Numbers and Operations
Write this number in expanded form: 4,305.
4,305 = 4,000 + 300 + 0 + 5
How many centimeters are in 2 meters? Write the number and show the unit conversion.
200 cm.
0,1,1,2,0,1,3,1,2,0,1,1,2,1,0,1,1,1,2,0 — what is the mode?
Mode = 1
Name the shape with 4 equal sides and 4 right angles.
Square.
Fill in the blank: 8 × ___ = 64.
8 × 8 = 64.
Multiply: 76 × 4. Show a quick strategy or reasonableness check.
76 × 4 = 304. (70×4=280, 6×4=24, 280+24=304)
A rectangular classroom is 24 feet long and 15 feet wide. What is the perimeter?
Perimeter = 24 +24 + 15+15 = 78 feet.
Make a simple line plot idea: If measurements (in inches) are 6, 6 1/2, 7, 6 1/2, 7 1/4, what fraction increments would you use on the line plot?
Use ticks at 1/4-inch increments (e.g., 6, 6 1/4, 6 1/2, 6 3/4, 7, etc.).
Draw or describe a ray and a line segment. How are they different?
Ray has one endpoint and extends forever in one direction; segment has two endpoints and is finite.
The rule is “Add 3.” Starting at 2, list the first five terms. Identify whether terms alternate odd/even and explain why.
Terms: 2, 5, 8, 11, 14. They alternate even, odd, even, odd — yes, because adding 3 toggles parity each time.
A recipe calls for 3/8 cup of sugar. If you triple the recipe, how much sugar do you need? Give the answer as a fraction and a mixed number if needed.
3/8 × 3 = 9/8 = 1 1/8 cups.
The area of a rectangle is 84 square meters and its length is 12 meters. What is the width?
Width = area ÷ length = 84 ÷ 12 = 7 meters.
The line plot shows lengths: 3/4, 1, 1 1/4, 3/4, 1. Find the difference between the longest and shortest. Show work with fractions.
Longest 1 1/4 (5/4), shortest 3/4. Difference = 5/4 − 3/4 = 2/4 = 1/2.
Identify whether a triangle with angles 90°, 45°, and 45° is isosceles, right, both, or neither. Explain.
Triangle is isosceles (two 45° angles equal) and right (has 90°) — so both.
Write an equation with a letter for the unknown: Mia has 24 marbles. She shares them equally into 6 bags. How many marbles per bag? Then show the division equation.
Equation: 24 ÷ 6 = m or 6 × m = 24. m = 4.
Which is greater: 3/5 or 5/8? Explain how you know (use a comparison method appropriate for grade 4)
Convert to common denominator: 3/5 = 24/40; 5/8 = 25/40. 5/8 is greater
Convert 2 hours and 30 minutes to minutes.
2 hr 30 min = 150 min.
A bar graph shows class scores: 4 students got 90, 6 got 80, 5 got 70, 5 got 60. What is the median score for the class?
Arrange scores (60,60,70,70,70,80,80,80,80,80,80,90,90,90,90) median is middle of 20 values: average of 10th and 11th values = (80+80)/2 = 80
Draw a line of symmetry for a rectangle and for an isosceles triangle. How many lines of symmetry does each have?
Rectangle: 2 lines of symmetry (through midlines); isosceles triangle: 1 line of symmetry (through vertex to base midpoint).
Solve: 5 × n = 135. What is n? Show how you check your answer.
5 × n = 135 → n = 135 ÷ 5 = 27. Check: 5×27=135.
Find all factor pairs of 36. Is 36 prime or composite? Explain.
Factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6). 36 is composite.
Use a protractor: draw or describe how to construct an angle of 135 degrees. Name whether it is acute, right, or obtuse.
135° is obtuse. To construct: draw a baseline ray, place center, measure 135° from baseline with protractor; sketch second ray.
0.62, 0.7, 0.59, 0.62, 0.91. Order all five from least to greatest.
0.59, 0.62, 0.62, 0.7, 0.91. 0.62
Classify this quadrilateral: has one pair of parallel sides, other pair not parallel, and two right angles. Name the figure and explain.
This is a right trapezoid (one pair of parallel sides, two right angles).
Create a number pattern that starts at 10 and follows “multiply by 2, then subtract 3,” for three steps. Write each step as an expression and evaluate.
Start 10. Step1: 10×2−3 = 17. Step2: 17×2−3 = 31. Step3: 31×2−3 = 59. Expressions: (10×2)−3=17, (17×2)−3=31, (31×2)−3=59.