The interactive Paper Pool game provides an opportunity for students to
develop their understanding of ratio, proportion, greatest common factor
and least common multiple.
In this investigation, students are asked to play a game called Paper
Pool. The game is played on rectangular grids made of congruent
squares.
The Paper Pool unit was adapted with
permission and guidance from the Connected Mathematics Project.
Math Content
Students will:
- Develop their understanding of ratios, proportions, and equivalent fractions.
- Find the greatest common factor and the least common multiple.
- Investigate similar figures.
- Gather and organize data.
- Search for patterns.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th
Stats & Probability
Algebraic Thinking
Summarize and describe distributions.
Generate and analyze patterns.
4.OA.C.5, 6.SP.B.5b
Model linear functions using Barbie dolls and rubber bands.
Lesson Plan
Grades: High School, 6th to 8th, 9th to 12th
Stats & Probability
Interpreting Categorical and Quantitative Data
Investigate patterns of association in bivariate data.
8.SP.A.1, 8.SP.A.2, 8.SP.A.3, HSS-ID.B.6a, HSS-ID.B.6c, HSS-ID.C.7
Use volume and unit rates to determine best values for hay bales.
Lesson Plan
Grades: 6th to 8th
Geometry
Expression/Equation
The Number System
Ratio & Proportion
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
See first hand the sheer size of 1 million while introducing sampling and its use in mathematics.
Lesson Plan
Grades: 6th to 8th
Stats & Probability
Ratio & Proportion
Use random sampling to draw inferences about a population.
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.3a, 7.RP.A.3, 7.SP.A.1, 7.SP.A.2
Use beans to physically represent quotients that have remainders, and compare remainders written as fractions of whole groups to the results obtained with a calculator.
Lesson Plan
Grades: 6th to 8th
The Number System
Expression/Equation
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Know that there are numbers that are not rational, and approximate them by rational numbers.
Compute fluently with multi-digit numbers and find common factors and multiples.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.3, 6.NS.B.2, 8.NS.A.1, 7.NS.A.2d
Develop an understanding of the Fibonacci Sequence, Golden Ratio, Golden Rectangle, and the term ratio.
Lesson Plan
Grades: 9th to 12th, 6th to 8th
Geometry
Functions
Number & Quantity
Ratio & Proportion
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
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 polydrons to build nets and create the most appealing fish tank.
Lesson Plan
Grades: 9th to 12th, High School, 6th to 8th
Geometry
Congruence
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, HSG-CO.A.1
Explore the concept of slope through a student-centered problem of data collection and evaluation.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Functions
Expression/Equation
Geometry
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.
Draw construct, and describe geometrical figures and describe the relationships between them.
7.G.A.1, 8.EE.B.6, 8.F.B.4, 7.RP.A.2b
Enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein.
Lesson Plan
Grades: 6th to 8th
The Number System
Ratio & Proportion
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.
6.RP.A.3c, 7.NS.A.3
Explore volume using virtual and origami boxes.
Lesson Plan
Grades: 6th to 8th
Geometry
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
Create aluminum foil boats and then test them by filling them with plastic bears until they sink. The data is collected and used to make two class box-and-whisker plots with some surprising results.
Lesson Plan
Grades: 6th to 8th, 3rd to 5th
Stats & Probability
Draw informal comparative inferences about two populations.
Summarize and describe distributions.
Develop understanding of statistical variability.
Investigate patterns of association in bivariate data.
6.SP.A.3, 6.SP.B.4, 6.SP.B.5c, 8.SP.A.1, 6.SP.A.1, 6.SP.A.2, 6.SP.B.5a, 7.SP.B.3, 7.SP.B.4
Conduct a coin tossing experiment to discover a line graph that progresses toward the theoretical probability.
Lesson Plan
Grades: 6th to 8th
Stats & Probability
Ratio & Proportion
Investigate chance processes and develop, use, and evaluate probability models.
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1, 6.RP.A.3a, 7.SP.C.5, 7.SP.C.6, 7.SP.C.7a, 7.SP.C.7b, 7.SP.C.8c
Draw a mat plan when given a three dimensional
figure built from cubes and vice versa.
Grades: 6th to 8th
Geometry
Draw construct, and describe geometrical figures and describe the relationships between them.
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.4, 7.G.A.2
Use your knowledge of rectangles to discover the area formula for parallelograms.
Grades: 6th to 8th
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.A.1
Form a physical interpretation of slope and y-intercept by running across a football field.
Lesson Plan
Grades: 6th to 8th, High School, 9th to 12th
Ratio & Proportion
Stats & Probability
Functions
Algebra
Expression/Equation
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Summarize and describe distributions.
Interpreting Categorical and Quantitative Data
Linear, Quadratic, and Exponential Models
Interpreting Functions
Creating Equations
Investigate patterns of association in bivariate data.
Use functions to model relationships between quantities.
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.6, 8.F.B.4, 8.SP.A.2, 8.SP.A.3, HSA-CED.A.2, HSF-IF.B.4, HSF-LE.A.1a, HSF-LE.A.2, HSS-ID.B.6a, HSS-ID.B.6c, HSS-ID.C.7, 6.SP.B.5b, 7.RP.A.2b
Finalize work, and write a
report that summarizes all the findings on the game Paper Pool.
Grades: 6th to 8th
Stats & Probability
Develop understanding of statistical variability.
Investigate patterns of association in bivariate data.
Summarize and describe distributions.
6.SP.B.5b, 8.SP.A.1, 6.SP.A.1
Explore using the isometric drawing tool and gain practice and experience in manipulating drawings.
Grades: 6th to 8th
Geometry
Draw construct, and describe geometrical figures and describe the relationships between them.
7.G.A.2
Estimate and use decomposition to find the areas of highly irregular shapes.
Grades: 6th to 8th
Geometry
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.B.6
Use class schedules to create time-distance graphs.
Lesson Plan
Grades: 6th to 8th
Ratio & Proportion
Stats & Probability
Functions
Expression/Equation
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Summarize and describe distributions.
Use functions to model relationships between quantities.
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5, 8.EE.B.6, 8.F.B.4, 8.F.B.5, 6.SP.B.5b, 7.RP.A.2b, 7.RP.A.2d