Question

basketball bonanza
directions: use the pictures of the basketball scoreboard to answer each question.
questions:

1. what is the difference between the \home\ and \guest\ scores on the scoreboard?
2. what is the average of the two scores?
3. circle all of the following that give the home teams score.

-1+(-5)(-7) -7-(-3)+27 4+(-19)(-2)
50-(-12)-20 3 + 81/2 5-(-36)+1

1. what math can you do to get from 0 points to the guest teams score? be sure to write down each step (there are multiple possible answers that could be correct).

Explanation:

Step1: Find the difference between scores

The home - team score is 42 and the guest - team score is 23. The difference is calculated by subtracting the guest - team score from the home - team score.
$42−23 = 19$

Step2: Calculate the average of the two scores

The formula for the average of two numbers $a$ and $b$ is $\frac{a + b}{2}$. Here, $a = 42$ and $b = 23$. So, $\frac{42+23}{2}=\frac{65}{2}=32.5$

Step3: Evaluate each expression for the home - team score

• For $-1+(-5)(-7)$: First, calculate $(-5)(-7)=35$, then $-1 + 35=34$.
• For $-7-(-3)+27$: First, $-7 + 3+27=-4 + 27 = 23$.
• For $4+(-19)(-2)$: First, $(-19)(-2)=38$, then $4 + 38=42$.
• For $50-(-12)-20$: First, $50 + 12-20=62 - 20 = 42$.
• For $3 + 81/2$: $3+\frac{81}{2}=\frac{6 + 81}{2}=\frac{87}{2}=43.5$.
• For $5-(-36)+1$: First, $5 + 36+1=42$.

The expressions that give the home - team score are $4+(-19)(-2)$, $50-(-12)-20$, $5-(-36)+1$.

Step4: Find ways to get to the guest - team score from 0

One way is $0+23 = 23$. Another way could be $0+(10 + 13)=23$ or $0+(5\times4+3)=23$ etc.

Answer:

1. 19
2. 32.5
3. $4+(-19)(-2)$, $50-(-12)-20$, $5-(-36)+1$
4. $0 + 23$ (and other possible arithmetic combinations that sum to 23)