formative assessments unit 2: operations with rational numbers learning target problem error analysis 7 ns 1 i can add and subtract rational numbers. yes no not sure 1. complete the equation to make a true statement. use the number bank to fill in the statement. -7 -4 -2 1 2 3 enter your answers in the boxes: 7 - = 7 + correct incorrect direction error calculation error concept error application error teacher feedback: (enter feedback here) 2 the locations of the values for p and r are shown on the number line. determine the location on the number line that best represents the sum of p + r select a place on the number line to plot the point (click on the image and select edit to plot your point)

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Accepted Answer

### Problem 1:
# Explanation:
## Step1: Recall the rule of subtracting a number is adding its opposite.
We know that $ a - b = a + (-b) $. So for the equation $ 7 - \square = 7 + \square $, let the first blank be $ x $ and the second blank be $ y $. Then $ 7 - x = 7 + y $, which implies $ -x = y $, so $ x=-y $. Looking at the number bank $-7, -4, -2, 1, 2, 3$, we need two numbers where one is the opposite of the other. The pairs are: if we take $ x = 2 $, then $ y=-2 $ (since $ -2 $ is in the number bank) or $ x = 4 $ (but 4 is not in the bank), $ x = 7 $ (7 not in bank). Wait, the number bank has $-2$ and $ 2 $? Wait the number bank is $-7, -4, -2, 1, 2, 3$. So let's check: $ 7 - 2 = 5 $, $ 7 + (-2)=5 $. So the first blank is $ 2 $, the second blank is $ -2 $. Wait, let's verify the rule: $ a - b = a + (-b) $, so $ 7 - b = 7 + (-b) $. So the number we subtract (b) and the number we add (which is -b) should be such that b is in the number bank and -b is also in the number bank. Looking at the number bank, $ b = 2 $, then $ -b=-2 $, both are in the bank. Similarly, $ b = 4 $ (not in bank), $ b=7 $ (not in bank), $ b = 1 $: $ -1 $ not in bank, $ b=3 $: $ -3 $ not in bank, $ b=-2 $: then $ -b = 2 $, so $ 7 - (-2)=9 $, $ 7 + 2 = 9 $. Oh, that's also a solution. Wait, $ 7 - (-2)=7 + 2 $, because subtracting a negative is adding the positive. So let's check both possibilities. Let's see the number bank: $-7, -4, -2, 1, 2, 3$. So if we take the first blank as $-2$, then the second blank is $ 2 $, because $ 7 - (-2)=7 + 2 $. Let's calculate: $ 7 - (-2)=9 $, $ 7 + 2 = 9 $. Correct. Or $ 7 - 2 = 5 $, $ 7 + (-2)=5 $. Both work, but let's check the number bank. The number bank has $-2$ and $ 2 $. So either $ 2 $ and $-2$ or $-2$ and $ 2 $. Let's see the equation: $ 7 - \square = 7 + \square $. Wait, the second square is inside the absolute value? No, the equation is $ 7 - \underline{\quad} = 7 + \underline{\quad} $. Wait, maybe I misread. Wait the equation is $ 7 - \underline{\quad} = 7 + \underline{\quad} $. So according to the rule of subtraction of rational numbers: $ a - b = a + (-b) $, so the number we subtract (b) and the number we add (which is -b) must satisfy that. So if we let the first blank be $ b $, the second blank be $ -b $. So from the number bank, possible $ b $ values where $ -b $ is also in the bank: $ b = 2 $, $ -b=-2 $ (both in bank); $ b=-2 $, $ -b = 2 $ (both in bank); $ b = 4 $ (not in bank), $ b=7 $ (not in bank), $ b=1 $ ($-1$ not in bank), $ b=3 $ ($-3$ not in bank), $ b=-4 $ ($4$ not in bank), $ b=-7 $ ($7$ not in bank). So two possible solutions: $ b = 2 $, $ -b=-2 $ or $ b=-2 $, $ -b = 2 $. Let's check both:

1. $ 7 - 2 = 5 $, $ 7 + (-2)=5 $: correct.
2. $ 7 - (-2)=9 $, $ 7 + 2 = 9 $: correct.

Now, looking at the number bank, both $ 2 $ and $-2$ are present. So we can choose either. Let's pick $ b = 2 $, so first blank is $ 2 $, second blank is $-2$ or $ b=-2 $, first blank is $-2$, second blank is $ 2 $.

### Problem 2:
(Assuming the number line has $ p $ and $ r $ plotted. Let's assume from the partial number line shown: $ p $ is at $-3$ (wait the partial number line at the bottom has marks: let's see the yellow text says "click on the image...", but from the visible part, the number line has marks around -5, -4, -3, -2, -1, 0, 1, 2, 3, 4. Let's assume $ p $ is at $-3$ (the dot labeled $ p $) and $ r $ is at $ 1 $ (the dot labeled $ r $)? Wait no, the visible part: "the locations of the values for p and r are shown on the number line. Determine the location on the number line that best represents the sum of $ p + r $". Let's suppose $ p $ is at $-3$ (since there's a dot near -3) and $ r $ is at $ 1 $ (dot near 1). Then $ p + r=-3 + 1=-2 $. So we plot the point at $-2$ on the number line. Or if $ p $ is at $-2$ and $ r $ is at $ 1 $, then $ p + r=-1 $. Wait, the partial number line has "p" and "r" with p to the left of r. Let's assume the number line has p at $-3$ and r at $ 1 $, so sum is $-2$. Or p at $-4$ and r at $ 0.5 $, sum is $-3.5$, but likely integer values. Since the number bank has integers, maybe p is at $-3$ and r is at $ 1 $, sum $-2$, or p at $-2$ and r at $ 1 $, sum $-1$. But without the exact number line, we can use the rule of adding rational numbers: if $ p $ is negative and $ r $ is positive, the sum is between $ p $ and $ r $ (if $ |p| > |r| $, sum is negative; if $ |p| < |r| $, sum is positive). Suppose $ p=-3 $ and $ r = 1 $, then $ p + r=-2 $, so plot at $-2$.

### For Problem 1 (Final Answer for the equation):
If we take the first blank as $ 2 $ and the second as $-2$ (or vice versa), the equation becomes $ 7 - 2 = 7 + (-2) $ (or $ 7 - (-2)=7 + 2 $). So the answers are $ 2 $ (first box) and $-2$ (second box) or $-2$ (first box) and $ 2 $ (second box).

### For Problem 2 (Final Answer for the sum):
Assuming $ p=-3 $ and $ r = 1 $, the sum $ p + r=-2 $, so we plot the point at $-2$ on the number line. (If the actual positions are different, adjust accordingly, but using the rule of adding a negative and positive number: $ p + r $ is calculated by finding the distance between them. If $ p $ is at $ a $ and $ r $ is at $ b $, then $ p + r=a + b $, plot at $ a + b $ on the number line.)

### Problem 1 Step-by-Step (Revised):
# Explanation:
## Step1: Recall the subtraction rule.
The rule for subtracting a number is $ a - b = a + (-b) $, so $ 7 - b = 7 + (-b) $. We need $ b $ and $ -b $ from the number bank $\{-7, -4, -2, 1, 2, 3\}$.

## Step2: Identify opposite pairs.
Check which number $ b $ has $ -b $ in the bank:
- If $ b = 2 $, then $ -b=-2 $ (both in bank).
- If $ b=-2 $, then $ -b = 2 $ (both in bank).

## Step3: Verify the equation.
For $ b = 2 $: $ 7 - 2 = 5 $ and $ 7 + (-2)=5 $, so $ 7 - 2 = 7 + (-2) $ (true).
For $ b=-2 $: $ 7 - (-2)=9 $ and $ 7 + 2 = 9 $, so $ 7 - (-2)=7 + 2 $ (true).

# Answer (Problem 1):
First box: $ 2 $, Second box: $-2$ (or First box: $-2$, Second box: $ 2 $)

### Problem 2 Step-by-Step (Assuming $ p=-3 $, $ r = 1 $):
# Explanation:
## Step1: Identify $ p $ and $ r $ values.
From the number line, assume $ p=-3 $ (negative, left of zero) and $ r = 1 $ (positive, right of zero).

## Step2: Add the rational numbers.
Using the rule $ a + b $ where $ a=-3 $ and $ b = 1 $, we calculate $ -3 + 1=-2 $ (since we move 1 unit to the right from $-3$ on the number line).

## Step3: Plot the sum.
Plot the point at $-2$ on the number line (the position corresponding to $-2$).

# Answer (Problem 2):
Plot the point at $-2$ on the number line (or the correct position based on actual $ p $ and $ r $ values, e.g., if $ p=-2 $ and $ r = 1 $, plot at $-1$, etc.)

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Recall the rule of subtracting a number is adding its opposite.

Problem 2:

Step1: Recall the subtraction rule.

Step2: Identify opposite pairs.

Step3: Verify the equation.

Step1: Identify \( p \) and \( r \) values.

Step2: Add the rational numbers.

Step3: Plot the sum.

Answer:

Problem 2 Step-by-Step (Assuming \( p=-3 \), \( r = 1 \)):