Middle School Math Tasks for Grades 6–8

Common Core & MYP Math Tasks

Expressions and Equations

Grade 6

Grade 7

Grade 8

High School

Grade 6

Standard	Standard Focus	Task	Task Type	Mathematical Focus
6.EE.B.7	Solve one-variable equations	Peas in a Pod	3-Act Task	Build and solve a one-variable equation from a visual context.
6.EE.B.7	Solve one-variable equations	The Candyman	3-Act Task	Represent a contextual relationship with an equation and justify the solution.
6.EE.C.9	Represent relationships between two quantities	Bucky the Badger	3-Act Task	Identify how two quantities vary together and construct a rule for the relationship.
6.EE.C.9	Represent relationships between two quantities	Bucky the Badger (Desmos)	Desmos	Use multiple representations to refine a rule connecting two quantities.
6.EE.C.9	Represent relationships between two quantities	Turbo Texting	3-Act Task	Represent two related quantities using a table, graph, and equation.
6.EE.C.9	Represent relationships between two quantities	Visual Patterns	Rich Task	Generalize a growing pattern and connect the rule to tables and graphs.

Grade 7

Standard	Standard Focus	Task	Task Type	Mathematical Focus
7.EE.B.4a	Solve word problems using linear equations	Peas in a Pod	3-Act Task	Build and solve an equation from a visual context while reasoning about angle relationships.
7.EE.B.4a	Solve word problems using linear equations	The Candyman	3-Act Task	Represent a contextual relationship with an equation and justify the solution.

Grade 7

Standard Standard Focus Task Task Type Mathematical Focus
7.EE.B.4a Solve word problems using linear equations
Peas in a Pod
3-Act Task Build and solve an equation from a visual context while reasoning about angle relationships.
7.EE.B.4a Solve word problems using linear equations
The Candyman
3-Act Task Represent a contextual relationship with an equation and justify the solution.

Grade 8

Standard	Standard Focus	Task	Task Type	Mathematical Focus
8.EE.A.1	Apply properties of integer exponents	Equivalent Exponents	Open Middle	Construct equivalent exponential expressions using exponent laws.
8.EE.A.1	Apply properties of integer exponents	Exponent: Maximum Value	Open Middle	Choose values strategically to maximize an exponential expression.
8.EE.A.1	Apply properties of integer exponents	Giant Burgers	Rich Task	Use powers and scientific notation to model extreme quantities.
8.EE.A.1	Apply properties of integer exponents	Open Middle: Exponent Collection	Open Middle	Apply exponent laws in open-ended numerical challenges.
8.EE.A.1	Apply properties of integer exponents	Penny Pyramid	3-Act Task	Model exponential growth in a stacked arrangement.
8.EE.A.1	Apply properties of integer exponents	Properties of Integer Exponents	Open Middle	Use exponent properties to create equivalent expressions.
8.EE.A.1	Apply properties of integer exponents	Scientific Notation 2	Open Middle	Represent and compare very large or very small quantities using scientific notation.
8.EE.A.1	Apply properties of integer exponents	Zero and Negative Exponent Patterns	Desmos	Use numerical patterns to develop zero- and negative-exponent rules.
8.EE.A.2	Use square and cube roots to solve equations	Amazing Watermelons	3-Act Task	Estimate and use square roots in a contextual measurement problem.
8.EE.A.2	Use square and cube roots to solve equations	Best Squares	3-Act Task	Compare square areas and side lengths using square-root reasoning.
8.EE.A.2	Use square and cube roots to solve equations	Perfect Blue and Purple	Desmos	Identify perfect squares and estimate non-perfect square roots.
8.EE.A.2	Use square and cube roots to solve equations	Rational Roots	Open Middle	Estimate square roots and determine whether their values are rational.
8.EE.A.2	Use square and cube roots to solve equations	Square Builder	Desmos	Construct squares and reason about side length from area.
8.EE.A.2	Use square and cube roots to solve equations	Square Dance	Desmos	Connect perfect squares, square roots, and benchmark values.
8.EE.A.2	Use square and cube roots to solve equations	Square Root Expression	Open Middle	Create and evaluate expressions involving square roots.

High School

Geometry

Grade 6

Grade 7

Grade 8

High School

Grade 6

Standard	Standard Focus	Task	Task Type	Mathematical Focus
6.G.A.1	Find areas of triangles, quadrilaterals, and composite polygons	An Area Task — Nat Banting	Rich Task	Compare multiple strategies for finding the area of a non-routine figure.
6.G.A.1	Find areas of triangles, quadrilaterals, and composite polygons	Area of Saskatchewan	3-Act Task	Estimate the area of an irregular region through decomposition and measurement.
6.G.A.2	Find volumes of right rectangular prisms	Fill ‘er Up	3-Act Task	Estimate and calculate container capacity using volume.
6.G.A.2	Find volumes of right rectangular prisms	Got Cubes	3-Act Task	Build and compare solids using unit cubes and volume reasoning.
6.G.A.2	Find volumes of right rectangular prisms	Overflow	3-Act Task	Connect displaced liquid to the volume of an object.
6.G.A.2	Find volumes of right rectangular prisms	Packing Sugar	3-Act Task	Determine how much material fits in a rectangular container.
6.G.A.2	Find volumes of right rectangular prisms	The Fish Tank	3-Act Task	Determine tank capacity and interpret volume in context.
6.G.A.2	Find volumes of right rectangular prisms	Volume of Rectangular Prisms	Open Middle	Create rectangular prisms that satisfy specified volume constraints.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	3D Shapes	Lesson	Connect nets, faces, dimensions, and surface area of three-dimensional figures.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	Cube Conversations	Rich Task	Use cube arrangements to reason about visible faces, surface area, and volume.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	Pentomino Puzzle	Rich Task	Compose and decompose nets to investigate surface area.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	Rectangular Prism Surface Area	Open Middle	Determine surface area while reasoning about dimensions and nets.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	Solid Fusing Task	Rich Task	Analyze how joining solids changes exposed surface area.
6.G.A.4	Use nets to represent three-dimensional figures and find surface area	Surface Area and Volume of Prisms	Open Middle	Compare surface area and volume for prisms with constrained dimensions.

Grade 7

Standard	Standard Focus	Task	Task Type	Mathematical Focus
7.G.B.6	Solve area, surface area, and volume problems	1600 Pennsylvania A	Lesson	Apply area and measurement reasoning to a real-world design context.
7.G.B.6	Solve area, surface area, and volume problems	3D Shapes	Lesson	Connect nets, faces, dimensions, and surface area of three-dimensional figures.
7.G.B.6	Solve area, surface area, and volume problems	An Area Task — Nat Banting	Rich Task	Compare strategies for finding area in a non-routine configuration.
7.G.B.6	Solve area, surface area, and volume problems	Area of Saskatchewan	3-Act Task	Estimate the area of an irregular region using decomposition and measurement.
7.G.B.6	Solve area, surface area, and volume problems	Cube Conversations	Rich Task	Use cube arrangements to reason about surface area and volume.
7.G.B.6	Solve area, surface area, and volume problems	Filing Cabinet	Desmos	Use dimensions and surface-area reasoning to analyze a three-dimensional object.
7.G.B.6	Solve area, surface area, and volume problems	Pentomino Puzzle	Rich Task	Compose and decompose shapes to investigate area and surface area.
7.G.B.6	Solve area, surface area, and volume problems	Pop Box Design	3-Act Task	Design a package while balancing surface area, volume, and dimensions.
7.G.B.6	Solve area, surface area, and volume problems	Rectangular Prism Surface Area	Open Middle	Determine surface area while reasoning about dimensions and nets.
7.G.B.6	Solve area, surface area, and volume problems	Solid Fusing Task	Rich Task	Analyze how joining solids changes surface area and volume.
7.G.B.6	Solve area, surface area, and volume problems	Surface Area and Volume of Prisms	Open Middle	Compare surface area and volume for prisms with constrained dimensions.
7.G.B.6	Solve area, surface area, and volume problems	The Big Pad	3-Act Task	Apply area, surface area, and volume reasoning through a 3-act task.

Grade 8

Standard	Standard Focus	Task	Task Type	Mathematical Focus
8.G.A.4	Understand similarity using transformations	Eye to Eye: Similar Triangles	Lesson / Rich Task	Use similar triangles to estimate an inaccessible height or distance.
8.G.B.7	Apply the Pythagorean Theorem	Exploring the Pythagorean Theorem	Lesson	Investigate why the Pythagorean relationship holds for right triangles.
8.G.B.7	Apply the Pythagorean Theorem	Oops, I Forgot… It Was This Length	Rich Task	Find a missing side length using the Pythagorean Theorem.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Coca Cola Slim	3-Act Task	Compare cylinder dimensions, capacity, and efficiency.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Cylinders	Desmos	Explore how radius and height affect cylinder volume.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Fill ‘er Up	3-Act Task	Estimate and calculate container capacity.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Got Cubes	3-Act Task	Build and compare solids using unit cubes and volume reasoning.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Illegal Money	3-Act Task	Estimate the volume and dimensions of a large stack of money.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Maximizing Volume of a Cylinder Given Lateral Area	Open Middle	Optimize cylinder volume under a fixed surface-area constraint.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Overflow	3-Act Task	Connect displaced volume to the amount of liquid that overflows.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Packing Sugar	3-Act Task	Use volume to determine how much material fits in a container.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Penny Wars	3-Act Task	Use volume and packing assumptions to estimate a large quantity of coins.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Popcorn Picker	3-Act Task	Compare container designs using volume.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Soup de Jour	3-Act Task	Model and compare the volume of cylindrical containers.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	The Fish Tank	3-Act Task	Determine tank capacity and interpret volume in context.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	Volume of Rectangular Prisms	Open Middle	Create rectangular prisms that satisfy specified volume conditions.
8.G.C.9	Solve volume problems involving cylinders, cones, and spheres	You Pour, I Choose	3-Act Task	Compare differently shaped containers and justify which holds more.

High School

Number System

Grade 6

Grade 7

Grade 8

High School

Grade 6

Standard	Standard Focus	Task	Task Type	Mathematical Focus
6.NS.B.4	Use factors, multiples, GCF, and LCM	Animated Factorization	Interactive Visual	Explore prime factorization and recognize multiplicative structure visually.
6.NS.C.6	Represent rational numbers on number lines and coordinate planes	Polygraph: Rational Numbers	Desmos	Describe and compare rational numbers using location, sign, and magnitude.
6.NS.C.7	Order rational numbers and interpret absolute value	Clothesline Math Cards	Rich Task	Place rational numbers in order and justify comparisons using distance from zero.

Grade 7

Standard	Standard Focus	Task	Task Type	Mathematical Focus
7.NS.A.1	Add and subtract rational numbers	Adding Two Digit Numbers Middle School	Open Middle	Use integer reasoning and strategic placement to create valid sums.
7.NS.A.1	Add and subtract rational numbers	Adding and Subtracting Integers	Open Middle	Develop efficient strategies for adding and subtracting signed numbers.
7.NS.A.1–3	Apply all four operations with rational numbers	Adding Fractions	Desmos / Menu Math	Develop fraction-addition strategies through visual and numerical representations.
7.NS.A.1–3	Apply all four operations with rational numbers	Butter	3-Act Task	Operate with rational numbers in a measurement context.
7.NS.A.1–3	Apply all four operations with rational numbers	Polygraph: Rational Numbers	Desmos	Describe, compare, and classify rational numbers using precise mathematical language.

Grade 8

Standard	Standard Focus	Task	Task Type	Mathematical Focus
8.NS.A.2	Approximate irrational numbers and compare their values	Cycling Squares	Rich Task	Investigate patterns created by repeatedly applying square and square-root operations.
8.NS.A.2	Approximate irrational numbers and compare their values	Rational Roots	Open Middle	Estimate square roots and determine whether their values are rational.
8.NS.A.2	Approximate irrational numbers and compare their values	Rational, Irrational, or Whole Roots	Open Middle	Classify square roots as whole, rational, or irrational.
8.NS.A.2	Approximate irrational numbers and compare their values	Square Dance: Exploring Square Roots & Benchmarks	Desmos	Estimate irrational square roots using nearby perfect-square benchmarks.
8.NS.A.2	Approximate irrational numbers and compare their values	Taco Cart	3-Act Task	Use distance and square-root reasoning to compare possible routes.
8.NS.A.2	Approximate irrational numbers and compare their values	Taco Cart (Desmos)	Desmos	Model route distances and compare square-root values dynamically.

High School

Statistics & Probability

Grade 6

Grade 7

Grade 8

High School

Grade 6

Standard	Standard Focus	Task	Task Type	Mathematical Focus
6.SP.B.4	Display numerical data on plots and histograms	Card Sort: Bar Graph vs Histogram	Desmos	Distinguish between categorical and numerical displays and analyze histogram structure.

Grade 7

Grade 8

High School

Function

Grade 8

High School

Grade 8

Standard	Standard Focus	Task	Task Type	Mathematical Focus
8.F.B.4	Model linear relationships and interpret rate of change	100×100 Hamburger	Rich Task	Use a linear model and proportional reasoning to analyze an extreme order.
8.F.B.4	Model linear relationships and interpret rate of change	Bucky the Badger	3-Act Task	Build a linear model from a visual or contextual pattern.
8.F.B.4	Model linear relationships and interpret rate of change	Bucky the Badger (Desmos)	Desmos	Explore and refine a linear model using multiple representations.
8.F.B.4	Model linear relationships and interpret rate of change	Incorrect Linear Equations	Open Middle	Analyze errors and determine which linear equations match given conditions.
8.F.B.4	Model linear relationships and interpret rate of change	Linear Function from Table of Values	Open Middle	Determine a linear rule from a table of values.
8.F.B.4	Model linear relationships and interpret rate of change	Solution of Two Linear Equations	Open Middle	Reason about where two linear relationships have the same value.
8.F.B.4	Model linear relationships and interpret rate of change	Stacking Cups	3-Act Task	Model stack height as a linear relationship with a starting value and constant rate.
8.F.B.4	Model linear relationships and interpret rate of change	Turbo Texting	3-Act Task	Model a linear relationship and interpret its rate of change and initial value.
8.F.B.4	Model linear relationships and interpret rate of change	Two Truths and a Lie: Lines	Desmos	Interpret and compare linear representations to identify a false statement.
8.F.B.4	Model linear relationships and interpret rate of change	Visual Patterns	Rich Task	Generalize a growing pattern using tables, graphs, and linear rules.
8.F.B.4	Model linear relationships and interpret rate of change	Write a Linear Function	Open Middle	Construct a linear equation that satisfies stated conditions.

High School

Ratios & Proportions

Grade 6

Standard	Standard Focus	Task	Task Type	Mathematical Focus
6.RP.A.2	Understand and use unit rates	Nana’s Chocolate Milk	3-Act Task	Use a ratio and unit rate to scale a mixture and compare equivalent recipes.
6.RP.A.2	Understand and use unit rates	Sugar Packets	3-Act Task	Determine and compare unit rates in a context involving quantities and packaging.
6.RP.A.3	Use ratio and rate reasoning to solve problems	Energy Bites	3-Act Task	Scale a recipe and reason about equivalent ratios in a real-world context.
6.RP.A.3	Use ratio and rate reasoning to solve problems	Minnie’s Juice Cup	3-Act Task	Compare quantities and use proportional reasoning to determine an unknown amount.
6.RP.A.3	Use ratio and rate reasoning to solve problems	Proportion Explosion	3-Act Task	Use proportional reasoning to scale quantities and justify multiplicative comparisons.
6.RP.A.3c	Find a percent of a quantity and convert among forms	Calvin’s Clearance	3-Act Task	Solve a discount problem and connect percent, decimal, and fraction representations.
6.RP.A.3c	Find a percent of a quantity and convert among forms	Clothesline Math Cards	Rich Task	Order and compare fractions, decimals, and percents using benchmarks.