Algebraic Thinking
Write an expression for "the product of 6 and the sum of 4 and 5." (Answer should use parentheses.)
6 (4+5)
On a coordinate grid, point A is at (8, 6). Which directions (right/left, up/down) describe how to get to A from the origin? Give the ordered pair and words.
(8, 6): go right 8, up 6. R
Which decimal is greater than 5.206? Choose from: 5.200, 5.301, 5.026, 5.198. Explain.
5.301
234 divided by 4
58 1/2 or 58.5
Sherry wrote (2 × 16) + 9 for "twice the sum of 16 and 9." Explain the mistake and write the correct expression.
She wrote (2 × 16) + 9 which equals 41; "twice the sum of 16 and 9" is 2 × (16 + 9) = 2 × 25 = 50.
Convert 21.06 ÷ 9. Show the quotient (include work).
2.34
Vernon has points A(2,3), B(2,7), C(6,7). Where must point D be to form a square ABCD? Explain reasoning and give coordinates.
D should be at (6,3) to complete the square. Review this closely for accuracy, especially in math, as AI may have limitations.
Multiply 3,614 × 72. Show the product (use standard algorithm or partial product or area model).
260,208.
Prime factors of 72 as an equation.
2 X 2 X 2 X 3 X 3 = 72
Use the numbers 20, 3, 8, and 1 to make an expression (using operations and parentheses) whose value is less than 100. Show one valid example and evaluate it.
Example: (20 − 8) × (3 − 1) = 12 × 2 = 24 (less than 100).
A rectangular prism has dimensions 15 mm × 9 mm × 10 mm. What is its volume in cubic millimeters? Show work.
1359mm3
Find the volume of a composite display case made of two rectangular prisms stacked: bottom prism 5 ft × 4 ft × 3 ft, top prism 4 ft × 2 ft × 3 ft). Show work and the total volume.
5×4×3 = 60 ft3. Top = 4×2×3 = 24 ft3.
Total = 84 ft3.
Add 6 1/3 hours each day Monday–Thursday. How many hours total? Show work
25 1/3
or 25 hours and 20 minutes (extra 100 points)
220/20
Matt has a quadrilateral with both pairs of opposite sides parallel and equal. Which named figures could it be? Explain using properties (mark all that apply).
A. It could be a rectangle
B. It must be a square
C. It could be a triangle.
D. It must be a parallelogram
E. It could be a rhombus
B. It must be a square
C. It could be a triangle.
E. It could be a rhombus
Jamie walks to school in 3/4 hour each day. Draw a model that shows total hours over 3 days. How many hours did she walk in all. Write the multiplication expression for an extra 100 points
3/4 X 3 =9/4 or 2 1/4 or 2 hours and 15 minutes
Classify the figure: a quadrilateral with both pairs of opposite sides parallel and equal. Which categories does it belong to (parallelogram, rectangle, rhombus, square)? Explain using properties.
all squares are parallelograms and rhombuses
Juan bought 230 muffins at $0.50 each and sold at $1.25 each. How much money will he raise (profit for the party) if he sells all? Show calculations.
172.50 profit
Bought for 115 and sold all for 287.50
10.49
Create a two-step word problem that requires writing and evaluating an expression with parentheses (example: twice the sum of a fraction plus a whole number). Provide the expression and solution
x (y/z + w)= a
A line plot records measurements in eighths (example from the PDF). Given the measurements: 3/8, 1/2, 5/8, 3/8, 7/8, make a line plot, then find the total of all measurements and the average measurement.
2 3/4
Given a rectangular prism 6 in × 4 in × 4 in, students use different methods. Which student methods are correct and why?
A (6X4)+4=28
B (6X4X4)=96
C (6X4) =24 then 24 X4 =96
B and C are both correct
A group of 12 people equally share 3 sandwiches. Draw or describe a model to show each person's share and write an equation for f (fraction per person). Then find f.
Extra 100: Also, if 2 salads are shared by 6 people (equal shares), what fraction of a salad does each of the 6 get? Show work.
3 sandwiches ÷ 12 people = 1/4 each.
Equation: f = 3 ÷ 12 = 1/4.
For salads: 2 salads ÷ 6 people = 1/3 each.
7 and 3/8 subtracted by 4 and 1/2.
2 7/8