The purpose of this curriculum guide is to provide OER lesson material and support activities for Pythagorean Theorem instruction. It is geared towards GED® requirements. Both printable and online options are provided.

Students are given a short video clip with a simple octagon. Can they predict where the arrow will be after a series of transformations?It might not be where you expect it.This great activity reinforces the ability of students to visualize geometric transformations in real-time, made predictions, analyze a bit of visual data, and the engagement tends to be through the roof!

This problem was designed to explore equivalence of change (ie. if a 10% decrease isn't the opposite of a 10% increase, what is? ) and to move students towards the concept: exponential growth and decay.

Unit 5: Arithmetic in Base Ten
Lesson 5: Decimal Points in Products

In earlier grades, students have multiplied base-ten numbers up to hundredths (either by multiplying two decimals to tenths or by multiplying a whole number and a decimal to hundredths). Here, students use what they know about fractions and place value to calculate products of decimals beyond the hundredths. They express each decimal as a product of a whole number and a fraction, and then they use the commutative and associative properties to compute the product. For example, they see that (0.6 x 0.5) can be viewed as (6 x 0.1 x 5 x 0.1) and thus as (6 x 1/10) x (5 x 1/10). Multiplying the whole numbers and the fractions gives them (30 x 1/100) and then 0.3.

Through repeated reasoning, students see how the number of decimal places in the factors can help them place the decimal point in the product (MP8).

Unit 2: Introducing Ratios
Lesson 5: Defining Equivalent Ratios

Previously, students understood equivalent ratios through physical perception of different batches of recipes. In this lesson, they work with equivalent ratios more abstractly, both in the context of recipes and in the context of abstract ratios of numbers. They understand and articulate that all ratios that are equivalent to a:b can be generated by multiplying both a and b by the same number (MP6).

By connecting concrete quantitative experiences to abstract representations that are independent of a context, students develop their skills in reasoning abstractly and quantitatively (MP2). They continue to use diagrams, words, or a combination of both for their explanations. The goal in subsequent lessons is to develop a general definition of equivalent ratios.

In this activity, students will learn to define variables that can be used to reference values and expressions. Once defined, their variables can be used repeatedly throughout a program as substitutes for the original values or expressions.

Unit 8: Data Sets and Distributions
Lesson 8: Describing Distributions on Histograms

In this lesson, students explore various shapes and features of a distribution displayed in a histogram. They use the structure (MP7) to look for symmetry, peaks, clusters, gaps, and any unusual values in histograms. Students also begin to consider how these features might affect how we characterize a data set. For example, how might we describe what is typical in a distribution that shows symmetry? What about in a distribution that has one peak that is not symmetrical? This work is informal, but helps to prepare students to better understand measures of center and spread later in the unit. Students also distinguish between the uses and construction of bar graphs and histograms in this lesson.

Unit: Area and Surface Area
Lesson 19: Designing a Tent

In this culminating lesson, students use what they learned in this unit to design a tent and determine how much fabric is needed for the tent. The task prompts students to model a situation with the mathematics they know, make assumptions, and plan a path to solve a problem (MP4). It also allows students to choose tools strategically (MP5) and to make a logical argument to support their reasoning (MP3).

The lesson has two parts. In the first part, students learn about the task, gather information, and begin designing. The introduction is important to ensure all students understand the context. Then, after answering some preparatory questions in groups and as a class, students work individually to design and draw their tents. They use their knowledge of area and surface area to calculate and justify an estimate of the amount of fabric needed for their design.

The second part involves reflection and discussion of students’ work. Students explain their work to a partner or small group, discuss and compare their designs, and consider the impact of design decisions on the surface areas of their tents.

Depending on instructional choices made, this lesson could take one or more class meetings. The time estimates are intentionally left blank, as the time needed will vary based on instructional decisions made. It may depend on:

whether students use the provided information about tents and sleeping bags or research this information.
whether the Tent Design Planning Sheet is provided or students organize their work with more autonomy.
expectations around drafting, revising, and the final product.
how student work is ultimately shared with the class (not at all, informally, or with formal presentations).
Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

This lesson should be used after students have completed the introductory Lego EV3 block building.  This lesson wil help students get a better understanding of how to use input and output parameters.  Students will explore and identify previously used software that uses block programming.  Students will connect early interactions in Computer Science programming with the input and output parameters in Math. This lesson review input and output functions associated with the mechanics of a computer

Unit 8: Data Sets and Distributions
Lesson 11: Deviation from the Mean

In a previous lesson, students computed and interpreted distances of data points from the mean. In this lesson, they take that experience to make sense of the formal idea of mean absolute deviation (MAD). Students learn that the MAD is the average distance of data points from the mean. They use their knowledge of how to calculate and interpret the mean to calculate (MP8) and interpret (MP2) the MAD.

Students also learn that we think of the MAD as a measure of variability or a measure of spread of a distribution. They compare distributions with the same mean but different MADs, and recognize that the centers are the same but the distribution with the larger MAD has greater variability or spread.

'Tricks' tap into children's natural curiosity and can provide the motivation for exploring the underlying mathematics in order to unpick how they are done. This Nrich problem explores a "trick" to provide an engaging context in which to explore place value and in particular 'adding nine' as 'adding ten and subtracting one'.

Students have fun creating, sharing and reading their own digital fractions math book created on storyjumper.

e-Learning for Kids is an educational website for kids grades K-5. Lessons are organized by grade level as well as skill topics. Students can easily sort the lessons and then select the lesson they want to work on.

The Nrich problem offers opportunities to think about area, proportion and fractions, while offering an informal introduction to the mathematics of infinity and convergence which would not normally be met by younger students, to tempt their curiosity.

Unit 7: Rational Numbers
Lesson 14: Distances on a Coordinate Plane

In this lesson, students explore ways to find vertical and horizontal distances in the coordinate plane. In the first activity, students use repeated reasoning to explore the relationship between points with opposite coordinates (MP8). In the second activity, students develop strategies for finding the distance between two points where the coordinates might not be integers. Students can use previous strategies, such as considering the distance of a point from zero, or counting squares. Students will use these skills in Grade 7 to find distances on maps. In Grade 8, they will use these skills to draw slope triangles in the coordinate plane and find the lengths of their sides when considering graphs of proportional and non-proportional relationships.

Unit: Area and Surface Area
Lesson 16: Distinguishing Between Surface Area and Volume

In this optional lesson, students distinguish among measures of one-, two-, and three-dimensional attributes and take a closer look at the distinction between surface area and volume (building on students' work in earlier grades). Use this lesson to reinforce the idea that length is a one-dimensional attribute of geometric figures, surface area is a two-dimensional attribute, and volume is a three-dimensional attribute.

By building polyhedra, drawing representations of them, and calculating both surface area and volume, students see that different three-dimensional figures can have the same volume but different surface areas, and vice versa. This is analogous to the fact that two-dimensional figures can have the same area but different perimeters, and vice versa. Students must attend to units of measure throughout the lesson.

Note: Students will need to bring in a personal collection of 10–50 small objects ahead of time for the first lesson of the next unit. Examples include rocks, seashells, trading cards, or coins.

Unit 6: Expressions and Equations
Lesson 9: The Distributive Property, Part 1

This is the first of three lessons about the distributive property. In this lesson students recall the use of rectangle diagrams to represent the distributive property, and work with equations involving the distribute property with both addition and subtraction.

Unit 6: Expressions and Equations
Lesson 10: The Distributive Property, Part 2

The purpose of this lesson is to extend the work with the distributive property in the previous lesson to situations where one of the quantities is represented by a variable, as in 2(a+3) = 2a + 2x3. Students use the same rectangle diagrams as before to represent these situations, reinforcing the idea that the work they do with expressions is simply an extension of the work they previously did with numbers. They see that the distributive property can arise out of writing areas of rectangles in two different ways, which emphasizes the idea of equivalent expressions as being two different ways of writing the same quantity.

Unit 6: Expressions and Equations
Lesson 11: The Distributive Property, Part 3

This is an optional lesson to practice identifying and writing equivalent expressions using the distributive property. If your students don’t need additional practice at this point, this lesson can be skipped (or saved for a review days later) without missing any new material.

Unit 5: Arithmetic in Base Ten
Lesson 13: Dividing Decimals by Decimals

In the previous lesson, students learned how to divide a decimal by a whole number. They also saw that multiplying both the dividend and the divisor by the same power of 10 does not change the quotient. In this lesson, students integrate these two understandings to find the quotient of two decimals. They see that to divide a number by a decimal, they can simply multiply both the dividend and divisor by a power of 10 so that both numbers are whole numbers. Doing so makes it simpler to use long division, or another method, to find the quotient. Students then practice using this principle to divide decimals in both abstract and contextual situations.