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Number and Operations

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.

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Algebra

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.
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Algebra

Fibonacci Trains

6-8
In this lesson, students use Cuisenaire Rods to build trains of different lengths and investigate patterns.  Students make algebraic connections by writing rules and representing data in tables and graphs.
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Data Analysis and Probability

Using NBA Statistics for Box and Whisker Plots

6-8
In this lesson, students use information from NBA statistics to make and compare box and whisker plots. The data provided in the lesson come from the NBA, but you could apply the lesson to data from the WNBA or any other sports teams or leagues for which player statistics are available.
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Algebra

Trains, Fibonacci, and Recursive Patterns

6-8, 9-12
In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns.
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Number and Operations

How Much Is a Million?

6-8
This lesson focuses students on the concept of 1,000,000. It allows students to see first hand the sheer size of 1 million while at the same time providing them with an introduction to sampling and its use in mathematics. Students will use grains of rice and a balance to figure out the approximate volume and weight of 1,000,000 grains of rice.
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Algebra

Distributing and Factoring Using Area

6-8
In this lesson, expressions representing area of a rectangle are used to enhance understanding of the distributive property.  The concept of area of a rectangle can provide a visual tool for students to factor monomials from expressions.
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Algebra

More Trains

6-8, 9-12
In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns.  Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns. 
Algebra

Recursive and Exponential Rules

6-8, 9-12
In this lesson make connections between exponential functions and recursive rules.  Students will use tables to create graphs, define recursive rules and find exponential formulas.
Algebra

Extending to Symbols

6-8
In this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations, they use variables as place holders or unknowns. This investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.