Number Sense
Represent and explain: A submarine is at 30 meters below sea level, and a helicopter is 120 meters above sea level. Write each as an integer and explain the meaning of 0 in this situation.
Sub is -30
Helicopter is 120
0 is sea level
Unit rate: If 5 apples cost $3.75, what is the unit price per apple? Show your calculation
$0.75 per apple
Evaluate an expression: Evaluate 3(4)+5
Angle sum idea: A triangle has angles the measure 40 and 65. Find the third angle.
75 degrees
Statistical question: Which of these is a statistical question: "How tall am I?" or "How tall are the students in the class?" Explain why.
How tall am I? is the statistical question because answers would vary.
Opposites on the number line: What is the opposite of −47−47? Then identify the opposite of that opposite and explain why it matches the original number.
47
Opposite of that opposite is −47, which returns to the original number because the opposite of a number is its additive inverse.
Equivalent ratios table: Complete the table for the ratio 2:5
4 : __
10 : __
10
25
Order of operations: Evaluate 2+3×42
50
Volume with fractional edges: Find the volume of a rectangular prism with edges 1/2 m, 3 m, and 2 m.
3 cubic meters
Line plot: Given data of pencil lengths in cm: 8, 9, 8, 7, 9, 10, 8. Create a simple frequency table and identify the mode.
Mode is 8
Ordering rationals: Place these numbers in order from least to greatest:3/4; -0.75 -1.2; 0.
-1.2; -0.75; 0; 3/4
Unit conversions using ratio reasoning: A recipe calls for 3 cups of flour; you need to make one-quarter of the recipe. How many cups of flour are needed? Show work as a fraction and decimal.
3/4 cup of flour
0.75 cup of flour
Properties & equivalent expressions: Use the distributive property to rewrite 5(x+6).
5x+30
Coordinates & distance: On the coordinate plane, point A is (2,−1) and point B is (2,4). Find the distance between A and B
5
Measures of center: For the data set {4, 7, 7, 10, 12}, find the median and mean.
Mean is 8
Absolute value context: A bank account shows a balance of −150 dollars. Write the absolute value and explain what it tells you about the account in dollars.
Shows you the debt (dollars owed) without the sign-the account is overdrawn 150
Rate problem: At a constant speed, a cyclist travels 18 miles in 1.5 hours. How many miles per hour is the cyclist traveling? Then find how far the cyclist will ride in 4 hours at that rate.
12 miles per hour
48 miles
Solve simple equations: Solve x+7=19 and show the steps. Then write a real-world sentence that could be modeled by this equation.
x+12
Real-world sentence example: "I had x stickers, I found 7 more, and now I have 19; how many did I start with?"
Customary/metric conversion: Convert 3 feet to centimeters using the conversion factor 1 inch=2.54 cm and 12 in=1 ft. Show steps.
91.44 cm
What is the definition of mean, median, mode, and range?
Mean-average
Median-middle number when written least to greatest
Mode-the number listed most
Range-largest number - smallest number
Mixed conversion & plotting: Convert 7/10 to a decimal and to a percent, then plot the decimal on a number line from −1 to 1.
0.7 and 70%
Real-world proportional equation: A landscaper charges $12 per hour. Let h be hours worked and C the charge. Write an equation relating C and h.
C=12h
Two-variable proportional situation: A taxi charges a $2 flat fee plus $0.90 per mile. Let C be cost and m miles. Write the equation, then for m=7 evaluate C. Explain which variable is independent and which is dependent.
C=2 + 0.90m
$8.30
independent variable is miles
dependent variable is cost
Conversion within systems: Convert 5 kilometers to meters and then to centimeters. Show steps using unit conversions.
5,000 m
5,000,000 cm
Mixed data problem: A class recorded the number of books read in a month: {0, 1, 2, 3, 4, 4, 5, 10}. Compute the mean and median.
Mean is 3.625
Median is 3.5