Interactive Problem Bank

  • Fraction Circle Manipulative
    Fraction Circles
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Grade 3Grade 4Grade 5Grade 6
  • 6.NS.1
  • 6.NS.5
  • 6.NS.6a
  • 6.NS.6b
  • 6.NS.6c
  • 6.NS.7a
  • 6.NS.7b
  • 6.NS.7c
  • 6.RP.1
  • 6.RP.2
  • 6.RP.3a
  • 6.RP.3b
Grade 7
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Grade 6 - 6.NS - The Number System

6.NS.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Division with Fractions in Context

6.NS.1 practice problems division with fractions in context
Number line digital manipulative indicator
6.NS.1 practice problems division with fractions in context
Number line digital manipulative indicator

Dividing Fractions by Whole Numbers in Context

6.NS.1 practice problems dividing fractions by whole numbers in context
Fraction circle digital manipulative indicator

Dividing Non-unit Fractions with Common Denominators

6.NS.1 practice problems dividing non-unit fractions with common denominators
Fraction bar digital manipulative indicator
6.NS.1 practice problems dividing non-unit fractions with common denominators
Fraction bar digital manipulative indicator

Division as Repeated Adding Up or Subtracting Down

6.NS.1 practice problems division as repeated adding up or subtracting down
Number line digital manipulative indicator
6.NS.1 practice problems division as repeated adding up or subtracting down

Dividing Non-unit Fractions with Uncommon Denominators

6.NS.1 practice problems dividing non-unit fractions with uncommon denominators
Fraction bar digital manipulative indicator
6.NS.1 practice problems dividing non-unit fractions with uncommon denominators
Number line digital manipulative indicator

Dividing Mixed Numbers and Proper Fractions

6.NS.1 practice problems dividing mixed numbers and proper fractions
Fraction bar digital manipulative indicator
6.NS.1 practice problems dividing mixed numbers and proper fractions
Fraction bar digital manipulative indicator

Division Involving Mixed Numbers on a Number Line

6.NS.1 practice problems division involving mixed numbers on a number line
Number line digital manipulative indicator
6.NS.1 practice problems division involving mixed numbers on a number line
Number line digital manipulative indicator

Division of a Mixed Number by a Fraction Using Models

6.NS.1 practice problems division of a mixed number by a fraction using models

Mixed Number Quotients Using Bars

6.NS.1 practice problems mixed number quotients using bars
Fraction bar digital manipulative indicator
6.NS.1 practice problems mixed number quotients using bars
Fraction bar digital manipulative indicator

Repartitioning Number Line for Division

6.NS.1 practice problems repartitioning number line for division
Number line digital manipulative indicator
6.NS.1 practice problems repartitioning number line for division
Number line digital manipulative indicator

Dividing Mixed Numbers and Non-unit Fractions with Remainders

6.NS.1 practice problems dividing mixed numbers and non-unit fractions with remainders
Fraction bar digital manipulative indicator
6.NS.1 practice problems dividing mixed numbers and non-unit fractions with remainders
Fraction bar digital manipulative indicator

Conceptualizing Quotients Less Than 1

6.NS.1 practice problems conceptualizing quotients less than 1
Number line digital manipulative indicator

Finding the Whole We Started With

6.NS.1 practice problems finding the whole we started with
Number line digital manipulative indicator
6.NS.1 practice problems finding the whole we started with
Number line digital manipulative indicator

Mixed Numbers Divided by Whole Numbers

6.NS.1 practice problems mixed numbers divided by whole numbers
6.NS.1 practice problems mixed numbers divided by whole numbers
Number line digital manipulative indicator

6.NS.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Temperatures Above & Below Zero

6.NS.5 practice problems temperatures above & below zero
6.NS.5 practice problems temperatures above & below zero

Modeling Temperatures

6.NS.5 practice problems modeling temperatures
6.NS.5 practice problems modeling temperatures

6.NS.6a

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

Exploring Opposites

6.NS.6a practice problems exploring opposites
Number line digital manipulative indicator
6.NS.6a practice problems exploring opposites
Number line digital manipulative indicator

Identifying Opposites

6.NS.6a practice problems identifying opposites
Number line digital manipulative indicator
6.NS.6a practice problems identifying opposites
Number line digital manipulative indicator

Labeling Opposites

6.NS.6a practice problems labeling opposites
Number line digital manipulative indicator
6.NS.6a practice problems labeling opposites
Number line digital manipulative indicator

6.NS.6b

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.

Exploring the Coordinate Plane

6.NS.6b practice problems exploring the coordinate plane
6.NS.6b practice problems exploring the coordinate plane

Naming Points on Coordinate Plane

6.NS.6b practice problems naming points on coordinate plane
6.NS.6b practice problems naming points on coordinate plane

6.NS.6c

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.

Identifying Integers

6.NS.6c practice problems identifying integers
Number line digital manipulative indicator
6.NS.6c practice problems identifying integers
Number line digital manipulative indicator

Representing Positive and Negative Rational Numbers

6.NS.6c practice problems representing positive and negative rational numbers
Number line digital manipulative indicator
6.NS.6c practice problems representing positive and negative rational numbers
Number line digital manipulative indicator

Locating Rational Numbers

6.NS.6c practice problems locating rational numbers
Number line digital manipulative indicator
6.NS.6c practice problems locating rational numbers
Number line digital manipulative indicator

Navigating Number Lines and Coordinate Planes

6.NS.6c practice problems navigating number lines and coordinate planes
Number line digital manipulative indicator
6.NS.6c practice problems navigating number lines and coordinate planes

Finding Distances

6.NS.6c practice problems finding distances
Number line digital manipulative indicator
6.NS.6c practice problems finding distances

Connecting with Integers

6.NS.6c practice problems connecting with integers
Number line digital manipulative indicator
6.NS.6c practice problems connecting with integers
Number line digital manipulative indicator

6.NS.7a

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

Ordering Integers on a Number Line

6.NS.7a practice problems ordering integers on a number line
Number line digital manipulative indicator
6.NS.7a practice problems ordering integers on a number line
Number line digital manipulative indicator

Exploring Inequality Statements

6.NS.7a practice problems exploring inequality statements
Number line digital manipulative indicator
6.NS.7a practice problems exploring inequality statements
Number line digital manipulative indicator

6.NS.7b

Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.

Estimating on a Vertical Number Line

6.NS.7b practice problems estimating on a vertical number line
Number line digital manipulative indicator
6.NS.7b practice problems estimating on a vertical number line
Number line digital manipulative indicator

Connecting with Inequality Statements

6.NS.7b practice problems connecting with inequality statements
6.NS.7b practice problems connecting with inequality statements

6.NS.7c

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

Modeling Distance on a Number Line

6.NS.7c practice problems modeling distance on a number line
Number line digital manipulative indicator

Finding Distances from Zero

6.NS.7c practice problems finding distances from zero
Number line digital manipulative indicator
6.NS.7c practice problems finding distances from zero
Number line digital manipulative indicator

Understanding Absolute Value as Distance

6.NS.7c practice problems understanding absolute value as distance
Number line digital manipulative indicator
6.NS.7c practice problems understanding absolute value as distance
Number line digital manipulative indicator

Making Sense of Absolute Value Notation

6.NS.7c practice problems making sense of absolute value notation
Number line digital manipulative indicator
6.NS.7c practice problems making sense of absolute value notation
Number line digital manipulative indicator

Absolute Value as a Distance

6.NS.7c practice problems absolute value as a distance
Number line digital manipulative indicator
6.NS.7c practice problems absolute value as a distance
Number line digital manipulative indicator

Finding Differences

6.NS.7c practice problems finding differences
Number line digital manipulative indicator

Absolute Value to Describe Differences

6.NS.7c practice problems absolute value to describe differences
6.NS.7c practice problems absolute value to describe differences

Grade 6 - 6.RP - Ratios and Proportional Relationships

6.RP.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

The Language of Ratios

6.RP.1 practice problems the language of ratios
6.RP.1 practice problems the language of ratios

Ratio as a Mixture

6.RP.1 practice problems ratio as a mixture
6.RP.1 practice problems ratio as a mixture

Modeling Ratios

6.RP.1 practice problems modeling ratios
6.RP.1 practice problems modeling ratios

Naming Mixtures with Ratios

6.RP.1 practice problems naming mixtures with ratios
6.RP.1 practice problems naming mixtures with ratios

Using Tables to Name Ratios

6.RP.1 practice problems using tables to name ratios
6.RP.1 practice problems using tables to name ratios

6.RP.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

Exploring Unit Rates and Equivalent Ratios

6.RP.2 practice problems exploring unit rates and equivalent ratios
6.RP.2 practice problems exploring unit rates and equivalent ratios

Finding Unit Rates

6.RP.2 practice problems finding unit rates
6.RP.2 practice problems finding unit rates

Equal Sharing

6.RP.2 practice problems equal sharing
6.RP.2 practice problems equal sharing

Equal Sharing with Remainders

6.RP.2 practice problems equal sharing with remainders
6.RP.2 practice problems equal sharing with remainders

6.RP.3a

Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Ratio Tables and the Number Line

6.RP.3a practice problems ratio tables and the number line
Number line digital manipulative indicator
6.RP.3a practice problems ratio tables and the number line
Number line digital manipulative indicator
6.RP.3a practice problems ratio tables and the number line
Number line digital manipulative indicator
6.RP.3a practice problems ratio tables and the number line
Number line digital manipulative indicator

Finding Lengths

6.RP.3a practice problems finding lengths
Number line digital manipulative indicator
6.RP.3a practice problems finding lengths
Number line digital manipulative indicator

Scaling Lengths

6.RP.3a practice problems scaling lengths
Number line digital manipulative indicator
6.RP.3a practice problems scaling lengths
Number line digital manipulative indicator
6.RP.3a practice problems scaling lengths
Number line digital manipulative indicator
6.RP.3a practice problems scaling lengths
Number line digital manipulative indicator

Modeling Equivalent Ratios

6.RP.3a practice problems modeling equivalent ratios
6.RP.3a practice problems modeling equivalent ratios
6.RP.3a practice problems modeling equivalent ratios
6.RP.3a practice problems modeling equivalent ratios

Equivalent Ratios on a Number Line

6.RP.3a practice problems equivalent ratios on a number line
Number line digital manipulative indicator
6.RP.3a practice problems equivalent ratios on a number line
Number line digital manipulative indicator

Scaling Along a Number Line

6.RP.3a practice problems scaling along a number line
Number line digital manipulative indicator
6.RP.3a practice problems scaling along a number line
Number line digital manipulative indicator

6.RP.3b

Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Mixing Paint with Unit Rates

6.RP.3b practice problems mixing paint with unit rates
6.RP.3b practice problems mixing paint with unit rates

Modeling Unit Pricing

6.RP.3b practice problems modeling unit pricing
6.RP.3b practice problems modeling unit pricing

Solving Missing Value Problems

6.RP.3b practice problems solving missing value problems
6.RP.3b practice problems solving missing value problems

Comparing Unit Rates

6.RP.3b practice problems comparing unit rates
6.RP.3b practice problems comparing unit rates