Multiplication and Division
Multiplication and Division
Objectives
In this unit, students will explore the operations of multiplication and division. Students will:
- represent and solve problems involving multiplication and division.
- apply the commutative and associative properties to solve problems involving multiplication.
- use inverse operations to determine the missing value in multiplication and division equations.
Essential Questions
- How is mathematics used to quantify, compare, represent, and model numbers?
- How can mathematics support effective communication?
- How are relationships represented mathematically?
- How can expressions, equations, and inequalities be used to quantify, solve, model, and/or analyze mathematical situations?
Related Unit and Lesson Plans
Related Materials & Resources
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
- Single Step Real-World Problem
http://www.beaconlearningcenter.com/WebLessons/CameronsTrip/default.htm
- Multistep Real-World Problems
http://www.prongo.com/farm/game.html http://www.studyzone.org/testprep/math4/d/twostep4p.cfm http://www.mathplayground.com/WordProblemsWithKatie2.html
- Four-Fact Families
http://www.mathcats.com/explore/factfamilies/multinfo.html
- Solving Equations—Challenging
http://www.mathplayground.com/algebraic_reasoning.html
- Properties of Multiplication
http://www.aaamath.com/pro74b-propertiesmult.html
Formative Assessment
-
View
Multiple-Choice Items:
- Tara and her friends are making blankets. They used 4 yards of fabric for each blanket. They made 7 blankets. Which expression can be used to find how many yards of fabric Tara and her friends used in all?
- At the pet shop, there are 20 puppies. The puppies are in 5 cages. The same number of puppies are in each cage. Which expression can be used to find how many puppies are in each cage?
- There are 5 rows of desks in a classroom. There are 7 desks in each row. How many desks are there in the classroom?
A
12
B
35
C
42
D
75
- In the equation
, what is p?
A
7
B
8
C
42
D
54
- In the equation
, what is h?
A
4
B
14
C
40
D
45
- Part of a fact family is shown below.
Which number sentence also belongs in this family?
- Which is equal to
?
- Which is equal to
?
- What is the product of
?
Multiple-Choice Answer Key:
1. A
2. D
3. B
4. B
5. D
6. C
7. C
8. A
9. A
Short-Answer Items:
- There are 48 sheets of colored paper in a pack. There are 6 different colors of paper in the pack. The pack has the same number of sheets of each color.
Write a number sentence to find how many sheets of each color there are. Explain why you chose to multiply or divide.
- Geno found the missing number in the equation
. Geno says 
because 
. What did Geno do wrong? What is the correct answer?
- Rhea is multiplying
. Rhea is trying to multiply 
but this is hard for her. Explain to Rhea an easier way to multiply , Be sure to find the answer for her.
Short-Answer Key and Scoring Rubrics:
- There are 48 sheets of colored paper in a pack. There are 6 different colors of paper in the pack. The pack has the same number of sheets of each color.
Write a number sentence to find how many sheets of each color there are. Explain why you chose to multiply or divide.
The number sentence
will help determine that there are 8 sheets of each color of paper. A correct explanation would include both this number sentence and an explanation that division is used to separate or divide the total number of sheets into equal groups.Points
Description
2
The student writes the correct number sentence and explains that division will separate the 48 sheets of paper into 6 equal groups of 8.
1
The student writes the correct number sentence or explains that division will separate 48 sheets of paper into 6 equal groups.
0
The student does not write the correct number sentence and does not adequately explain why the operation is division.
- Geno found the missing number in the equation . Geno says because . What did Geno do wrong? What is the correct answer?
Geno incorrectly multiplied the values of 2 and 8. Instead, Geno should have used the inverse operation of division and/or used the fact family including
and 
. A correct explanation would include that Geno should have used the inverse operation of division or the four-fact family, and a correct explanation would also include the correct solution 
.Points
Description
2
The student explains using a four-fact family or the inverse operation of division that Geno is incorrect since
and explains that the correct answer is since 
1
The student explains using a four-fact family or the inverse operation of division that Geno is incorrect since
or explains that the correct answer is since 0
The student provides no correct statements about why Geno is incorrect and does not provide the correct answer.
- Rhea is multiplying . Rhea is trying to multiply
but this is hard for her. Explain to Rhea an easier way to multiply , Be sure to find the answer for her.
Rhea could make this product much easier to find if she would multiply the numbers in this order and with these groupings instead:
. The 5 and 2 may be switched and/or the 6 and 7 may be switched. Rhea would then multiply 
and get a product of 420. A correct explanation includes suggesting reordering and regrouping and providing a correct product of 420.Points
Description
2
The student correctly shows or explains the reordering and regrouping and finds the correct product of 420.
1
The student correctly shows or explains the reordering or regrouping, or the student finds the correct product of 420.
0
The student does not correctly explain the regrouping or reordering and does not find the correct product of 420.
Performance Assessment:
Maria and Jakob work together at a pet store where they help care for the animals. There are
8 kittens and 5 puppies at the pet store.- Maria will feed the puppies today. Each puppy eats 2 cups of food each day. How many cups of food does Maria need to feed all of the puppies?
- Jakob has 32 ounces of milk to feed the kittens. Jakob wants to feed each kitten the same amount. How many ounces of milk should Jakob feed each kitten?
- The pet store will sell each puppy for the same price. The pet store will sell the puppies for a total of $750. Write an equation to find the price p of each puppy.
- The pet store sells the kittens for $120 each. Write an equation to find how many kittens k the pet store needs to sell to earn $600.
- The pet store received 2 shipments of food for the puppies. There were 6 boxes of food delivered in each shipment. In each box, there are 8 bags of puppy food. Each bag of puppy food costs $5. The number sentence
can be used to decide how much the pet store paid in all for the puppy food. How much did the pet store pay in all for the puppy food?
Performance Assessment Key:
- Maria will feed the puppies today. Each puppy eats 2 cups of food each day. How many cups of food does Maria need to feed all of the puppies?
- Jakob has 32 ounces of milk to feed the kittens. Jakob wants to feed each kitten the same amount. How many ounces of milk should Jakob feed each kitten?
- The pet store will sell each puppy for the same price. The pet store will sell the puppies for a total of $750. Write an equation to find the price p of each puppy.
- The pet store sells the kittens for $120 each. Write an equation to find how many kittens k the pet store needs to sell to earn $600.
- The pet store received 2 shipments of food for the puppies. There were 6 boxes of food delivered in each shipment. In each box, there are 8 bags of puppy food. Each bag of puppy food costs $5. The number sentence
can be used to decide how much the pet store paid in all for the puppy food. How much did the pet store pay in all for the puppy food?
Performance Assessment Scoring Rubric:
Points
Description
4
- All answers are complete and correct.
- Work is shown and demonstrates clear understanding of solving real-world problems using multiplication and division.
- Advanced understanding of applying multiplication properties is demonstrated.
3
- Most answers are complete and correct.
- Work is shown for most problems and demonstrates some understanding of solving real-world problems using multiplication and division.
- Some understanding of applying multiplication properties is demonstrated.
2
- Many answers are complete and correct.
- Little work is shown, and limited understanding of solving real-world problems using multiplication and division is demonstrated.
- A limited understanding of applying multiplication properties is demonstrated.
1
- Some answers are complete and correct.
- Very little correct work is shown.
- The student’s response demonstrates a very limited understanding of solving real-world problems using multiplication and division and applying multiplication properties.
0
- Very few or no answers are correct.
- No work is attempted, or no work shown is correct.
- The student’s response demonstrates no understanding of solving real-world problems using multiplication and division and no understanding of applying multiplication properties.
06/07/2013
