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New York - Mathematics: 7th Grade
Next Generation Learning Standards | Adopted: 2017
NY-7.RP: : Ratios and Proportional Relationships
1.1: : Analyze proportional relationships and use them to solve real-world and mathematical problems.
NY-7.RP.1: : Compute unit rates associated with ratios of fractions.
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
![Screenshot of Unit Conversions](/Assets/img/blank.gif)
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
NY-7.RP.2: : Recognize and represent proportional relationships between quantities.
NY-7.RP.2.a: : Decide whether two quantities are in a proportional relationship.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
NY-7.RP.2.b: : Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
NY-7.RP.2.c: : Represent a proportional relationship using an equation.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
NY-7.RP.2.d: : Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
![Screenshot of Direct and Inverse Variation](/Assets/img/blank.gif)
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
NY-7.RP.3: : Use proportional relationships to solve multistep ratio and percent problems.
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
![Screenshot of Polling: Neighborhood](/Assets/img/blank.gif)
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
NY-7.NS: : The Number System
2.1: : Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
NY-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.
NY-7.NS.1.a: : Describe situations in which opposite quantities combine to make 0.
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
NY-7.NS.1.b: : Understand addition of rational numbers; p + q is 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.
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
NY-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.
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
NY-7.NS.1.d: : Apply properties of operations as strategies to add and subtract rational numbers.
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
NY-7.NS.2: : Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
NY-7.NS.2.d: : Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
NY-7.NS.3: : Solve real-world and mathematical problems involving the four operations with rational numbers.
![Screenshot of Adding and Subtracting Integers](/Assets/img/blank.gif)
Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview
![Screenshot of Adding and Subtracting Integers with Chips](/Assets/img/blank.gif)
Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
NY-7.EE: : Expressions, Equations, and Inequalities
3.1: : Use properties of operations to generate equivalent expressions.
NY-7.EE.1: : Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
![Screenshot of Equivalent Algebraic Expressions II](/Assets/img/blank.gif)
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions I](/Assets/img/blank.gif)
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
3.2: : Solve real-life and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
NY-7.EE.3: : Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.
![Screenshot of Adding on the Number Line](/Assets/img/blank.gif)
Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
![Screenshot of Fractions with Unlike Denominators](/Assets/img/blank.gif)
Fractions with Unlike Denominators
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview
![Screenshot of Improper Fractions and Mixed Numbers](/Assets/img/blank.gif)
Improper Fractions and Mixed Numbers
Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview
![Screenshot of Percent of Change](/Assets/img/blank.gif)
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
![Screenshot of Percents, Fractions, and Decimals](/Assets/img/blank.gif)
Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
NY-7.EE.4: : Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NY-7.EE.4.a: : Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
![Screenshot of Perimeter and Area of Rectangles](/Assets/img/blank.gif)
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
NY-7.EE.4.b: : Solve word problems leading to inequalities of the form px + q > r, px + q is greater than or equal to r, px + q is less than or equal to r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem.
![Screenshot of Solving Linear Inequalities in One Variable](/Assets/img/blank.gif)
Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
NY-7.G: : Geometry
4.1: : Draw, construct, and describe geometrical figures and describe the relationships between them.
NY-7.G.1: : Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
![Screenshot of Dilations](/Assets/img/blank.gif)
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
![Screenshot of Similar Figures](/Assets/img/blank.gif)
Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
NY-7.G.2: : Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
![Screenshot of Classifying Triangles](/Assets/img/blank.gif)
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
![Screenshot of Triangle Inequalities](/Assets/img/blank.gif)
Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
4.2: : Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
NY-7.G.4: : Apply the formulas for the area and circumference of a circle to solve problems.
![Screenshot of Circumference and Area of Circles](/Assets/img/blank.gif)
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
NY-7.G.5: : Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
![Screenshot of Triangle Angle Sum](/Assets/img/blank.gif)
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
NY-7.G.6: : Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three-dimensional objects composed of right rectangular prisms.
![Screenshot of Area of Parallelograms](/Assets/img/blank.gif)
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
![Screenshot of Balancing Blocks (Volume)](/Assets/img/blank.gif)
Balancing Blocks (Volume)
This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
Chocomatic (Multiplication, Arrays, and Area)
Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview
![Screenshot of Fido's Flower Bed (Perimeter and Area)](/Assets/img/blank.gif)
Fido's Flower Bed (Perimeter and Area)
Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview
![Screenshot of Perimeter and Area of Rectangles](/Assets/img/blank.gif)
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
![Screenshot of Prisms and Cylinders](/Assets/img/blank.gif)
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
![Screenshot of Surface and Lateral Areas of Prisms and Cylinders](/Assets/img/blank.gif)
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
NY-7.SP: : Statistics and Probability
5.1: : Draw informal comparative inferences about two populations.
NY-7.SP.1: : Construct and interpret box-plots, find the interquartile range, and determine if a data point is an outlier.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
NY-7.SP.3: : Informally assess the degree of visual overlap of two quantitative data distributions.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
NY-7.SP.4: : Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
![Screenshot of Reaction Time 1 (Graphs and Statistics)](/Assets/img/blank.gif)
Reaction Time 1 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview
![Screenshot of Reaction Time 2 (Graphs and Statistics)](/Assets/img/blank.gif)
Reaction Time 2 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview
5.2: : Investigate chance processes and develop, use, and evaluate probability models.
NY-7.SP.8: : Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.
NY-7.SP.8.a: : Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
NY-7.SP.8.b: : Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
NY-7.SP.8.c: : Design and use a simulation to generate frequencies for compound events.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
Correlation last revised: 12/9/2022
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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