Addition
Subtraction
Multiplication
Decimals and Fractions
Vocab
100
Use any type of model (strip model, set model, or number line) to show 9 + 14.
Answer: 23
100
Use any model (strip model, set model, or number line) to show 14-9.
Answer: 5
100
Use any multiplication model (strip diagram, array model, or tree/organized list) to solve 56 x 8 in base 10.
Answer: 448
100
Solve 0.74 - 0.59 using any of the decimal models and algorithms. Explain what you used to solve this problem and how you got to the answer.
Answer: 0.15
100
Label the sum, addends, and terms in the equation 10+20.
Answer: 30
Sum= 30
Addends= 10 and 20
200
Use integer chips or a number line (think Mr. Turtle) to model 4+ (-9).
Answer: -5
200
Use integer chips or a number line (think Mr. Turtle) to model (-6) - (-4).
Answer: -2
200
Use any algorithm or model to multiple integers. Solve: 39 x (-17) in base 10. Explain why the answer is positive or negative.
Answer: -663
200
Using any fraction model or algorithm, solve. 2/17 + 3/16.
Answer: 83/272
200
Label the summands, difference, minuend, and subrahend in the equation 20-10.
Answer: 10
Difference= 10
Minuend= 20
Subrahend= 10
Summands refers to the individual numbers or quantities that are being added together to form a sum
300
Use any of the addition algorithms (besides standard) to show 186+57 in base 10. Name and explain the algorithm of your choice.
Answer: 243
Algorithms:
1. Concrete model
2. Partial sums
3. Column-addition
4. Lattice
5. Opposite change rule
300
Use any of the subtraction algorithms (besides standard) to show 186-57 in base 10. Name and explain what algorithm you chose.
Answer: 129
Algorithms:
1. Concrete
2. Left to right
3. Counting up
4. Trades first
5. Equal addition
6. Partial Differences
300
Use any of the multiplication algorithms (concrete, standard, partial products, and lattice) to solve 30 x 45 in base 10. Name the algorithm you chose and explain how to use that algorithm
Answer: 1,350
300
Using decimal squares, solve 3.56 - 1.29. Explain how to use decimal squares to solve this problem.
Answer: 2.27
300
Define closure. Which properties are closed under both addition and subtraction?
Closure: the property of a set where performing an operation on any two elements within that set always results in another element that is also within the set; essentially, the set is "closed" under that operation, meaning the result of the operation stays within the set boundaries
400
Use any of the addition algorithms (besides standard) to show 54+321 in base 6. Name and explain the algorithm of your choice.
Answer: 415
Algorithms:
1. Concrete model
2. Partial sums
3. Column-addition
4. Lattice
5. Opposite change rule
400
Use one of any of the subtraction algorithms (besides standard) to show 326-51 in base 7. Name and explain what algorithm you chose.
Answer: 245
Algorithms:
1. Concrete
2. Left to right
3. Counting up
4. Trades first
5. Equal addition
6. Partial Differences
400
Use any algorithm (besides standard) to do 122 x 112 in base 5. Name the algorithm you chose and explain how to use that algorithm.
Answer: 14214
400
Sarah is planning a weekend road trip. She plans to rent a car, and the rental company charges a flat fee of $40 per day plus $0.15 per mile driven.
- Sarah estimates she will drive about 120 miles during the trip.
- After driving the 120 miles, she decides to extend her rental for another day, which adds an extra flat fee of $40 to her total cost.
Questions:
- Part 1: What will be the total cost of the car rental for the 120-mile trip?
- Part 2: If Sarah extends her rental by one more day, what will the total cost be for the two days and the miles she drove?
- Part 1: The total cost for the 120-mile trip is $58.
- Part 2: The total cost for the trip, including the extra day, is $98.
400
What are the properties of multiplication? Name them and define each term.
1. Communitive property
2. Associative property
3. Identity element
4. Closure
5. Multiplication by 0
6. Distributive
500
Use the opposite change rule to show 123 + 321 in base 4. Explain how to use the opposite change rule.
Answer: 1110
Opposite change: If you subtract a number from one addend and add the same number to the other addend, the sum remains the same.
500
Use the trade's first algorithm to show 123-31 in base 4. Explain what is trades first.
Answer: 32
Trades First: all trades are completed before any subtracting.
500
Use any algorithm (besides standard) to do 123 x 322 in base 4. Name the algorithm you chose and explain how to use that algorithm.
Answer: 120132
500
Amara is preparing a batch of her favorite homemade granola. For the recipe, she needs the following ingredients:
- 2/3 cup of oats
- 1/4 cup of honey
- 3/8 cup of nuts
- 5/6 cup of dried fruits
She wants to make enough granola for a party, so she decides to triple the recipe. After tripling the amounts, Amara realizes that she only has 2 cups of oats and 1 1/2 cups of honey available at home.
- How much of each ingredient will Amara need after tripling the recipe?
- Does Amara have enough oats and honey to follow the tripled recipe? If not, how much more does she need of each?
So after tripling, she will need:
- 2 cups of oats
- 3/4 cup of honey
- 1 1/8 cups of nuts
- 2 1/2 cups of dried fruits
She has enough oats and honey to make the tripled recipe, and she won’t need to buy any more.
500
Define these terms and give an example of each.
1. Multiplication:
2. Product:
3. Factors:
4. Multiple of:
Multiplication is a mathematical operation where you find the "product" of two or more numbers by repeatedly adding one number to itself a specified number of times, essentially representing the process of adding a number multiple times.
Product: The result you get when you multiply two or more numbers together
Factors- A number or algebraic expression that divides another number or expression evenly—i.e., with no remainder
Multiple of—The numbers you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30