Place Value and Decimals
What is 3.407 written in expanded form?
3 × 1 + 4 × 0.1 + 0 × 0.01 + 7 × 0.001
or 3 x .4 + .007
Add: 1/4 + 1/4 = ?
1/2 or 2/4
Evaluate: 8 + 6 × 2 (use order of operations).
8 + (6 × 2) = 8 + 12 = 20 200
Convert 300 centimeters to meters.
3.00 meters
Plot the point (3, 2) in the first quadrant. How far to the right and how far up from the origin is it?
Right 3, up 2
0.376 and 0.37. Use >, =, or <
0.376 > 0.37
Find the area of a rectangle with side lengths 2 1/2 units and 3 units. Show the multiplication as a fraction.
2 1/2 × 3 = 7 1/2 square units (or 15/2)
Evaluate: (9 − 3) × (4 + 2).
(9 − 3) × (4 + 2) = 6 × 6 = 36
A line plot shows pencil lengths: 1/2, 3/4, 1/2, 1/4. What is the total length when all are added? Express as a fraction.
1/2 + 3/4 + 1/2 + 1/4 = (2/4 + 3/4 + 2/4 + 1/4) = 8/4 = 2
A point on a map is at (4, 5). If each unit equals 1 mile, how many miles east and how many miles north is the point from the origin?
4 miles east, 5 miles north
Write the decimal three hundred twenty-five and six hundred twelve thousandths as a numeral.
325,612,400
Solve: 6 ÷ (1/3) = ?
18
A pattern rule: Start at 5 and add 7 each time. What is the 6th number in this sequence?
Sequence: 5, 12, 19, 26, 33, 40 → 6th is 40
Find the volume of a rectangular prism with length 4 units, width 3 units, and height 2 units.
V = 4×3×2 = 24 cubic units
True or false: Every square is a rectangle. Explain.
True. All squares have four right angles and opposite sides equal, so they meet rectangle properties.
Round 4.689 to the nearest tenth and to the nearest whole number.
Nearest tenth 4.7; Nearest whole number: 5
Compute: (2/3) × 9 and explain the meaning of the product in words.
(2/3) × 9 = 6; meaning: two-thirds of nine equals six
Evaluate: 36 ÷ 6 + 4 × 3.
36 ÷ 6 + 4 × 3 = 6 + 12 = 18
A box measures 6 in by 5 in by 2 in. Use V = l × w × h to find its volume. If three identical boxes fit in a larger container, what is the total volume of the three boxes?
6×5×2 = 60 in^3; three boxes → 180 in^3
Classify the figure that has four sides, opposite sides equal, and four right angles. What is it? Explain how it fits into a hierarchy of quadrilaterals.
Rectangle; in hierarchy: quadrilateral → parallelogram → rectangle (and square as a subcategory if sides equal)
Add: 12.305 + 0.799. Write the answer in standard form and explain any place-value regrouping.
12.305 + 0.799 = 13.104
A recipe needs 3/4 cup of sugar. If you want to make half the recipe, how much sugar is needed? Show your work.
(3/4) × 1/2 = 3/8 cup
Write a real-world word problem that requires multiplying a two-digit whole number by a decimal (e.g., $ per unit × units). Then solve it.
If apples cost $1.25 each and you buy 24, total = $1.25 × 24 = $30.00
A solid figure is made of two non-overlapping right rectangular prisms. Prism A: 3×4×2. Prism B: 2×3×3. Find the total volume and show addition of volumes.
Prism A: 3×4×2 = 24; Prism B: 2×3×3 = 18; Total = 42 cubic units
A point is at (6, 3). A second point is at (6, 7). Describe the movement between the points and state whether they lie on the same horizontal or vertical line.
Move up 4 units; same x-coordinate so they lie on a vertical line.