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...
Noyce Foundation
Part and Whole
Now you'll never have trouble cutting a cake evenly again. Here is a set of five problems all about partitioning shapes into a given number of pieces and identifying the fractional amount of each piece. As learners progress through the...
Concord Consortium
Circling Trains
And round and round the park we go! Given a description of an amusement park with the locations of three attractions connected by walkways, learners consider what happens when additional attractions join the mix by doubling the length of...
Concord Consortium
Systematic Solution II
Up the difficulty level by solving a system of equations with variable coefficients. Young scholars devise a plan to solve for x and y in terms of a and b. They represent their solutions as expressions and explain their process and the...
Concord Consortium
School Bus Routes
Plan the way to school. Given a map of a school district, class members portray a transportation consultant hired to develop a bus transportation plan that will pick up the eligible riders and get them to school. The plan must contain...
EngageNY
Computing Actual Lengths from a Scale Drawing
The original drawing is eight units — how big is the scale drawing? Classmates determine the scale percent between a scale drawing and an object to calculate the length of a portion of the object. They use the percent equation to find...
EngageNY
The Relationship of Multiplication and Division
Take any number, multiply it by five, and then divide by five. Did you end up with the original number? In the same vein as the previous lesson, pupils discover the relationship between multiplication and division. They develop the...
EngageNY
Read Expressions in Which Letters Stand for Numbers III
Those key operation words sure come in handy. Groups continue their work with converting between different notations for algebraic expressions. They work in stations to write the symbolic form for given verbal phrases. This is the 17th...
EngageNY
Introduction to Simultaneous Equations
Create an understanding of solving problems that require more than one equation. The lesson introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...
EngageNY
Some Facts About Graphs of Linear Equations in Two Variables
Develop another way to find the equation of a line. The lesson introduces the procedure to find the equation of a line given two points on the line. Pupils determine the two points from the graph of the line.
EngageNY
Changing Scales
Pupils determine scale factors from one figure to another and the scale factor in the reverse direction. Scholars compute the percent changes between three figures.
EngageNY
Solving Area Problems Using Scale Drawings
Calculate the areas of scale drawings until a more efficient method emerges. Pupils find the relationship between the scale factor of a scale drawing and the scale of the areas. They determine the scale of the areas is the square of the...
EngageNY
Counting Problems
Solving these percent problems is a matter of counting. Pupils find percents by counting the number of events that meet the criteria and the total number of possibilities. Participants create the ratio and convert it to a percent to...
EngageNY
From Ratio Tables to Equations Using the Value of a Ratio
Use the value of a ratio to set up equations. The teacher leads a discussion on determining equations from ratio tables in the 13th portion of a 29-part series. Pupils determine which of two equations to use to find the solution. They...
EngageNY
Positive and Negative Numbers on the Number Line—Opposite Direction and Value
Make your own number line ... using a compass. The first installment of a 21-part series has scholars investigate positive and negative integers on a number line by using a compass to construct points that are the same distance from zero...
Mathematics Assessment Project
Pythagorean Triples
What special relationships exist in right triangles? In the high school performance task, learners investigate Pythagorean triples. They then determine rules for the perimeter and area of right triangles given the shortest side.
Curated OER
Skip Counting to Multiply
In this multiplication worksheet, students solve 6 word problems where they use skip counting to multiply. Blanks are provided as scaffolding.
Curated OER
Arithmetic Algorithms
In this math worksheet, students solve a variety of arithmetic algorithms. Students use multiplication, division, addition, and subtraction skills to solve the problems.
Curated OER
Circumference and Area of Circles
In this circumference and area worksheet, students find each for a set of 12 given circles; either diameter or radius are given. A website reference for additional resources and answers are provided.
Curated OER
Circumference and Area of Circles
In this circumference and area of circles worksheet, students find each to 1 decimal place of 12 given circles. A website reference for additional resources and answer key are given.
WindWise Education
What Factors Influence Offshore Wind?
What is that out in the water on the horizon? Teams work together to study the coastline using maps to determine the best and worst locations to place an offshore wind farm. The teams then build a scale model wind farm to see what it...
EngageNY
Perimeter and Area of Triangles in the Cartesian Plane
Pupils figure out how to be resourceful when tasked with finding the area of a triangle knowing nothing but its endpoints. Beginning by exploring and decomposing a triangle, learners find the perimeter and area of a triangle. They then...
EngageNY
Perimeter and Area of Polygonal Regions in the Cartesian Plane
How many sides does that polygon have? Building directly from lesson number eight in this series, learners now find the area and perimeter of any polygon on the coordinate plane. They decompose the polygons into triangles and use Green's...
West Contra Costa Unified School District
Solving Exponential Equations
The power to solve exponential equations lies in the resource. Scholars first learn how to solve exponential equations. An activity matching cards with equations, intermediate steps, and solutions strengthens this skill.