indicate ordered pairs in their correct

1

1.

What is the standard algorithm for dividing multi-digit numbers?

1. When will I use division in the real world?

2.

Why do we need to know how to add, subtract, multiply, and divide decimals?

3.

How do I graph positive and negative numbers on a number line and coordinate grid? a.

What does a negative number represent, and what is the opposite of the negative number? b.

How do I find an ordered pair on a grid and its opposite/reflected pair?

quadrants on a coordinate plan. Students will also understand the reflections of points across one or both axes are different only by their signs. c.

how to position integers and rational numbers on a horizontal or vertical number line.

Students will also be able to plot pair of integers and rational numbers on a coordinate plane.

4.

how to find the greatest common factor of two whole numbers and find the least common multiple of two whole numbers. Students will also understand how to use the distributive property to express a sum of two whole numbers. c.

How will positioning numbers on a horizontal and vertical number lines and coordinate grids help me in the real world?

4.

How can I express a sum of two numbers by using common factors as a multiple of a sum of two whole numbers?

Students will know

1.

how to use a standard algorithm in order to divide multi-digit numbers

2.

how to add, subtract, multiply, and divide multidigit decimals.

3.

how to extend a number lines and coordinates axes to represent points on a number line and a coordinate plane using negative number coordinates. a.

how to recognize and indicate numbers and its opposite located on opposite sides of zero on a number line. b.

how to indicate ordered pairs in their correct quadrants on a coordinate plane.

Students will also understand the reflections of points across one or both axes are different only by their signs. c.

how to position integers and rational numbers on a horizontal or vertical number line. Students will also be able to plot pairs of integers and rational numbers on a coordinate plane.

4.

how to find the greatest common factor of two whole numbers and find the least common multiple of two whole numbers.

Students will also understand how to use the distributive property to express a sum of two whole numbers.

Students will be able to

1.

explain how to divide multi-digit numbers

2.

explain how to add, subtract, multiply, and divide multi-digit decimals

3.

demonstrate how to extend a number line and coordinate axes to represent points on a number line/coordinate plane using negative numbers. a.

identify numbers and the opposite on both sides of zero on a number line b.

identify ordered pairs ordered pairs and their opposites in the correct quadrants on a coordinate plane. c.

describe how to plot pairs of integers and rational numbers on a coordinate plane.

4.

explain how to find the greatest common factor and least common multiple of two whole numbers.

4.

describe how to use the distributive property to express a sum of two whole numbers.

2

Unit Enduring Understanding:

Students will understand that there are rules to mathematical procedures and how to apply them.

Unit Question:

How do you use mathematical operations by using decimals and negative numbers and plotting points on a coordinate grid?

Stage 2 - Assessment Evidence

Goal: The student’s task is to solve mathematical operations involving rational numbers and plotting the numbers on a coordinate grid (students will be given two operations to solve for each point). As they plot each plot they connect it to the previous point. When they are finished plotting the points it will make a picture. Students will present their picture to the teacher and students.

Role: Investigator

Audience: Teacher and Students

Situation: Students want to discover the hidden picture. In order to discover the picture the students have to solve mathematical operations involving rational numbers and plotting points on coordinate grids. Students have to connect the points as they go. When they have completed, they will have discovered a picture. They will color their finished product.

Product: A discovered picture they found by solving mathematical operations and plotting the points on a coordinate grid.

Standards and Criteria for Success: Students will be graded on their ability to solve mathematical operations involving rational numbers. Students will also be graded on their ability to plot the points on a coordinate grid and connecting them point by point. Finally, students will be graded on their ability to discover a picture from the points they plotted and neatly coloring it.

Key Criteria:

CATEGORY 4

Operations 90% - 100% of the mathematics operations are correct.

Coordinate

Grid

90% - 100% of the points plotted are correct.

Illustrations The plotted points make a detailed picture and it is colored.

3

70% - 89% of the mathematics operations are correct.

70% - 89% of points plotted are correct.

Most of the plotted points make a picture and is partially colored.

2

50% - 69% of the mathematics operations are correct

50% - 69% of points plotted are correct

Some of the plotted points make a picture and is partially colored.

The points plotted do not illustrate a picture and is not colored.

1

Operations are not correct.

Points plotted are not correct.

3

Other Evidence:

BEFORE

Pretest: teacher created

KWL

Bellwork Questions

Questioning: To get a quick grasp of where students are at.

DURING

Think/Pair/Share: To see where students are struggling

Observation

Daily Assignments: teacher created and book items

MBWA (Manage By Walking

Around)

Entrance/Exit Slips: to see what students have retained from previous day or what they learned after a lesson

Drawings: Vertical and Horizontal

Number Lines, Coordinate Grids

AFTER

Entrance/Exit Slips: to see what students have retained from previous day or what they learned after a lesson

Observation

Quiz: teacher created

Test: teacher created

Describe the assessment/s and state the prompt if applicable.  F  S

What type of scoring tools will be used for evaluation?

 Analytic rubric  Checklist

 Holistic rubric  Answer Key

 Criterion rubric  Other

Student Self-Assessment and Reflection:

Each student will write about what they knew at the beginning of the unit and what they know now. The students will reflect on the real-world application and tell how it helped them to understand operations and rational numbers.

Stage 3 - Learning Plan

Differentiated Instruction:

LAYER C: (50 points)

1.

Vocabulary Journal of key terms from the Operations and Rational Numbers Unit * (15 points) a.

CHOICE 1: Write definitions of key terms in Vocabulary Journal b.

CHOICE 2: Draw a picture to represent key terms in Vocabulary Journal c.

CHOICE 3: Type definitions of key terms on a mini laptop (Electronic Vocabulary Journal)

2.

Notebook of daily assignments (Checklist will be used to grade notebooks)* (20 points)

4

Stage 3 - Learning Plan

3.

Bellwork Log from “Before Activities” * (15 points)

LAYER B: (50 Points)

(Students need to pick one activity from each of the following groups: 1, 2, or 3; 4, 5, or 6; 7 or 8; 9, 10, or 11;

12 or 13)

1.

Complete a 10 problem worksheet on dividing multi-digit numbers (10 points)

2.

On a poster write the algorithm and show an example of how to divide multi-digit numbers (10 points)

3.

(10 points)

4.

Complete a 10 problem worksheet on adding, subtracting, multiply, and dividing multi-digit decimals

(10 points)

5.

On a poster write the algorithm and show an example of how to add, subtract, multiply, and divide multi-digit numbers (10 points)

6.

Play “Adding and Subtracting Multi-Digit Decimals” & “Multiplying and Dividing Multi-Digit Numbers” http://www.ixl.com/math/grade-6 (10 points)

7.

Complete a 10 problem worksheet on plotting points on a 4-quadrant plane. (10 points)

8.

Play “Coordinate Graphs as Maps” http://www.ixl.com/math/grade-6/coordinate-graphs-as-maps (10 points)

9.

Complete a 10 problem worksheet on finding the Greatest Common Factor and Least Common

Multiple of two whole numbers. (10 points)

10.

On a poster write about what the Greatest Common Factor and Least Common Multiple is, and show at least 3 examples of each showing how you found what the Greatest Common Factor and Least

Common Multiple is of two whole numbers. (10 points)

11.

Play “Greatest Common Factor” and “Least Common Multiple” http://www.ixl.com/math/grade-

12.

Complete a 10 problem worksheet on using the distributive property to express two whole numbers.

(10 points)

13.

Play “Distributive Property” http://www.ixl.com/math/grade-6/distributive-property (10 points)

LAYER A: (70 Points)

(Students must do 1 & 2 and have a choice between 3 and 4)

1.

Hidden Picture (GRASP)* – Finding the hidden picture solving mathematical operations and graphing points on a coordinate plane (40 points)

2.

Unit Test* (20 points)

3.

Reflect Daily in Math Notebook (10 points)

4.

Complete KWL Chart on Operations and Rational Numbers (10 points)

*denotes Mandatory Activities

5

Stage 3 - Learning Plan

Learning Activities:

W: Where are we going? To a deeper understanding of operations and rational numbers

Why? Because it allows students to apply their knowledge of operations and rational numbers to real world problems.

What is expected? Go over rubric and course overview.

H: I will hook student interest by becoming a “Discoverer” by solving simple mathematical operations to decode a phrase. I will tell the class, “Throughout this unit you will be taking on the role of the

‘discoverer,’ except from this point forward your tasks will become more challenging. It will be your job at the end of the unit to ‘Discover the Hidden Picture.’”

E: Students will be equipped to do well on this unit through journaling, a variety of lessons and assignments (written, artistic, & web-based), class discussions, and the “Hidden Picture” activity.

R: Students will be asked to rethink and revise their work through their K-W-L charts at different times during the unit to rethink the use and understanding of operations and rational numbers. Students will also have an opportunity to share their thinking during class discussions.

E: Students will self-evaluate through daily entrance and exit slips and through the, “End of the Unit

Reflection.”

T: Learning will be tailored by using the differentiated instruction above.

O: The unit will be organized so that key concepts build upon one another. See calendar below for day-byday schedule.

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Essential Vocabulary

Add: to find the sum of two or more numbers

Algorithm: Steps to solving a problem

Axes: a central line that bisects a two-dimensional body or figure.

Coordinate Axis: one of the fixed reference lines of a coordinate system.

Coordinate Plane: a plane containing two perpendicular axes (x and y) intersecting at a point called the origin

(0,0).

Coordinates: Shown as a pair of letters or numbers. Example (2,4)

Diagram: a graph, map, or plane

Distributive Property: a product can be written as, the sum of, or difference between, two products.

Divide: sharing or grouping a number into equal parts.

Factor: a whole number that divides exactly into another number or a whole number that multiplies with another number to make a third number.

Fluent: spoken or written fluently

Greatest Common Factor: The largest/biggest number that will divide two or more other numbers exactly

Horizontal Number Line: a number line that is parallel to the horizon. (Left to Right)

Integers: a positive number, a negative number or zero. NOT: a fraction or a decimal

Least Common Multiple: the smallest number that is the multiple of two or more other numbers.

Multi-Digit: a number that has two or more numbers.

Multiply: a mathematical operation where a number is added to itself a number of times.

Negative Number: a number less than zero.

Number Line: line marked with numbers, used to show operations.

Operation: there are four basic operations in arithmetic used to solve problems. They are Addition,

Subtraction, Multiplication, and Division.

Opposite Numbers: Two numbers that have the same numeral but have opposite signs.

Ordered Pairs: a pair of numbers where order is important. It is often used to indicate a point on a coordinate plane, graph, or map. Example: (4,6) is different to (6,4)

Plane: A flat surface

Quadrants: any quarter of a plane divided by an x and y axis.

Rational Numbers: A real number that can be written as: a ratio of two integers (fraction), excluding zero as a denominator, a repeating or terminating decimal, or an integer.

Reflection: a mirror view

Subtract: to take one quantity away from another

Sum: the total or whole amount. It is the result of adding

7

Vertical Number Line: a number line that goes from top to bottom. It makes a right angle with the horizon.

Whole Numbers: a counting number from zero to infinity

Monday

Pretest

Monday

Subtracting Decimals

Think/Pair/Share

LEVEL C Activities

LEVEL B Activities

Exit Slip

Monday

Plotting Points on a

Think/Pair/Share

LEVEL C Activities

LEVEL B Activities

Exit Slip

Monday

Distributive Property

Entrance Slip

Think/Pair/Share

LEVEL C Activities

LEVEL B Activities

Tuesday

Hook: “Discoverer”

Begin K-W-L

Class Discussion

Sequencing the Learning

Wednesday

Dividing Multi-Digit

Numbers

LEVEL C Activities

LEVEL B Activities

Exit Slip

Thursday

Dividing Multi-Digit

Numbers

Entrance Slip

LEVEL C Activities

LEVEL B Activities

Tuesday

Multiplying and

Dividing Decimals

K-W-L

LEVEL C Activities

Tuesday

Plotting Points on a

Entrance Slip

LEVEL C Activities

LEVEL B Activities

Tuesday

“Hidden Picture”

Level A

GRASP Activity

Wednesday

Multiplying and

Dividing Decimals

Entrance Slip

LEVEL C Activities

LEVEL B Activities

Wednesday

Greatest Common

Factor & Least

Common Multiple

K-W-L

LEVEL C Activities

Wednesday

“Hidden Picture”

Level A

GRASP Activity

Thursday

QUIZ:

Math Check-Up

Thursday

Greatest Common

Factor & Least

Common Multiple

Entrance Slip

LEVEL C Activities

LEVEL B Activities

Thursday

Unit Test Review

Finish K-W-L

Friday

Subtracting

Decimals

K-W-L

LEVEL C Activities

Friday

Plotting Points on a

K-W-L

LEVEL C Activities

Friday

Distributive

Property

K-W-L

LEVEL C Activities

LEVEL B Activities

Exit Slip

Friday

Unit Test

Post-Unit

Reflection

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