Lesson 10-1: Math Is Everywhere

Warm-Up 1

A grocery store sells 3 avocados for $2. At that rate, how much would 12 avocados cost?

Hint: This is a ratio problem. Find how many groups of 3 fit into 12, then multiply by the price per group.

✓Correct! 12 ÷ 3 = 4 groups, and 4 × $2 = $8.

✗Not quite. 12 ÷ 3 = 4 groups of avocados. Each group costs $2, so 4 × $2 = $8 (C).

Warm-Up 2

A survey shows that 60% of students prefer pizza for lunch. If there are 40 students, how many prefer pizza?

Hint: To find a percent of a number, convert the percent to a decimal and multiply. 60% = 0.60.

✓Correct! 60% of 40 = 0.60 × 40 = 24 students.

✗Convert 60% to 0.60, then multiply: 0.60 × 40 = 24 students (B).

Practice 1

A recipe calls for 2 cups of flour for every 5 cups of mix. If you want to make 20 cups of mix, how many cups of flour do you need?

Strategy: Set up an equivalent ratio: 2/5 = ?/20. Find what you multiply 5 by to get 20, then do the same to 2.

Cups of flour =

Show your ratio reasoning:

Sentence frame: "Since 5 × ___ = 20, I multiplied 2 × ___ = ___. So I need ___ cups of flour."

✓Correct! 5 × 4 = 20, so 2 × 4 = 8 cups of flour.

✗The scale factor is 20 ÷ 5 = 4. Multiply: 2 × 4 = 8 cups of flour.

Practice 2

A shirt originally costs $25. It is on sale for 20% off. What is the sale price?

Hint: Find 20% of $25 first, then subtract from the original price. 20% = 0.20.

Show your work:

Sentence frame: "20% of $25 is $___, so the sale price is $25 − $___ = $___."

✓Correct! 20% of $25 = $5. Sale price = $25 − $5 = $20.

✗20% of $25 = 0.20 × 25 = $5 discount. $25 − $5 = $20 (C).

Practice 3

Sort each real-world situation into the correct math category.

Remember: A ratio compares two quantities. A statistic describes data (like mean, median, range).

3 wins for every 2 losses

The average test score was 82

$4.50 per gallon

The range of heights is 8 inches

120 miles in 2 hours

The median shoe size is 7

Ratios / Rates

Statistics

✓All correct! Ratios compare quantities or rates. Statistics describe data sets (mean, median, range).

✗Some items are in the wrong group. Ratios compare two quantities; statistics summarize data. Try again!

Practice 4

The data set shows daily high temperatures for one week: 68, 72, 75, 70, 68, 74, 73. What is the median?

Strategy: First, put the numbers in order from least to greatest. The median is the middle value.

Show the ordered list:

Sentence frame: "In order the values are ___. The middle value is ___, so the median is ___."

✓Correct! Ordered: 68, 68, 70, 72, 73, 74, 75. The middle (4th) value is 72.

✗Order the data: 68, 68, 70, 72, 73, 74, 75. The 4th value is the median: 72 (C).

Practice 5

A car travels 180 miles using 6 gallons of gas. What is the car's unit rate in miles per gallon?

Remember: A unit rate tells how much per one unit. Divide the total miles by the total gallons.

Unit rate = miles per gallon

Show your division:

Sentence frame: "I divided ___ miles by ___ gallons and got ___ miles per gallon."

✓Correct! 180 ÷ 6 = 30 miles per gallon.

✗Divide: 180 ÷ 6 = 30 miles per gallon.

Challenge

A store has two deals on trail mix:
Deal A: 3 pounds for $7.50
Deal B: 5 pounds for $11.00
Which deal gives a better price per pound? How much would you save buying 15 pounds with the better deal?

Strategy: Find the unit rate for each deal (price ÷ pounds). Then compare and calculate the total savings on 15 pounds.

Better deal:

Savings on 15 lbs: $

Show your unit rate work:

Sentence frame: "Deal A costs $___ per pound. Deal B costs $___ per pound. The better deal is ___. Buying 15 lbs saves $___. "

✓Correct! Deal A = $2.50/lb, Deal B = $2.20/lb. Deal B is cheaper. Savings: 15 × ($2.50 − $2.20) = 15 × $0.30 = $4.50.

✗Deal A: $7.50 ÷ 3 = $2.50/lb. Deal B: $11 ÷ 5 = $2.20/lb. Deal B is better. Savings: 15 × $0.30 = $4.50.

🟠 Level 0 — Extra Support

Warm-Up

Practice

Challenge