Running the Track: Standard 8.F.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

So Radical: Standard 8.NS.3 - Understand how to perform operations and simplify radicals with emphasis on square roots.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

Summer Reading: Standard 8.EE.6 (Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b.)
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

Swimming Pool: Standard 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

Videos: Standard 8.EE.5 (Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of the two moving objects has greater speed.).
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

Volleyball Bake Sale: Standard 8.F.1.Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in grade 8.)
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

Why Be Rational?: Standard 8.NS.2 - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
This formative assessment exemplar was created by a team of Utah educators to be used as a resource in the classroom. It was reviewed for appropriateness by a Bias and Sensitivity/Special Education team and by state mathematics leaders. While no assessment is perfect, it is intended to be used as a formative tool that enables teachers to obtain evidence of student learning, identify assets and gaps in that learning, and adjust instruction for the two dimensions that are important for mathematical learning experiences (i.e., Standards for Mathematical Practice, Major Work of the Grade).

TuvaLabs Data Stories provide resources for teachers to engage students in rich discourse about an interesting topic and then allows students to come to conclusions using mathematical reasoning and tools.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

In this task students explore changing areas and patterns of numbers. It is a low floor high ceiling task that can be used with many grade levels. The question posed is : what is the biggest fence that can be made out of 36 pieces of fence?

Our friends at the Monterey Bay Aquarium Research Institute have created an interesting task where they share data they collected from Blue Whales. We send many thanks to the MBARI scientists and the American Museum of Natural History for creating and posting these wonderful resources. This collection of videos, text passages and interactive data graphs will light up minds as students explore data that has been collected to explain what goes on when a Blue Whale is under the surface of the ocean.

Maybe some of you recall from childhood, discovering a set of 6 little cardboard cards filled with numbers that came as a prize in a Cracker Jack Box? I clearly remember the day I got this prize. I was fascinated that it always worked, playing it over and over again with anyone who would engage me. I carried the cards with me everywhere and eventually they ended up wet mush after spinning through the washing machine in the pocket of my pants. Decades later they were reintroduced into my life. It was Christmas day in London and everyone was excited about Òcrackers.Ó I didnÕt understand the excitement until Jo explained that it was a little game between two people where the winner got a prize Ð not food. Guess what prize I won? The 6 cards were back in my life!

This activity provides students an opportunity to go through the data cycle process focusing on a statistical investigative question based on something students would like to learn about themselves. In our day-to-day experiences we are surrounded by variability and this activity provides students an opportunity to formulate a question that can be answered with data, as they collect, consider, and analyze the data and then interpret and communicate their findings. We are thankful for Giorgia Lupi and Stefanie Posavec who shared their Dear Data journey with the world.

At youcubed we are so excited to share this activity derived from a problem in Core-Plus Mathematics, Course 1. The problem included here is from Unit 3, Linear Functions, where students explore a small sample data set from the World Health Organization, Global Health Observatory Data Repository, faostat3.fao.org. We love the use of real data as students work, in this case, with linear functions and data.

This activity allows students to explore how numbers are composed, by having them look at different ways of grouping them. There are many different strategies and methods students can use to come up with a solution. Students can use actual pennies, draw diagrams, and use charts to keep track of their findings. As students explore they will notice many different patterns in the numbers they are exploring.

It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them. It was years later when these Black cabs became important again, as some of the first evidence on the plasticity of brains Ð even adult brains Ð came from studying the brains of drivers of Black cabs in London (see video link below). Researchers found that after their intensive spatial training the brains of the drivers of Black cabs strengthened and grew. Years later I was teaching my freshman class when I met Tessa, who proposed this taxi activity for youcubed.