EngageNY
The Euclidean Algorithm as an Application of the Long Division Algorithm
Individuals learn to apply the Euclidean algorithm to find the greatest common factor of two numbers. Additionally, the lesson connects greatest common factor to the largest square that can be drawn in a rectangle.
EngageNY
Divisibility Tests for 3 and 9
Who knew the sum of a number's digits gives such interesting information? The 18th installment of a 21-part module has scholars investigate division by three and nine. After looking at several examples, they develop divisibility tests...
EngageNY
Even and Odd Numbers
Even or not, here I come. Groups investigate the parity of products and sums of whole numbers in the 17th lesson in a series of 21. Using dots to represent numbers, they develop a pattern for the products of two even numbers; two odd...
EngageNY
Fraction Multiplication and the Products of Decimals
Class members come up with a hypothesis on the number of decimal digits in the product of two decimals. Learners work in groups to complete several decimal multiplication problems. The results help groups develop a conjecture on the...
EngageNY
The Distributive Property and the Products of Decimals
Make multiplication of decimals easier by applying the distributive property. Pupils investigate how they can use the distributive property to multiply decimals. After learning the strategy, they work on some practice problems at...
EngageNY
The Structure of Ratio Tables—Additive and Multiplicative
Build tables by understanding their structure. Scholars take a closer look at the structure of ratio tables in the 10th segment in a 29-part series. Individuals realize that the tables can be built using an additive or...
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....
EngageNY
Comparing Ratios Using Ratio Tables
Decide which concentration of mixtures is the strongest. Pupils use tables to compare ratios involved in mixtures. They use two methods to make the comparisons — by finding equivalent values within the tables or by comparing the...
EngageNY
Tables of Equivalent Ratios
Don't table the discussion on equivalent ratios — do it now! Scholars create tables of equivalent ratios to represent contextual problems. Pupils go on to use the tables to answer questions within the context. The instructional activity...
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
Percent Increase and Decrease
Increase the percent of pupils that are fluent in solving change problems with an activity that asks class members to look at problems that involve either increases or decreases and to express the change in terms of the percent of...
Noyce Foundation
Between the Lines
Explore linear and square dimensions by comparing areas of similar figures. A creative set of five activities designed for elementary through high school classes asks young scholars to compare areas of specific polygons. The first two...
Noyce Foundation
Perfect Pair
What makes number pairs perfect? The resource provides five problems regarding perfect pairs of numbers, the definition of which changes in complexity with each task. Solutions require pupils to apply number sense and operations, as well...
Noyce Foundation
Fractured Numbers
Don't use use a fraction of the resource — use it all! Scholars attempt a set of five problem-of-the-month challenges on fractions. Levels A and B focus on creating fractions and equivalent fractions, while Levels C, D, and E touch on...
Noyce Foundation
Double Down
Double the dog ears, double the fun. Five problems provide increasing challenges with non-linear growth. Topics include dog ears, family trees and population data, and geometric patterns.
Noyce Foundation
Piece it Together
Score some problems all related to soccer balls. The first few problems focus on pattern blocks to see relationships between figures. More advanced problems focus on actual soccer balls, the patterns on the balls, and their volumes and...
Noyce Foundation
Lyle's Triangles
Try five problems on triangles. Levels A and B focus on shapes that can be created from right triangles. Level C touches upon the relationship between the area of a six-pointed star and the area of each triangle of which it is composed....
Noyce Foundation
Cubism
If cubism were a religion, would you follow it? Lower-level tasks focus primarily on counting the number cubes in a structure and relating the number to surface area. As learners progress to higher-level tasks, isometric drawings and...
Noyce Foundation
On Balance
Investigate the world of unknown quantities with a creative set of five lessons that provides problem situations for varying grade levels. Each problem presents a scenario of fruit with different weights and a balance scale. Using the...
Noyce Foundation
Once Upon a Time
Examine the relationship between time and geometry. A series of five lessons provides a grade-appropriate problem from elementary through high school. Each problem asks learners to compare the movement of the hands on a clock to an angle...
Noyce Foundation
Poly-Gone
Investigate polygons from rectangles to triangles to octagons. Each level of the five-problem series targets a different grade level. Beginning with the level A problem, learners examine the relationship between area and perimeter by...
Noyce Foundation
What's Your Angle?
Math can be a work of art! Reach your artistic pupils as they explore angle measures. A creative set of five problems of varying levels has young learners study interior and exterior angle measures of polygons. The introductory levels...
Noyce Foundation
Surrounded and Covered
What effect does changing the perimeter have on the area of a figure? The five problems in the resource explore this question at various grade levels. Elementary problems focus on the perimeter of rectangles and irregular figures with...
Noyce Foundation
The Shape of Things
Investigate the attributes of polygons. A thorough set of lessons presents problem scenarios for elementary through high school classes. The first lessons focus on basic characteristics of polygons, including the line of symmetry. As the...