Rigorous
Curriculum
Design
Showcase
Grade: 6th to 8th
Subject: Math
Summary of the CCSS Standards
6th and 7th Grade
• 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.
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.
Summary of the CCSS Standards
6th and 7th Grade
• 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.
• 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.
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.
Summary of the CCSS Standards
6th and 7th Grade
• 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 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.
Summary of the CCSS Standards
8th Grade
• The Number System
– Know that there are numbers that are not rational, and approximate them
by rational numbers.
• 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.
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.
Summary of the CCSS Standards
8th Grade
• Functions
– Define, evaluate, and compare functions.
– Use functions to model relationships between quantities.
• 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.
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.
Unit Overviews – 6th Grade
• 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 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.
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 Overviews – 6th Grade
• 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 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.
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 Overviews – 7th Grade
• 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.
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 Overviews – 7th Grade
• 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.
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 Overviews – 8th Grade
• 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.
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 Overviews – 8th Grade
• 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
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.
Authentic Performance Tasks (APTs)
7th Grade Example
Video Instructions
1)Brief introduction on topic and why you are creating the video
2) Define positive and negative integers on a number line
3) Define opposites and additive inverses
4) 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
examples
7) 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
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.
Engaging Scenario - Example
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.
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
Scoring Guide Task 1
Advanced
 Meets all of the
"Proficient" criteria
plus:
 Correctly shows some
common mistakes that
students can make
and how to avoid
them

Proficient
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
Progressing
Beginning
 Meets __6-7__of the  Meets fewer
"Proficient" criteria
than__6__ of the
"Proficient" criteria
A scoring guide is a written list of specific criteria describing different levels of student proficiency on a
standards‐based assessment task.