Place Value & Decimals
Write the decimal 347.392 in expanded form using place values.
300 + 40 + 7 + 0.3 + 0.09 + 0.002 (or equivalent expanded form showing place values)
What is 3/4 X 12? Show a simple example (e.g., 3/4 of a dozen).
1/4
Example: 1/2 of 1/2 dozen = 3 items (or similar reasonable interpretation)
How many cubic units are there in a 1 x 1 x 1 cube?
1 cubic unit
What are the coordinates of the origin in a coordinate plane?
(0, 0)
Which graph type would you use to display measurements of length for several students and why: bar graph, pictograph, or line plot?
Line plot or bar graph, because it shows individual measurements and makes it easy to compare lengths
Round 56.738 to the nearest tenth.
56.7
Compute and simplify: 2/3 x4/5
8/15
Find the volume of a rectangular prism with length 5 units, width 3 units, and height 4 units. Show the multiplication.
5 x 3 x 4 = 60 cubic units
Plot the point (4, 2) in the first quadrant. Explain what the first and second numbers tell you.
Point plotted at 4 units right, 2 units up. First number (x-coordinate) = horizontal position; second number (y-coordinate) = vertical position
Make a line plot (describe it in words) for this data measured in quarters: 1/4, 1/2, 3/4, 1/2. Then say which value appears most often.
Line plot shows: 1/4 (one X), 1/2 (two X's), 3/4 (one X). Most frequent value: 1/2
Explain what multiplying a decimal by 10 does to the decimal point's placement. Give an example using 3.47 x 10.
Multiplying a decimal by 10 moves the decimal point one place to the right. Example: 3.47 × 10 = 34.7
A recipe uses 3/4 cup of sugar. If you make 1/2 of the recipe, how much sugar do you need? Show your work.
3/8 cup
Convert 5 centimeters to meters and write the answer as a decimal.
0.05 meters
Name three attributes that all rectangles have. Then explain why a square is also a rectangle.
Rectangles have 4 sides and 4 right angles. A square is a special rectangle with all four sides equal in length.
After lunch, five students had milk left: 3/4 cup, 1/2 cup, 1/4 cup, 1/2 cup, and 3/4 cup. What is the total amount of milk left? Show addition of fractiorns.
3/4 + 1/2 + 1/4 + 1/2 + 3/4 = 2 3/4 cups
Compare these two decimals using >, =, or <:0.507 ? 0.57. Explain your reasoning.
0.507 < 0.57 (because 0.507 = 0.507 and 0.570 = 0.57, so 507 thousandths is less than 570 thousandths)
Explain why multiplying a number by a fraction less than 1 gives a smaller product. Give a numeric example.
When you multiply by a fraction less than 1, you're taking a part of the original number, making it smaller. Example: 12 × 1/2 = 6 (or similar example)
A right rectangular prism has base area 12 square units and height 5 units. Use a formula to find its volume.
12 x 5 = 60 cubic units
Classify this shape hierarchy: Quadrilaterals → ___________ → Squares. Fill the blank with the correct subcategory and give one attribute.
Quadrilaterals → Rectangles → Squares. Rectangles have 4 right angles and opposite sides equal; squares add the attribute that all sides are equal.
Use operations on fractions to solve: Five beakers contain 1/4, 1/2, 1/8, 3/8, 1/4 cups of liquid. If the total is redistributed equally, how much will be in each beaker?
1/4 + 1/2 + 1/8 + 3/8 + 1/4 = 12/8
12/8 x 1/5 = 12/40 = 3/10 cups per beaker
Convert 5,432 to scientific notation showing powers of 10 (for example: 5 x 10^3 style). Then explain the pattern in decimal placement when multiplying by powers of 10.
5.432 × 10³ (or 5.432 × 10^3). Pattern: Multiplying by 10¹ moves the decimal point to the right one time, 10² moves the decimal point to the right two times, etc.
Divide: 1/3 ÷ 4. Show a visual or numeric explanation and write the result as a fraction.
1/12
Two smaller rectangular prisms are joined to make a larger solid. Prism A is 3x4x2; Prism B is 3x4x5. Find the total volume and show work.
3x4x2=24
3x4x5=60
24+60=84
A point is graphed at (6, 3). A second point is at (6, 7). What is the vertical distance between them? Explain using coordinates.
Vertical distance = 7 - 3 = 4 units (subtract the y-coordinates since x-coordinates are the same)
A word problem: A contractor needs to fill a rectangular box (6 in x 4 in x 5 in) with unit cubes. He also has a smaller box with a volume of 24 cubic inches. How many smaller boxes will fit into the larger box? Show all steps and reasoning.
Large box volume: 6 × 4 × 5 = 120 cubic inches. Number of smaller boxes: 120 ÷ 24 = 5 smaller boxes will fit.