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Linear Alignment

6-8, 9-12

This lesson allows students to explore linear equations and the effects of changing the slope and y-intercept on a line. It gives students exposure to y = mx + b, and can be used as an introduction to the topic. Using graphing calculators, students are challenged to overlap lines onto the sides of polygons. To achieve this goal, students change slopes and y-intercepts of lines, noting observations about behavior as they work. As students change the y-intercept of a line, they see it raise or lower the line. As students change the slope, they see it affect the steepness of the line.

Rise-Run Triangles

6-8, 9-12

This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.

Bean Counting and Ratios

6-8, 9-12

By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions.

This lesson can be adapted for lower-skilled students by using a more common fraction, such as 2/3. It can be adapted for upper grades or higher-skilled students by using ratios that are less instinctual, such as 12/42 (which reduces to 2/7).

Scaffold the level of difficulty in this lesson by going from a simple ratio such as 2/3 to more complicated ratios such as 2/7 or 5/9.

Constructing a Three-Dimensional Model

3-5

In this lesson, students build a three‑dimensional model from their two‑dimensional blueprint. In addition, they solve problems related to constructing and decorating their clubhouse.

Scaling Away

6-8

Students will measure the dimensions of a common object, multiply each dimension by a scale factor, and examine a model using the multiplied dimensions. Students will then compare the surface area and volume of the original object and the enlarged model.

Inch by Inch

3-5

In this lesson, students use a ruler to represent various fractions as lengths. This lesson builds on the work done in the previous lessons with as students use a standard instrument to measure a variety of items, including items which can be measured to the nearest half and quarter of an inch.

Investigating Equivalent Fractions with Relationship Rods

3-5

Students investigate the length model by working with relationship rods to find equivalent fractions. Students develop skills in reasoning and problem solving as they explain how two fractions are equivalent (the same length).

Investigating Fraction Relationships with Relationship Rods

3-5

Students use relationship rods to explore fraction relationships. This work with relationships lays the foundation for work with more challenging fraction concepts.

Relationship rods are wooden or plastic rods in ten different colors. They range in length from one to ten centimeters. Each length is a different color.

More Fun with Fraction Strips

3-5

Students continue to work with fraction strips to compare and order fractions. This lesson builds on the work done with fraction relationships in the previous lesson. Students develop skills in problem solving and reasoning as they make connections between various fractions.

Making and Investigating Fraction Strips

3-5

Students make and use a set of fraction strips to represent the length model, discover fraction relationships, and work with equivalent fractions.

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