Prodigy is an online curriculum aligned math practice website. Students complete math tasks and earn play time which is in a video game format. It is an adaptive math program.

Rhyming Words Coding is a cross-curricular lesson designed by an Elementary Computer Resource Teacher to support Math instruction.

(Students will learn how to use directional coding to code a robot. Students will learn how to identify rhyming words. )

“Have you ever followed step by step directions? What happens when you don’t follow them correctly?”

“Can anyone explain what a rhyming word is or can you give us an example?”

“Today we will be using step by step directions and rhyming words”

“Are you ready to see what exciting things we are going to do? “

These materials help educators use literature to get students excited about science, technology, engineering, and math (STEM) by actively involving them in the design thinking process. Each book shares a story where something was built or invented by designing, planning, gathering materials, and creating. There is a book card/lesson plan for each title that includes a maker-STEM connection; pre, during, and post questions; and a design challenge.

This problem gives practice in calculating with percentages. It can be approached by trial and improvement but the equivalence between fractions and percentages is very useful.

Unit 8: Data Sets and Distributions
Lesson 15: Quartiles and Interquartile Range

Previously, students learned about decomposing a data set into two halves and using the halfway point, the median, as a measure of center of the distribution. In this lesson, they learn that they could further decompose a data set—into quarters—and use the quartiles to describe a distribution. They learn that the three quartiles—marking the 25th, 50th, and 75th percentiles—plus the maximum and minimum values of the data set make up a five-number summary.

Students also explore the range and interquartile range (IQR) of a distribution as two ways to measure its spread. Students reason abstractly and quantitatively (MP2) as they find and interpret the IQR as describing the distribution of the middle half of the data. This lesson prepares students to construct box plots in a future lesson.

Reasoning to Find Area: Lesson 3
This lesson is the third of three lessons that use the following principles for reasoning about figures to find area:

If two figures can be placed one on top of the other so that they match up exactly, then they have the same area.
If a figure is composed from pieces that don't overlap, the sum of the areas of the pieces is the area of the figure. If a given figure is decomposed into pieces, then the area of the given figure is the sum of the areas of the pieces.
Following these principles, students can use several strategies to find the area of a figure. They can:

Decompose it into shapes whose areas they can calculate.
Decompose and rearrange it into shapes whose areas they can calculate.
Consider it as a shape with one or more missing pieces, calculate the area of the shape, then subtract the areas of the missing pieces.
Enclose it with a figure whose area they can calculate, consider the result as a region with missing pieces, and find its area using the previous strategy.
Use of these strategies involves looking for and making use of structure (MP7); explaining them involves constructing logical arguments (MP3). For now, rectangles are the only shapes whose areas students know how to calculate, but the strategies will become more powerful as students’ repertoires grow. This lesson includes one figure for which the “enclosing” strategy is appropriate, however, that strategy is not the main focus of the lesson and is not included in the list of strategies at the end.

Unit 2: Introducing Ratios
Lesson 3: Recipes

This is the first of two lessons that develop the idea of equivalent ratios through physical experiences. A key understanding is that if we scale a recipe up (or down) to make multiple batches (or a fraction of a batch), the result will still be “the same” in some meaningful way. Students see this idea in two contexts, taste and color:

In this lesson, a mixture containing two batches of a recipe tastes the same as a mixture containing one batch. For example, 2 cups of water mixed thoroughly with 8 teaspoons of powdered drink mix tastes the same as 1 cup of water mixed with 4 teaspoons of powdered drink mix.
In the next lesson, a mixture containing two batches of a recipe for colored water will produce the same shade of the color as a mixture containing one batch. For example, 10 ml of blue mixed with 30 ml of yellow produces the same shade of green as 5 ml of blue mixed with 15 ml of yellow.
The fact that two equivalent ratios yield the same taste or produce the same color is a physical manifestation of the equivalence of the ratios. In this lesson, students start to use the term equivalent ratios.

Students see that scaling a recipe up (or down) requires multiplying the amount of each ingredient by the same factor, e.g., doubling a recipe means doubling the amount of each ingredient (MP7). They also gain more experience using a discrete diagram as a tool to represent a situation.

An interactive applet and associated web page that show the definition and properties of a rectangle in coordinate geometry. The applet has a rectangle with draggable vertices. As the user re-sizes the rectangle the applet continuously recalculates its width, height and diagonals from the vertex coordinates. Rectangle can be rotated on the plane to show the more complex cases. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a rectangle when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Unit 9: Putting It All Together
Lesson 3: Rectangle Madness

This lesson is optional. In this exploration in pure mathematics, students tackle a series of activities that explore the relationship between the greatest common factor of two numbers and related fractions using a geometric representation. The activities in this lesson build on each other, providing students an opportunity to express the relationship between the greatest common factor of two numbers and related fractions through repeated reasoning (MP8). Thus, the activities should be done in order. Doing all of the activities would take more than a single class period—possibly as many as four. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of problems to get some benefit from the activities in this lesson, although more connections are made the farther one gets. As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

An interactive applet and associated web page showing how to find the area and perimeter of a rectangle from the coordinates of its vertices. The rectangle can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Unit 4: Dividing Fractions
Lesson 13: Rectangles with Fractional Side Lengths

This lesson builds on students’ work on area and fractions in grade 5. Students solve problems involving the relationship between area and side lengths of rectangles, in cases where these measurements can be fractions. Knowing that the area of a rectangle can be found by multiplying its side lengths, and knowing the relationship between multiplication and division, they use division to find an unknown side length when the other side length and the area are given.

This problem would be a good one when doing calculations with fractions. It also requires logical thinking and organizing of results. Different strategies and approaches can be taken: knowledge of addition, or multiples, or an understanding of fractions can be used to arrive at a solution.

An interactive applet and associated web page that show the relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does NOT have a constant area. The applet has a triangle with one vertex draggable and a constant perimeter. As you drag the vertex, it is clear that the area varies, even though the perimeter is constant. Optionally, you can see the path traced by the dragged vertex and see that it forms an ellipse. A link takes you to a page where this effect is exploited to construct an ellipse with string and pins. The applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This Nrich problem offers carefully chosen examples intended to give students the opportunity to prove that any recurring decimal can be written as a fraction. Together with the problems Terminating or Not and Tiny Nines, this problem offers valuable insights into the relationship between fractional and decimal representations.

Unit 8: Data Sets and Distributions
Lesson 3: Representing Data Graphically

In this lesson, students represent distributions of numerical (and optionally categorical) data after organizing them into frequency tables. They construct dot plots for numerical data (and bar graphs for categorical data). Using graphical representations of distributions, they continue to develop a spatial understanding of distributions in preparation for understanding the concepts of “center” and “spread” in future lessons. Students make use of the structure of dot plots (MP7) to describe distributions and draw conclusions about the data.

* This unit is an adaptation of the Everyday Mathematics (EM) Kindergarten Curriculum, 4th Edition, published by McGraw Hill Education.  The source material is copyrighted and all rights are reserved.  With this in mind, only the adaptations will be explored in this document.  To access the Everyday Mathematics curriculum and some online components, your school or district must purchase them from McGraw Hill.

The Everyday Mathematics curriculum does not teach concepts in the historical unit-by-unit format.  Rather, key concepts are introduced and revisited in several units throughout the year.  The focus on returning to concept strands is referred to as "spiralling."  The spiral strand targeted in this unit is focussed on data collection and representation.  Students will learn how to represent data on (and read data from) charts and graphs.

Unit 2: Introducing Ratios
Lesson 2: Representing Ratios with Diagrams

Students used physical objects to learn about ratios in the previous lesson. Here they use diagrams to represent situations involving ratios and continue to develop ratio language. The use of diagrams to represent ratios involves some care so that students can make strategic choices about the tools they use to solve problems. Both the visual and verbal descriptions of ratios demand careful interpretation and use of language (MP6).

Students should see diagrams as a useful and efficient ways to represent ratios. There is not really a right or wrong way to draw a diagram; what is important is that it represents the mathematics and makes sense to the student, and the student can explain how the diagram is being used. However, a goal of this lesson is to help students draw useful diagrams efficiently.

When students are asked to draw diagrams, they often include unnecessary details such as making each cup look like an actual cup, which makes the diagrams inefficient to use for solving problems. Examples of very simple diagrams help guide students toward more abstract representations while still relying on visual or spatial cues to support reasoning.

While students may say “for every 2 cups of juice there is 1 cup of soda,” note that for now, we will not suggest writing the association as 2:1. Equivalent ratios will be carefully developed in upcoming lessons. Diagrams are referred to as "discrete diagrams" in these materials, but students do not need to know this term. In student-facing materials they are simply called "diagrams."

The discrete diagrams in this lesson are meant to reflect the parallel structure of double number lines that students will learn later in the unit. But for now, students do not need to draw them this way as long as they can explain their diagrams and interpret discrete diagrams like the ones shown in the lesson.

Unit 2: Introducing Ratios
Lesson 11: Representing Ratios with Tables

Over the course of this unit, students learn to work with ratios using different representations. They began by using discrete diagrams to represent ratios and to identify equivalent ratios. Later, they reasoned more efficiently about ratios using double number lines. Here, they encounter situations in which using a double number line poses challenges and for which a different representation would be helpful. Students learn to organize a set of equivalent ratios in a table, which is a more abstract but also a more flexible tool for solving problems.

Although different representations are encouraged at different points in the unit, allowing students to use any representation that accurately represents a situation and encouraging them to compare the efficiency of different methods will develop their ability to make strategic choices about representations (MP5). Whatever choices they make, they should be encouraged to explain how their method works in solving a problem.

Learn about the physics of resistance in a wire. Change its resistivity, length, and area to see how they affect the wire's resistance. The sizes of the symbols in the equation change along with the diagram of a wire.

This problem confronts students with the idea that when collecting data to try to answer a question it is important to identify all the relevant variables, and that an over-simplistic analysis with a limited amount of information can lead to the wrong decisions.

The problem also offers the opportunity for students to practice calculating ratios, percentages and proportions.