Noyce Foundation
Cutting a Cube
Teach the ins and outs of the cube! A series of five K–12 level activities explore the make-up of the cube. The beginning lessons focus on the vocabulary related to the cube. Later lessons explore the possible nets that describe a cube....
Noyce Foundation
Cut It Out
Explore the mathematics of the paper snowflake! During the five lessons progressing in complexity from K through 12, pupils use spatial geometry to make predictions. Scholars consider a folded piece of paper with shapes cut out....
EngageNY
Real-World Area Problems
Not all structures take the shape of a polygon. The 21st lesson in a series of 29 shows young mathematicians they can create polygons out of composite shapes. Once they deconstruct the structures, they find the area of the composite figure.
EngageNY
Population Problems
Find the percent of the population that meets the criteria. The 17th segment of a 20-part unit presents problems that involve percents of a population. Pupils use tape diagrams to create equations to find the percents of subgroups...
Virginia Department of Education
Permutations and Combinations
Counting is not all it adds up to be — sometimes it involves multiplying. The instructional activity introduces permutations and combinations as ways of counting, depending upon whether order is important. Pupils learn about factorials...
Virginia Department of Education
Simplifying Square Roots of Whole Numbers
Simplify your life by using a resource on simplifying square roots. Pupils review square roots and calculate values of given radical expressions using a calculator. The instructional activity concludes by having them consider the results...
EngageNY
Mixture Problems
What percent of the mixture is juice? Pairs use their knowledge of proportions to determine what percent a mixture is juice given the percent of juice in the components. Pupils use the procedure learned with the juice mixture problem to...
EngageNY
Part of a Whole as a Percent
Pupils use visual models, numeric methods, and equations to solve percent problems. To complete the second installment of 20, they find the part given the percent and the whole, find the percent given the part and the whole, and find the...
EngageNY
Distance on the Coordinate Plane
Apply the Pythagorean Theorem to coordinate geometry. Learners find the distance between two points on a coordinate plane by using the Pythagorean Theorem. The vertical and horizontal change creates a right triangle, which allows...
EngageNY
Converting Repeating Decimals to Fractions
Develop a process with your classes for converting repeating decimals to fractions. Through this process, pupils understand that any repeating decimal can be written as a fraction. The 10th instructional activity in this 25-part...
Virginia Department of Education
Adding and Subtracting Polynomials Using Algebra Tiles
Scholars learn how using algebra tiles to add and subtract polynomials can model how to combine polynomials. They use their newfound knowledge to complete a worksheet of problems.
Virginia Department of Education
Multiplying Polynomials Using Algebra Tiles
Tiles are not just for algebra—see how they can help with multiplication too. Young mathematicians learn to use algebra tiles to model the multiplication of polynomials. A follow-up worksheet provides practice with the skill.
02 x 02 Worksheets
Factoring
Factor in this resource when teaching how to factor polynomials. Scholars use algebra tiles to factor linear and quadratic expressions. They practice their skill by working on example problems from a worksheet.
02 x 02 Worksheets
Dividing Polynomials Using Algebra Tiles
Discover how algebra tiles can help in dividing polynomials. Pupils watch as instructors demonstrate how to use algebra tiles to solve problems involving the division of a quadratic expression by a linear expression. Once they get the...
EngageNY
Cones and Spheres
Explore methods for finding the volume of different three-dimensional figures. The 20th instructional activity in the 25-part series asks learners to interpret diagrams of 3-D figures and use formulas to determine volume. Scholars must...
Mathematics Assessment Project
Modeling Motion: Rolling Cups
Connect the size of a rolling cup to the size of circle it makes. Pupils view videos of cups of different sizes rolling in a circle. Using the videos and additional data, they attempt to determine a relationship between cup...
Illustrative Mathematics
Exploring Sinusoidal Functions
What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...
EngageNY
Finite and Infinite Decimals
Explore the patterns of fractions that produce finite and infinite decimals. The sixth lesson of the series asks learners to determine a similar feature of fractions that produce finite decimals. Using the patterns, pupils create...
Illustrative Mathematics
Sum and Difference Angle Formulas
Need practice deriving trigonometric angle formulas? With this worksheet, pupils derive the sum and difference formulas for cosine and tangent and the difference formula for sine. Scholars use the sine sum formula and other known...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
EngageNY
Nonlinear Models in a Data Context
How well does your garden grow? Model the growth of dahlias with nonlinear functions. In the lesson, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in compost and...
EngageNY
Using Linear Models in a Data Context
Practice using linear models to answer a question of interest. The 12th installment of a 16-part module combines many of the skills from previous lessons. It has scholars draw scatter plots and trend lines, develop linear models, and...
EngageNY
Informally Fitting a Line
Discover how trend lines can be useful in understanding relationships between variables with a lesson that covers how to informally fit a trend line to model a relationship given in a scatter plot. Scholars use the trend line to make...
EngageNY
Scatter Plots
Scholars learn to create scatter plots and investigate any relationships that exists between the variables with a lesson that also show them that statistical relationships do not necessarily indicate a cause-and-effect...