Grade: 6th to 8th Subject: Math

RigorousCurriculumDesignShowcase

Summary of the CCSS Standards6th and 7th Grade

The Common Core State Standards define the rigorous skills and knowledge in English Language Arts (ELA) and Mathematics that students need to succeed in college and workforce training programs.

• Expressions and Equations– Apply and extend previous understandings of arithmetic to algebraic

expressions

– Reason about and solve one-variable equations and inequalities.

– Represent and analyze quantitative relationships between dependent and independent variables.

– Use properties of operations to generate equivalent expressions.

– Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• Ratios and Proportional Relationships– Understand ratio concepts and use ratio reasoning to solve problems.

– Analyze proportional relationships and use them to solve real-world and mathematical problems.

Summary of the CCSS Standards6th and 7th Grade

The Common Core State Standards define the rigorous skills and knowledge in English Language Arts (ELA) and Mathematics that students need to succeed in college and workforce training programs.

• The Number System– Apply and extend previous understandings of multiplication and

division to divide fractions by fractions and to operations involving rational numbers.

– Analyze proportional relationships and use them to solve real-world and mathematical problems.

– Multiply and divide multi-digit numbers and find common factors and multiples.

Summary of the CCSS Standards6th and 7th Grade

The Common Core State Standards define the rigorous skills and knowledge in English Language Arts (ELA) and Mathematics that students need to succeed in college and workforce training programs.

• Geometry– Solve real-world and mathematical problems involving area, surface

area, volume, and angle measurements

– Draw, construct and describe geometrical figures and describe the relationships between them.

• Statistics and Probability– Develop understanding of statistical variability.

– Summarize and describe distributions.

– Use random sampling to draw inferences about a population and draw informal comparative inferences about two populations.

– Investigate chance processes and develop, use, and evaluate probability models.

• The Number System– Know that there are numbers that are not rational, and approximate

them by rational numbers.

Summary of the CCSS Standards8th Grade

The Common Core State Standards define the rigorous skills and knowledge in English Language Arts (ELA) and Mathematics that students need to succeed in college and workforce training programs.

• Expressions and Equations– Work with radicals and integer exponents.

– Understand the connections between proportional relationships, lines, and linear equations.

– Analyze and solve linear equations and pairs of simultaneous linear equations.

• Functions– Define, evaluate, and compare functions.

– Use functions to model relationships between quantities.

Summary of the CCSS Standards8th Grade

The Common Core State Standards define the rigorous skills and knowledge in English Language Arts (ELA) and Mathematics that students need to succeed in college and workforce training programs.

• Geometry– Understand congruence and similarity using physical models,

transparencies, or geometry software.

– Understand and apply the Pythagorean Theorem.

– Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

• Unit One – Rational Numbers

This unit combines the skill of dividing fractions with graphing skills both on a number line and on a coordinate grid in a meaningful way for the students.

Unit Overviews – 6th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit Two – Ratios and Proportions

Students use reasoning about multiplication and division to solve ratio and rate problems. By viewing equivalent ratios and rates, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems they can use multiplication and division to solve, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.

• Unit Three – Evaluating Expressions

Students understand the use of variables in mathematical expressions. They will write, use, solve and evaluate expressions that correspond to given situations. Students will understand that expressions in different forms can be equivalent and use the properties of operations to rewrite expressions in equivalent forms.

Unit Overviews – 6th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit Four – Solving Equations and Inequalities

Students write equations that correspond to given situations and use formulas to solve problems. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations and inequalities.

Unit Overviews – 7th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit One – Operations with Rational Numbers

Students develop a unified understanding of numbers, recognizing fractions, decimals (finite or repeating), and percent as different representations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationship between addition and subtraction and multiplication and division.

• Unit Two – Percent Problems

Students extend their learning of ratios and develop understanding of proportionality to solve single-and multi-step problems. Students use their understanding if ratios and proportionality to solve a wide variety of percent problems.

Unit Overviews – 7th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit Three – Expressions, Equations, and Inequalities

Students use the arithmetic of rational numbers to formulate, use, and solve expressions and equations with one variable.

• Unit Four – Functions and Proportionality

Students extend their understanding of ratios and develop understanding of proportionality to solve single or multi-step problems and to solve a wide variety of percent problems (discounts, interest, taxes, and percent increase or decrease). Students solve problems about scale drawings by relating corresponding lengths between objects or by using the fact that relationships of lengths within objects are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of steepness of the related line, called the slope, They distinguish proportional relationships from other relationships.

Unit Overviews – 8th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit One – Geometry

Analyze two- and three- dimensional space and figures using distance, angle, similarity, and congruence.

• Unit Two– Exponents, Roots, and Pythagorean Theorem

Students understand the statement of the Pythagorean Theorem and its converse and can explain why the Pythagorean Theorem holds, for example, by decomposing a square two different ways. They apply the Pythagorean Theorem to find distances between points on a coordinate plane.

Unit Overviews – 8th Grade

Big Ideas: The three or four main ideas, conclusions, or generalizations that teachers want their students to discover and state in their own words by the end of the unit. These are concepts students should remember long after instruction ends.

• Unit Three – Solve Equations

Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use properties of equality and the concept of logical equivalence they maintain the solutions of the original equation.• Unit Four– Functions

Students grasp the concept of a function as a rule that assigns to each input exactly an output. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in different representations

7th Grade Example

Video Instructions1)Brief introduction on topic and why you are creating the video2) Define positive and negative integers on a number line3) Define opposites and additive inverses4) State the rule for adding and subtracting integers when the signs are the same and show at least three examples 5) State the rule for adding and subtracting integers when the signs are not the same and show at least three different examples 6) Explain how to solve problems of the form -7-(-12), giving two more examples7) State the rule for multiplying and dividing integers when the signs are the same and show at least three examples 8) State the rule for multiplying and dividing integers when the signs are not the same and show at least three examples

Authentic Performance Tasks (APTs)

An APT is a performance assessment that involves a real-world context, where the tasks are either replicas of or similar to the kinds of problems faced by adults, consumers, and professionals in the field.

7th Grade

Your friend has not been at school for the past few days due to a terrible cold. You, being a great friend, don’t want them to fall behind. You have decided to create a video presentation on negative integer rules that your friend can watch before they come back to school.You will create a 5 minute video using the Educreation application on the web illustrating the number line, opposites, and additive inverses. The video will show the negative integer rules for adding, subtracting, multiplying, and dividing integers with multiple examples for your friend to see how you applied the rules. Make sure you point out some common mistakes that people make when doing these problems.

Engaging Scenario - Example

The Engaging Scenario is an interesting and compelling hypothetical situation provided to students at the start of each unit. It is designed to capture students’ imaginations and help them to buy into the lesson ahead.

Scoring Guides – Example 7th

A scoring guide is a written list of specific criteria describing different levels of student proficiency on astandards‐based assessment task.

Scoring Guide Task 1Advanced Proficient Progressing Beginning

Meets all of the "Proficient" criteria plus:

Correctly shows some common mistakes that students can make and how to avoid them

Brief introduction on topic and why you are creating the video (or visual aide)

Defines positive and negative integers on a number line

Defines opposites and additive inverses

States the rule for adding and subtracting integers when the signs are the same and show at least three examples

States the rule for adding and subtracting integers when the signs are not the same and show at least three different examples

Explains how to solve problems of the form -7-(-12), giving two more examples

States the rule for multiplying and dividing integers when the signs are the same and show at least three examples

States the rule for multiplying and dividing integers when the signs are not the same and show at least three examples

Meets __6-7__of the "Proficient" criteria

Meets fewer than__6__ of the "Proficient" criteria