Fractions
If two trapezoids represent 1 whole unit,
Convert From Base 10 Numbers to a Different Base
20 = 110 base 4
15 = 120 base 3
Compute the following mentally: 25, 130 has how many tens in it?
2,513 tens
Solve using column addition:
2590
+ 148
_______
2, 738
Consider the division of 37 by 6. Write four real-life word problems where the answer is 5, the answer is 6, the answer is 1, and the answer is 7.
Many possible responses
If 4 triangles represent 2/3, then what is one whole unit?
6 triangles
Convert From a Number in a Different Base to Base 10
Given 3, 261
+200
-2,000
+20
Overall change, -1, 780
Solve using trade first:
524
- 137
_______
387
Solve pictorially:
2/3 X 7/8
Show visually
For a puzzle design, Alex has 1 hexagon, 2 rhombi, 1 triangle, and 1 trapezoid. Lisa designs her own puzzle using 4/7 of the blocks Alex has. What blocks might Lisa have used?
1 hexagon and 1 rhombus or 8 triangles
Regroup the following group of base blocks as necessary in the given base. First, show the regrouping with circles/arrows, and then redraw with the correct representation. What is the number in base 2?
Base 2
1 cube, 1 Rod, and 3 small cubes (units)
1101 base 2
In the number 6435.7812 the value of the place occupied by the digit 4 is how many times as great as the value of the place occupied by the digit 7?
10^3 times greater or 1,000
Solve using partial products:
45
X 36
_______
1, 620
Solve pictorially:
Angie had 4/7 of a barrel of soap, and used 1/3 of what she had; what part of the barrel did she use?
4/21 of the barrel
Using a discrete model, identify the partition and unit :
Lucy has 1 blue rhombus, two red trapezoids, and one green triangle. This is 2/3 of the amount that Charlie Brown has. What pattern blocks could Charlie Brown have?
6 shapes (a combination of rhombi, trapezoids, and triangles)
Represent each addend in base block pictures. Be sure they all have matching scales. Label place value. Line them up vertically. Show any regrouping with circles/arrows. Draw and write the sum.
410 base 5
0.55, 0, 1, 0.05, 0.5, 0.055
a. Place in order from smallest to largest
c. Represent each using base ten blocks. Use this to compare 0.5 and 0.55
d. Write each number in expanded notation. Use this notation to compare 0.55 and 0.055.
a. 0, 0.05, 0.055, 0.5, 0.55, 1
C and D (show visually)
Solve using partial quotients:
190
÷45
_______
4 remainder 10
Answer each of the following questions and then compare the results.
a. Marty has 6/7 of a bag of candy and gives Jane a third of his candy. How much of a bag of candy does Marty have left?
b. Marty has 6/7 of a bag of candy and gives Jane a third of a bag of candy. How much of a bag of candy does Marty have left?
a. 4/7
b. 11/21
Jacob has a bag of king size candy bars. In the bag, 2/5 of the candy bars are Snickers, and there are 1/2 as many Milky Way bars as Snickers bars. Then, 1/3 of the remaining candy bars are Mars bars, and after that, 1/2 of what’s left are Butterfingers. Finally, there are 4 Kit Kats in the bag. How many of each kind of candy bar are in the bag?
Snickers: 6/15 (12)
Milky Way: 3/15 (6)
Mars: 2/15 (4)
Butter Fingers: 2/15 (4)
Kit-Kats: 2/15 (4)
Represent the minuend in base blocks in place value order. Then cross off the values of the subtrahend. Trade in when necessary. Show the trades. Write the difference
57 base 9
A teacher challenged her class to figure out how many ways the number 238.15 could be thought about. Following are five children’s answers. Indicate whether each child’s reasoning is correct or incorrect. If incorrect, fix and explain.
Austin: 238.15 could be thought about as 23 tens, 8 ones, and 15 tenths
Ally: 238.15 could be thought about as 230 ones and 81.5 tenths
Trish: 238.15 could be thought about as 2381.5 tenths
Dez: 238.15 could be thought about as 2.3815 hundreds
Chuck: 238.15 could be thought about as 238 ones and .15 hundredths
Austin is incorrect (15 hundredths)
Ally is correct
Trish is correct
Dez is correct
Chuck is incorrect (15 hundredths or .15 ones)
Solve in 6 different ways:
37
X 89
_______
3, 293
Jonny has 14/8 pounds of hamburger. Each serving of chili requires 2/4 pound of hamburger. Using the entire hamburger, exactly how many servings of chili can he make?
i. Solve the problem pictorially.
ii. Solve the problem using subtraction
iii. Write an algebraic equation using multiplication that describes the relationship in the problem. Then using this equation, write a corresponding division expression that gives the answer
Show visually