This is a task from the Illustrative Mathematics website that is one …

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: At the beginning of the month, Evan had \$24 in his account at the school bookstore. Use a variable to represent the unknown quantity in each transacti...

This is a task from the Illustrative Mathematics website that is one …

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: Conner and Aaron are working on their homework together to find the distance between two numbers, $a$ and $b$, on a number line. Conner count the units...

This is a task from the Illustrative Mathematics website that is one …

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: Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which runs from east to west. Aakash lives $5 \frac{1}{2}$ blocks to the...

This is a task from the Illustrative Mathematics website that is one …

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: Xiaoli was estimating the difference between two positive numbers $x$ and $y$ (where $x\gt y$). First she rounded $x$ up by a small amount. Then she ro...

This 7th grade Math parent guide explains the content in straightforward terms so they …

This 7th grade Math parent guide explains the content in straightforward terms so they can support their children’s learning at home and will encourage caretaker engagement with lessons.

Our Teacher Guides are meant to support the use of our online …

Our Teacher Guides are meant to support the use of our online course and unit content. Please use these to accompany the use of our content and for ideas to support struggling learners, those needing extension and for additional resources.

The Common Core State Standards (CCSS) videos are designed to support states, …

The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of selected math standards. Each video is an audiovisual resource that focuses on one or more specific standards through examples and illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard, although the examples can be adapted for instructional use.

In this lesson, students recognize that the rules for adding and subtracting …

In this lesson, students recognize that the rules for adding and subtracting integers apply to rational numbers. Given a number line, students use arrows to model rational numbers where the length of the arrow is the absolute value of the rational number and the sign of the rational number is determined by the direction of the arrow with respect to the number line. Students locate the sum p + q of two rational numbers on a number line by placing the tail of the arrow for q at p and locating p + q at the head of the arrow. They create an arrow for the difference p - q by first rewriting the difference as a sum, p + (- q), and then locating the sum.

In this lesson, students use properties of operations to add and subtract …

In this lesson, students use properties of operations to add and subtract rational numbers without the use of a calculator. Students recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of positive numbers only. Students use the commutative and associative properties of addition to rewrite numerical expressions in different forms. They know that the opposite of a sum is the sum of the opposites (e.g., - (3 + (-4)) = -3 + 4.

In this lesson, students use properties of operations to add and subtract …

In this lesson, students use properties of operations to add and subtract rational numbers without the use of a calculator. Students recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of positive numbers only. Students use the commutative and associative properties of addition to rewrite numerical expressions in different forms. They know that the opposite of a sum is the sum of the opposites; e.g., - ( 3 - 4) = -3 + 4.

In this lesson, students understand addition of integers as putting together or …

In this lesson, students understand addition of integers as putting together or counting up, where counting up a negative number of times is counting down. Students use arrows to show the sum of two integers, p + q, on a number line and to show that the sum is distance | q | from p to the right if q is positive and to the left if q is negative. Students refer back to the Integer Game to reinforce their understanding of addition.

In this activity, students will use the CelSheet App that multiplies the …

In this activity, students will use the CelSheet App that multiplies the fraction by “1” to help determine the common denominator. Then they will use what they have learned to add and subtract fractions without the same denominators. As an extension, they will use the LCM command to quickly obtain the best denominator to complete the operations.

This task is appropriate for assessing student's understanding of differences of signed …

This task is appropriate for assessing student's understanding of differences of signed numbers. Because the task asks how many degrees the temperature drops, it is correct to say that "the temperature drops 61.5 degrees." However, some might think that the answer should be that the temperature is "changing -61.5" degrees. Having students write the answer in sentence form will allow teachers to interpret their response in a way that a purely numerical response would not.

The purpose of this task is meant to reinforce students' understanding of …

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Students will use an Integer Card Game that creates a conceptual understanding …

Students will use an Integer Card Game that creates a conceptual understanding of integer operations and serves as a mental model students can rely on during the module. They will build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers.

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