What operation?
A juice box costs $2. You buy 3 juice boxes.
What operation helps you find the total cost?
Multiplication
A student solved: 6 + 4 = 24
What mistake did the student make?
They multiplied instead of adding
What does the word sum mean?
The answer to an addition problem
A gardener picked 426 tomatoes, and on the same clipboard someone wrote Section 12B, and yesterday the gardener picked 389 tomatoes. How many more tomatoes were picked today than yesterday?
TMI: Section 12B
Answer: 426 – 389 = 37
Maria has 5 apples and buys 3 more.
What is the problem asking you to find?
The total number of apples
A recipe uses 4 cups of flour for 2 batches of cookies.
What operation helps you find how many cups are used for 1 batch?
Division
A student wrote: 12 ÷ 3 = 12
What should they have done differently?
They should divide 12 by 3 to get 4
What does product tell you to do?
Multiply
A student counted 1,425 steps on her fitness tracker, but the tracker also displayed battery 13% at the same time. Yesterday she counted 1,098 steps. How many more steps did she take today than yesterday?
TMI: battery 13%
Answer: 1,425 − 1,098 = 327
A ribbon is cut into 4 equal pieces.
What is the question focusing on?
How many pieces each person gets (or the size of each piece)
A movie ticket costs $8.50. You buy 4 tickets.
What information tells you how to find the total cost?
The price of one ticket and the number of tickets
A student evaluated: 3 + 2 × 5 = 25
What rule did the student forget?
Order of operations (multiply before adding)
What is an integer?
A whole number that can be positive, negative, or zero
A freezer showed a temperature of –12°F in the morning. The store record sheet mentioned “Aisle 7B”, and by the afternoon the freezer read –3°F. What is the change in temperature?
TMI: “Aisle 7B”
Answer: –3 − (–12) = +9° increase
Write an expression for: “5 more than a number.”
What are you being asked to represent?
An expression that shows adding 5 to a number
A shirt is $20 and is on sale for 25% off.
What math operation helps you find the discount amount?
Multiplication (finding a percent of a number)
A student simplified: 2(x + 3) = 2x + 3
What is the error?
The 2 must be distributed to both terms (2x + 6)
What does unit rate mean?
A rate with a denominator of 1
A swimmer completed 42.6 laps in practice. Her coach wrote Practice Group C at the top of the sheet, then recorded another day of 39.8 laps. The swimmers also voted on their favorite music playlist, but you only want the difference in laps between days.
TMI: Practice Group C and favorite playlist
Answer: 42.6 − 39.8 = 2.8 laps
A recipe uses a ratio of 3 cups of juice for every 2 cups of soda. If this ratio stays the same, how much juice goes with a set amount of soda?
What is the problem asking for?
The amount of juice that matches the ratio.
A recipe uses a 3:4 ratio of oil to vinegar. You have 18 cups of vinegar and want to scale the recipe while keeping the ratio. Which operation finds how many cups of oil you need?
Multiplication — multiply 18 by (3/4)
A student simplified: x² + x² = x⁴
Why is this incorrect?
You add exponents only when multiplying, not adding like terms
What is an irrational number?
A number that cannot be written as a fraction and has a non-repeating, non-terminating decimal
A space model lists a star count of 7.5×108. Beside the value is a notation Sample Run #24, and below it a student recorded 6.2×107 from a different sample along with a sketch of a telescope. What is the difference in star counts?
TMI: Sample Run #24 and telescope sketch
Answer: 7.5×108−6.2×107=6.88×108
A linear function has a slope of 4 and goes through the point (2, 11). If the function is written as y = 4x + b, what value of b makes the equation true?
The y-intercept.