Check Your Readiness

1.

A dolphin is at the surface of the ocean. What is the dolphin’s elevation?
The dolphin dives 20 feet below the surface of the ocean. What is its new elevation?

Answer:

0 feet
-20 feet

Teaching Notes

In grade 6, students studied elevation as a context for signed numbers. In this unit, they will return to this context.

If most students struggle with this item, launch Activity 3 in Lesson 1 with a review of sea level and elevation since this context will be used throughout the unit. The elevation of the school could be searched and used to engage students in a discussion about why it makes sense geographically, especially if the school is far from the ocean. Pictures or videos highlighting the depth at which different animals hang out in the ocean can also be shown to prompt discussion about feet below sea level.

2.

Place and label the following numbers on the number line.

-1
1.75
-1.75
-2
$\text-2 \frac{1}{2}$
$\text-\frac 5 2$
$\frac{9}{4}$

Answer:

Teaching Notes

This problem has students order and compare signed numbers, including fractions and decimals; this was work that they did in grade 6. In this unit, students will make sense of operations on signed numbers by using number lines to visualize these operations.

If most students struggle with this item, do the optional activity in Lesson 1, Activity 4 “Card Sort with Rational Numbers.” The work with thermometers and vertical number lines in the Warm-up and previous activities can help students recall what they learned about ordering rational numbers in grade 6. Allow students to arrange the cards vertically or horizontally, and discuss how most number lines we see in this unit will be horizontal.

3.

Kiran says that $\text-2 < \text-5$ . Do you agree with Kiran? Explain or show your reasoning.

Answer:

No. Sample reasoning: A number line showing the true ordering of -2 and -5 is drawn, or a response describing how negative numbers with a small magnitude are greater than negative numbers with a large magnitude is given.

Teaching Notes

This is another problem about comparing signed numbers. Student responses should provide insight into the ways in which students are conceptualizing negative numbers and their magnitudes.

If most students struggle with this item, do the optional activity in Lesson 1, Activity 4 “Card Sort with Rational Numbers.” This will give students an opportunity to consider magnitude while ordering integers and rational numbers. Students will continue to work with this concept in future lessons. Students will have more opportunities to work on this skill in Lessons 2 and 3 as well.

4.

Put these numbers in order of their distance from 0 on the number line, starting with the smallest distance:

$\text-26, \:\text-12.7, \:\text-\frac 9 2, \:\frac 2 {100}, \:7, \:11 \frac 1 4, \:\frac {41} 2, \:35$
Find the values of $|\text-12.7|$ and $|11 \frac 1 4|$ .

Answer:

$\frac 2 {100},\, \text-\frac 9 2,\, 7,\, 11 \frac 1 4,\, \text-12.7,\, \frac{41} 2,\, \text-26,\, 35$
$|\text-12.7| = 12.7$ . $|11 \frac 1 4| = 11 \frac 1 4$ .

Teaching Notes

Students are asked to rank numbers according to their magnitude. The concept of magnitude, or distance from zero, is important for students to understand as they make sense of operations on signed numbers. While the main purpose of this problem is to make sure that students recall that “distance from zero” is without regard to sign, the problem will also reveal if students need to practice comparing decimals, fractions, and whole numbers.

If most students struggle with this item, do the optional activity in Lesson 1, Activity 4 “Card Sort with Rational Numbers.” This will give students an opportunity to consider magnitude while ordering integers and rational numbers. Students will continue to work with this concept in future lessons. Students will have more opportunities to work on this skill in Lessons 2 and 3 as well.

5.

Andre received and spent money in the following ways last month. For each example, write a positive or negative number to represent the change in money from his perspective.
1. His uncle gave him $25 as a present.
2. He earned $18 dollars tutoring.
3. He spent $10 on a book.

2. What does 0 mean in this situation?

Answer:

1. 25 or +25
2. 18 or +18
3. -10
That Andre neither received nor spent money.

Teaching Notes

In grade 6, students learned that we often use positive and negative numbers to represent money contexts. Students will return to this context in this unit and develop it further.

If most students struggle with this item, use this problem for some error analysis before doing Lesson 4, Activity 1 “Concert Tickets,” will provide some extra practice with this concept. Another option is to engage students in a shopping role play recording calculations from the perspective of the shopper and the seller.

6.

Plot and label these four points in the coordinate plane. $\displaystyle A(2,3), \:B(\text-2,1), \:C(4,\text-5), \:D(\text-3,\text-5)$
Find the distance between $C$ and $D$ .

Answer:

7 units

Teaching Notes

Graphing in the coordinate plane requires a different kind of visual interpretation of signed numbers: right or left and up or down. Students learned to graph signed numbers on the coordinate plane in grade 6.

If most students struggle with this item, do the optional Lesson 7, Activity 4 “Differences and Distances.” Students will continue thinking about distance (which is unsigned) and difference (which is signed).