Use volume and unit rates to determine best values for hay bales.
Lesson Plan
Grades: 6th to 8th
Mathematical Practices
Geometry
Expression/Equation
The Number System
Ratio & Proportion
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Solve real-world and mathematical problems involving area, surface area, and volume.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1, 6.RP.A.2, 6.RP.A.3b, 6.RP.A.3c, 6.G.A.2, 7.RP.A.1, 7.NS.A.3, 7.EE.B.3, 8.G.C.9, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7
Explore the concept of slope through a student-centered problem of data collection and evaluation.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Mathematical Practices
Functions
Expression/Equation
Geometry
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Attend to precision.
Model with mathematics.
Make sense of problems and persevere in solving them.
Use functions to model relationships between quantities.
Understand the connections between proportional relationships, lines, and linear equations.
Draw construct, and describe geometrical figures and describe the relationships between them.
7.G.A.1, 8.EE.B.6, 8.F.B.4, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP6, 7.RP.A.2b
Extend the Fibonacci Sequence through an algebra exploration.
Lesson Plan
Grades: 6th to 8th, 9th to 12th, 3rd to 5th
Ratio & Proportion
Mathematical Practices
Functions
Stats & Probability
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Attend to precision.
Reason abstractly and quantitatively.
Make sense of problems and persevere in solving them.
Interpreting Functions
Investigate patterns of association in bivariate data.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1, 8.SP.A.1, HSF-IF.A.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6, 7.RP.A.2a
Relate linear equations and graphs in a game of ships and attacks.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Functions
Expression/Equation
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Use functions to model relationships between quantities.
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5, 8.F.B.4, 7.RP.A.2b, 7.RP.A.2d
Use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building.
Lesson Plan
Grades: 6th to 8th
Stats & Probability
Develop understanding of statistical variability.
Summarize and describe distributions.
6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d, 6.SP.A.1
Use the formula for the volume of a cylinder and convert it into the same volume for rectangular prisms while trying to minimize the surface area.
Lesson Plan
Grades: 6th to 8th
Mathematical Practices
Geometry
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.2, 6.G.A.4, 8.G.C.9, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7
Use previous knowledge of multiplication to identify factors and form products.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th
Mathematical Practices
Algebraic Thinking
Model with mathematics.
Reason abstractly and quantitatively.
Make sense of problems and persevere in solving them.
Gain familiarity with factors and multiples.
Multiply and divide within 100.
Understand properties of multiplication and the relationship between multiplication and division.
3.OA.B.5, 3.OA.C.7, 4.OA.B.4, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP4
Use polydrons to build nets and create the most appealing fish tank.
Lesson Plan
Grades: 9th to 12th, 6th to 8th, High School
Geometry
Mathematical Practices
Congruence
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Geometric Measurement and Dimension
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.2, 6.G.A.4, 8.G.C.9, HSG-GMD.A.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7, HSG-CO.A.1
Use unit rates or proportions and think critically about the real world applications of a baking problem.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.3, 7.RP.A.2a
Participate in a modeling activity where they will learn the rules for translations, rotations, and reflections.
Lesson Plan
Grades: 9th to 12th, 6th to 8th
Mathematical Practices
Geometry
Make sense of problems and persevere in solving them.
Congruence
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.3, HSG-CO.A.2, HSG-CO.A.4, HSG-CO.A.5, HSG-CO.B.6, CCSS.Math.Practice.MP1
Explore the concept of genetics and inheritance using probability.
Lesson Plan
Grades: 9th to 12th, 6th to 8th
Stats & Probability
Mathematical Practices
Making Inferences and Justifying Conclusions
Model with mathematics.
Investigate patterns of association in bivariate data.
Investigate chance processes and develop, use, and evaluate probability models.
Summarize and describe distributions.
6.SP.B.5b, 7.SP.C.6, 7.SP.C.7a, 7.SP.C.7b, 8.SP.A.1, CCSS.Math.Practice.MP4, HSS-IC.A.2
Use manipulative blocks and counters to explore equations such as 3x = 2x + 12.
Lesson Plan
Grades: 6th to 8th
Expression/Equation
Mathematical Practices
Use properties of operations to generate equivalent expressions.
Reason about and solve one-variable equations and inequalities.
Apply and extend previous understandings of arithmetic to algebraic expressions.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4a, 6.EE.B.5, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7, 8.EE.C.7a, 8.EE.C.7b, 6.EE.A.3, 6.EE.B.6, 7.EE.A.1, 7.EE.A.2
Relate functions, tables, and graphs to roller coaster drops.
Lesson Plan
Grades: 6th to 8th
Expression/Equation
Functions
Mathematical Practices
Use properties of operations to generate equivalent expressions.
Apply and extend previous understandings of arithmetic to algebraic expressions.
Define, evaluate, and compare functions.
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
6.EE.A.2c, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7, 8.F.A.1, 6.EE.A.3, 7.EE.A.2
Combine five numbers using the standard arithmetic operations to create a target number.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th
Mathematical Practices
Algebraic Thinking
Attend to precision.
Reason abstractly and quantitatively.
Multiply and divide within 100.
3.OA.C.7, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6
Measure the length and width of a rectangle using both standard and non-standard units of measure.Then, discover that the ratio of length to width of a rectangle is constant.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Mathematical Practices
Stats & Probability
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Use appropriate tools strategically.
Investigate patterns of association in bivariate data.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1, 8.SP.A.1, 8.SP.A.2, CCSS.Math.Practice.MP5, 7.RP.A.2a
Explore volume using virtual and origami boxes.
Lesson Plan
Grades: 6th to 8th
Mathematical Practices
Geometry
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.2, 8.G.C.9, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7
Construct the 12 pentomino figures, and utilize them to explore area and perimeter.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th, Pre K to 2nd, PreK to 2nd
Mathematical Practices
Measurement & Data
Geometry
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Draw construct, and describe geometrical figures and describe the relationships between them.
Classify two-dimensional figures into categories based on their properties.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Reason with shapes and their attributes.
Analyze, compare, create, and compose shapes.
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
K.G.A.2, K.G.B.4, K.G.B.5, K.G.B.6, 1.G.A.1, 1.G.A.2, 2.G.A.1, 3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6, 3.MD.D.8, 5.G.B.4, 7.G.A.2, 7.G.B.6, 3.MD.C.7d, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7
Use geoboards to construct non-traditional, "tilted" squares whose side lengths are irrational numbers.
Lesson Plan
Grades: 6th to 8th
Expression/Equation
The Number System
Mathematical Practices
Work with radicals and integer exponents.
Know that there are numbers that are not rational, and approximate them by rational numbers.
Look for and make use of structure.
Use appropriate tools strategically.
Model with mathematics.
Make sense of problems and persevere in solving them.
CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP5, CCSS.Math.Practice.MP7, 8.NS.A.1, 8.NS.A.2, 8.EE.A.2
Develop an understanding of the Fibonacci Sequence, Golden Ratio, Golden Rectangle, and the term ratio.
Lesson Plan
Grades: 9th to 12th, 6th to 8th
Mathematical Practices
Geometry
Functions
Number & Quantity
Ratio & Proportion
Use appropriate tools strategically.
Congruence
Interpreting Functions
Quantities
Draw construct, and describe geometrical figures and describe the relationships between them.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1, 7.G.A.2, HSN-Q.A.3, HSF-IF.A.3, HSG-CO.D.12, CCSS.Math.Practice.MP5
Build a high-profit yielding hotel using snap cubes.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th
Mathematical Practices
Expression/Equation
The Number System
Ratio & Proportion
Measurement & Data
Attend to precision.
Model with mathematics.
Make sense of problems and persevere in solving them.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Understand ratio concepts and use ratio reasoning to solve problems.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
3.MD.C.6, 6.RP.A.3c, 7.NS.A.3, 7.EE.B.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP4, CCSS.Math.Practice.MP6