Created on:

July, 2015

Created by:

Elena Servedio, Brick; Arthur Epstein, Central

Revised on:

Revised by:

OCEAN COUNTY

MATHEMATICS

CURRICULUM

Content Area: Mathematics

Course Title: Grade 7 Mathematics

Grade Level: 7

The Number System

6 weeks

Expressions and Equations

4-5 weeks

Ratios and Proportions

5-6 weeks

Statistics and Probability

6-7 weeks

Geometry

7 weeks

The following Standards for Mathematical Practice and select Common Core Content Standards should be covered throughout the various units of the curriculum.

Standards for Mathematical Practices

MP.1

Make sense of problems and persevere in solving them.

Find meaning in problems

Look for entry points

Analyze, conjecture and plan solution pathways

Monitor and adjust

Verify answers

Ask themselves the question: Does this make sense?

MP.2

Reason abstractly and quantitatively.

Make sense of quantities and their relationships in problems

Learn to contextualize and decontextualize

Create coherent representations of problems

MP.3

Construct viable arguments and critique the reasoning of others.

Understand and use information to construct arguments

Make and explore the truth of conjectures

Recognize and use counterexamples

Justify conclusions and respond to arguments of others

MP.4

Model with Mathematics.

Apply mathematics to problems in everyday life

Make assumptions and approximations

Identify quantities in a practical situation

Interpret results in the context of the situation and reflect on whether the results make sense

MP.5

Use appropriate tools strategically.

Consider the available tools when solving problems

Are familiar with tools appropriate for their grade or course (pencil and paper, concrete models, ruler, protractor, calculator, spreadsheet, computer programs, digital content located on a website, and other technological tools)

Make sound decisions of which of these tools might be helpful

MP.6

Attend to precision.

Communicate precisely to others

Use clear definitions, state the meaning of symbols and are careful about specifying units of measure and labeling axes

Calculate accurately and efficiently

MP.7

Look for and make use of structure.

Discern patterns and structures

Can step back for an overview and shift perspective

See complicated things as single objects or as being composed of several objects

MP.8

Look for and express regularity in repeated reasoning.

Notice if calculations are repeated and look both for general methods and shortcuts

In solving problems, maintain oversight of the process while attending to detail

Evaluate the reasonableness of their immediate results

OCEAN COUNTY MATHEMATICS CURRICULUM

Unit Overview

Content Area: Mathematics

Domain: The Number System

Cluster: Operations with Rational Numbers

Cluster Summary: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Primary interdisciplinary connections: Infused within the unit are connections to the NJCCS for Mathematics, Language Arts Literacy and Technology.

21st century themes: Through instruction in life and career skills, all students acquire the knowledge and skills needed to prepare for life as citizens and workers in the 21st century. For further clarification see NJ World Class Standards at www.NJ.gov/education/aps/cccs/career/

Learning Targets

Content Statements

Number

Common Core Standard for Mastery

7.NS.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.1.a

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

7.NS.1.b

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.1.c

Understand subtraction of rational numbers as adding the additive inverse, p - q = p+ (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7.NS.1.d

Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.2.a

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.2.b

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2.c

Apply properties of operations as strategies to multiply and divide rational numbers

7.NS.2.d

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Number

Common Core Standard for Introduction

8.NS.1

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Unit Essential Questions

What are rational numbers?

How are fractions and decimals related?

How can the additive inverse be applied to solve problems involving rational numbers?

How can numbers be used to describe concepts such as sea level, losing yardage in a football game, or temperatures that drop below 0?

How can you determine if the sums, differences, products, and quotients of rational numbers are either positive or negative?

How can properties of rational numbers be applied to perform operations?

Unit Enduring Understandings

Students will understand that

Apply mathematical operations with rational numbers to real-world contexts.

Explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers.

Unit Objectives

Students will know

How to apply operations with rational numbers.

How to compare and order rational numbers.

The concept of absolute value and its application to integers.

How to use and justify the rules for adding, subtracting, multiplying, and dividing integers.

Unit Objectives

Students will be able to

Graph rational numbers by using a horizontal or vertical number line diagram.

Use a horizontal or vertical number line diagram to represent addition and subtraction.

Write fractions as terminating or repeating decimals.

Write decimals as fractions.

Compare and order rational numbers.

Add and subtract fractions with like and unlike denominators.

Add and subtract mixed numbers.

Multiply and divide fractions and mixed numbers.

Read and write integers, and find the absolute value of an integer.

Add and subtract integers.

Use commutative, associative, identity, and distributive properties to solve problems.

OCEAN COUNTY MATHEMATICS CURRICULUM

Evidence of Learning

Formative Assessments may include:

Observation

Homework

Class participation

Whiteboards/communicators

Do-Now

Notebook

Writing prompts

Exit passes

Technology/Manipulatives

Oral Assessments

Daily Classwork

Summative Assessments may include:

Chapter/Unit Test

Quizzes

Presentations

Unit Projects

National/State/District Wide Assessments

Modifications (ELLs, Special Education, Gifted and Talented)

Teacher tutoring

Peer tutoring

Cooperative learning groups

Modified assignments

Differentiated instruction

Native language texts and native language to English dictionary

Follow all IEP modifications/504 plans

Curriculum Development