Patterns and equations
What is the value of n in: n + 9 = 15?
n = 6
Write this in decimal form: 3 tenths and 7 thousandths.
0.307
What is 1/2 + 1/4? Show your work using a common denominator.
2/4 + 1/4 = 3/4
Convert: 120 centimeters = ? meters
1.2 meters
On a coordinate grid, what are the coordinates of the origin?
(0, 0)
A number pattern starts at 3 and adds 5 each time. What is the 4th number in the pattern?
18 --> (3, 8, 13, 18)
Which is greater: 0.406 or 0.46? Use >, <, or = and explain why.
0.406 < 0.46
Possible Explaination (0.406 = 0.406; 0.46 = 0.460; 460 > 406)
Sara had 2 1/2 yards of ribbon. She used 3/4 of a yard. How much ribbon is left?
2 2/4 − 3/4 = 1 3/4 yards
Here are five pencil lengths in inches: 2, 3, 2, 4, 3. What is the mode? What is the range?
Mode: 2 and 3 (both appear twice; they both occur the most often).
Range: 4 − 2 = 2 inches (subtract the lowest value from the highest value).
Given the following coordinate pair, (3, 2), which number tells you how far to go right? Which tells you how far to go up?
3 = go right (x-axis);
2 = go up (y-axis)
(Remember: run before you rise. Move the ladder, then climb the ladder)
Write an expression for 'a number p multiplied by 6, then add 4.'
(p × 6) + 4
or
6p + 4
Round 5.276 to the nearest tenth. Round it again to the nearest hundredth.
Nearest tenth: 5.3
Nearest hundredth: 5.28
Multiply: 2/5 × 3/4. Draw a model or show your steps.
6/20 or 3/10
What is the volume of a box that is 6 units long, 3 units wide, and 4 units tall? Write the formula and solve.
Volume = l × w × h = 6 × 3 × 4 = 72 cubic units
DOUBLE JEOPARDY!!!
This shape has 4 equal sides and 4 right angles — and it belongs to BOTH the rectangle and parallelogram families.
What is a square?
Jake is saving money. He starts with $12 and earns $8 each week. Write an expression for the total amount after w weeks. How much does he have after 5 weeks?
12 + 8w; after 5 weeks = $52
Multiply 12.3 × 10. Then multiply 12.3 × 100. What pattern do you notice with the decimal point?
12.3 × 10 = 123
12.3 × 100 = 1,230
The decimal moves right one place for each zero.
A recipe needs 3/4 cup of sugar. If you make 2/3 of the recipe, how much sugar do you need?
3/4 × 2/3 = 6/12 = 1/2 cup
A line plot shows these amounts of water (in liters): 1/2, 1/4, 1/2, 3/4, 1/4. If you poured all the water equally into 4 containers, how much would each container get?
Sum: 9/4 liters.
Divide by 4: 9/4 ÷ 4 = 9/16 liter each.
Point A is at (5, 4) and Point B is at (5, 8). Are they connected by a horizontal or vertical line? What is the distance between them?
Vertical line. Distance = 8 − 4 = 4 units.
Two patterns both start at 0. Pattern A adds 3 each time. Pattern B adds 6 each time. List the first 5 terms of each. What do you notice about the relationship between them?
A: 0, 3, 6, 9, 12
B: 0, 6, 12, 18, 24.
Pattern B's terms are always double Pattern A's terms.
A bag of apples weighs 4.8 pounds. If each apple weighs about 0.3 pounds, about how many apples are in the bag?
4.8 ÷ 0.3 = 16 apples
(multiply both by 10 to get rid of the decimal in the divisor: 48 ÷ 3 = 16)
You have 3 1/2 pizzas. Each person gets 1/4 of a pizza. How many people can you feed? Show your work dividing a whole number by a unit fraction.
3 1/2 ÷ 1/4 = 7/2 ÷ 1/4 = 7/2 × 4/1 = 28/2 = 14 people
(Remember: keep, change, flip)
You have a ribbon that is 2.5 meters long. You want to cut it into pieces that are each 25 centimeters long. How many pieces can you cut? Show all your unit conversions.
2.5 m = 250 cm. 250 ÷ 25 = 10 pieces.
On a map grid where each unit equals 1 kilometer, the school is at (2, 3) and the park is at (7, 3). This is the total distance you would walk if you went from school to the park and back.
What is 10 kilometers?