This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
Material Type: Activity/Lab
The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.
Material Type: Activity/Lab
This problem is a quadratic function example. The other tasks in this set illustrate F.BF.1a in the context of linear (Kimi and Jordan), exponential (Rumors), and rational (Summer Intern) functions.
Material Type: Activity/Lab
In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, tables, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.
Material Type: Activity/Lab
The intent of this problem is to have students think about how function addition works on a fundamental level, so formulas have been omitted on purpose.
Material Type: Activity/Lab
In this task students must figure out how much fresh water you must add to get a particular salt concentration in aquarium water.
Material Type: Activity/Lab
The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view. Instead of giving a starting value and asking for subsequent values, it gives an end value and asks about what happened in the past. The simple first question can generate a surprisingly lively discussion as students often think that the algae will grow linearly.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: What is the last digit of $7^{2011}$? Explain. What are the last two digits of $7^{2011}$? Explain....
Material Type: Activity/Lab
The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow.
Material Type: Activity/Lab
This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Material Type: Activity/Lab
This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: #### Materials * 10-15 quart plastic bags of various counters (different numbers of counters in each bag) * A recording sheet for the activity with pic...
Material Type: Activity/Lab
The purpose of the task is for students to compare signed numbers in a real-world context.
Material Type: Activity/Lab
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Material Type: Activity/Lab
This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. Students then have to use the expression to evaluate the perimeter for specific values of the two variables.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials * Sets of 3-6 "analog clock cards," enough for each student * Sets of 3-6 "digital clock cards," enough for each student * Paper and pencil A...
Material Type: Activity/Lab
This task is to introduce students to the concept of reading an analog clock.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials Set of cards from 1-100, these can be purchased or created using a black marker and index cards Setup Sort the 1-100 cards into sequential gr...
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Take a square with area 1. Divide it into 9 equal-sized squares. Remove the middle one. What is the area of the figure now? Take the remaining 8 square...
Material Type: Activity/Lab
In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.
Material Type: Activity/Lab
