SAMPLE - Standards Plus

Teacher Lesson Plan

St. Pg. 21

Standards Plus? ? Mathematics ? Grade 3

Domain: Operations & Algebraic Thinking

Focus: Relating Three Whole Numbers

Lesson: #13

Standard: 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Lesson Objective: The students will determine the related multiplication sentence to the division sentence to help determine the quotient.

Introduction: "Today we will relate three whole numbers to determine the unknown whole number in division."

Instruction: "We can use multiplication and division to help us determine unknown factors. Look at Example A. If we have 12 ? 3 = ?, we can say. `3 times what number equals 12?' (3 x ? = 12) Remember, we use a symbol to represent unknown numbers. By using our understanding of the connection between the two operations, we should be able to recall the missing number 4 to solve this problem."

Guided Practice: "Look at Example B on this page. Let's look at a problem involving an unknown number, 36 ? 4 = ?. We think multiplication to help us

E with finding the quotient. We use a question mark to represent the unknown

factor. Then we can record 4 ? ? = 36 and ? ? 4 = 36. Because we know that

L 36, 4, and 9 are related, we know the quotient is 9."

Independent Practice: "Now you will complete the problems independently.

P Write the number sentences to represent the multiplication equation.

Determine the quotient for each problem."

M Review: Discuss problems with the students. A Closure: "Today we learned how to relate three whole numbers to determine S the unknown whole number in multiplication and division situations."

Answers: 1. ? ? 6 = 42 and 6 ? ? = 42; 7 2. ? ? 8 = 48 and 8 ? ? = 48; 6 3. ? ? 4 = 32 and 4 ? ? = 32; 8

? 2020, 2013 Learning Plus Associates

Student Page

Standards Plus? ? Mathematics ? Grade 3

Domain: Operations & Algebraic Thinking

Focus: Relating Three Whole Numbers

Lesson: #13

Standard: 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Reminders: ? Division is the opposite of Multiplication ? The symbol "?" represents the unknown number

Example A:

Equation: 12 ? 3 = ?

Question: What multiplication facts relate to the unknown answer?

Relate: 3 ? ? = 12 3 ? 4 = 12

Answer: 12 ? 3 = 4

Example B:

Equation: 36 ? 4 = ?

Question: What multiplication facts relate to the unknown answer?

Relate: _______________ ____________

E Answer: 36 ? 4 =

The quotient is: _______________.

L Directions: Write a multiplication equation to help you find the quotient. Write the quotient P for each problem.

1. Equation: 42 ? 6 = ? Question: What multiplication facts relate to the unknown number?

M Relate: ___________ ___________

Answer: 42 ? 6 = ______ The quotient for this problem is: _______________

SA 2. Equation: 48 ? 8 = ?

Question: What multiplication facts relate to the unknown number?

Relate: ___________ ___________

Answer: 48 ? 8 = ______ The quotient for this problem is: _______________

3. Equation: 32 ? 4 = ? Question: What multiplication facts relate to the unknown number? Relate: ___________ ___________ Answer: 32 ? 4 = ______ The quotient for this problem is: _______________

? 2020, 2013 Learning Plus Associates

Teacher Lesson Plan

St. Pg. 22

Standards Plus? ? Mathematics ? Grade 3

Domain: Operations & Algebraic Thinking

Focus: Relating Three Whole Numbers

Lesson: #14

Standard: 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Lesson Objective: The students will determine the whole number in a multiplication or division equation by relating three whole numbers to each other.

Introduction: "Today we will use the equal sign as a symbol to mean the same as, and determine how we use it in multiplication and division."

Instruction: "Sometimes when we multiply or divide, we use different symbols to help us. By knowing the meaning of the symbols, we can understand the equation. In multiplication and division, we can use the equal sign to mean the same as. Look at the definitions at the top of the student page. Equal means that two quantities, expressions, or values are the same. Sometimes when we multiply or divide, we have unknown numbers, so we rewrite the number sentence in a different form without changing its meaning. We represent unknown numbers by using a symbol-such as a question mark, a letter, or a box."

Guided Practice: "Let's look at a problem with an unknown number. Listen as I read the example. Mark has 15 comic books that he bought from three friends. If each friend sold

him the same number of comic books, how many comic books did each of his friends sell to

him? Now we will record the number sentence for the problem. What do we know? Mark

E bought 15 comic books from 3 friends. How do we solve this problem? As I record, you

should record on your paper. We will record the situation as an equation, or 15 ? 3 = ?. We

will also record it as a multiplication equation, ? ? 3 = 15. Remember that we use a symbol

L to represent the unknown number. Today we will use a `?' as our symbol. We will explain

the meaning of the situation as some number times 3 is equal to 15, or 15 divided by three is

equal to some number. Because we know that 3 ? 5 is 15, we know that the missing factor

P is 5. We can record the number 5 as our unknown factor."

Independent Practice: "Now you will complete the problems independently. Read each problem below. Write two equations to represent the situation?multiplication and division.

M Explain the meaning of the equations and the equal sign. Record the unknown number."

You may want to do another problem as guided practice to help students explain the

equations.

A Review: Discuss problems with the students. Allow student volunteers to share their S explanations for each situation and the meaning of the equal sign.

Closure: "Today we used the equal sign to mean the same as, and determined how we use it in multiplication and division."

Answers:

1. ? ? 2 = 6; 6 ? 2 = ?. Some number times 2 is equal to 6 or 6 divided by 2 is equal to some number. ? = 3

2. ? ? 4 = 16; 16 ? 4 = ?; or 16 ? ? = 4. Some number times 4 equals 16 or 16 divided by 4 equals some number. ? = 4

3. ? ? 4 = 5; 4 ? 5 = ?; or ? ? 5 = 4. Four times 5 equals some number. Some number divided by 4 equals 5. ? = 20

? 2020, 2013 Learning Plus Associates

Student Page

Standards Plus? ? Mathematics ? Grade 3

Domain: Operations & Algebraic Thinking

Focus: Relating Three Whole Numbers

Lesson: #14

Standard: 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Equal sign (=) in an equation means the same as. Unknown Numbers are shown by using a symbol (?), a letter, or a box.

Example: Mark has 15 comic books that he bought from three friends. If each friend sold him the

same number of comic books, how many comic books did each of his friends sell to him?

Number Sentences: a)_________________________ b)___________________________

Explain: __________________________________________________________________

_________________________________________________ Unknown Number: _______

Directions: Read each problem below. Write two number sentences to represent the situation?one multiplication and one division. Explain the meaning of the number sentence and the equal sign. Record the unknown number. 1. Vicki bought six cupcakes. Each package of cupcakes had two in it. How many

E packages of cupcakes did Vicki buy? L Number Sentences: a) _________________________ b)_________________________ P Explain: _________________________________________________________________

_________________________________________________ Unknown Number: _______

M 2. Russ bought 16 golf balls to practice his swing. When he bought them they came in packages of 4 golf balls. How many packages of golf balls did Russ buy?

SA Number Sentences: a) _________________________ b)_________________________

Explain: _________________________________________________________________

_________________________________________________ Unknown Number: _______

3. Katrina bought five packages of cracker and cheese sandwiches. Each package had four cracker-and-cheese sandwiches in it. How many cracker-and-cheese sandwiches did Katrina get altogether?

Number Sentences: a) _________________________ b)_________________________ Explain: _________________________________________________________________ _________________________________________________ Unknown Number: _______

? 2020, 2013 Learning Plus Associates

Teacher Lesson Plan

St. Pg. 23

Standards Plus? ? Mathematics ? Grade 3

Domain: Operations & Algebraic Thinking

Focus: Relating Three Whole Numbers

Lesson: #15

Standard: 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Lesson Objective: The students will determine the known and unknown numbers in word problems, write an equation, and solve by relating multiplication and division to each other.

Introduction: "Today we will relate three whole numbers to determine the unknown whole number in multiplication and division."

Instruction: "We can use multiplication and division to help us determine unknown numbers. If we are faced with a situation in which we do not know one number in an operation, we can ask ourselves how those numbers relate. For instance, look at Example A. If we have 3 ? a = 18, we can say 18 ? 3 = a. By using the connection between the two operations, we should be able to recall the missing factor of 6 to solve this problem."

Guided Practice: "Let's look at a problem involving unknown numbers. Listen as I read the problem in Example B. Jeff walks 10 miles each week during P.E. class for the running club. If he walks the same number of miles each day during a five-day week, how many miles will he walk in five days? Think through the problem. What information do we know? Yes, we know that Jeff walked 10 miles and that he walked 5 days per week. As we

E determine information, we will record it on our sheet. (Pause as students write

information.) What information is unknown? (The number of miles he walked each day.) What number sentence represents Jeff's problem? (10 ? 5 = c) What multiplication

L sentence helps us find the unknown? (c ? 5 = 10 or 5 ? c = 10) What is the solution? (Two

miles per day.) Once we know what information is known and unknown, we can use our knowledge of the connection between multiplication and division to help us determine the

P missing information."

Independent Practice: "Now you will complete the problems independently. Read each problem. Record the known and unknown numbers and the equations for each. Record a

M division and multiplication sentence for each one and determine the solution for the

unknown number."

A Review: Discuss problems with the students. S Closure: "Today we related three whole numbers to determine the unknown whole

number in multiplication and division problems."

Answers:

1. Known amounts: oranges = 6? each; Peter spent 30?; Unknown numbers: number of oranges Peter bought; Division equation: 30 ? 6 = ?; Multiplication & number sentence: ? ? 6 = 30 or 6 ? ? = 30; Solution: 5 oranges.

2. Known amounts: Kara walked 5 hours per week, 3 miles per hour; Unknown numbers: total number of miles walked; Division equation: ? ? 5 = 3; Multiplication equation: 5 ? 3 = ? or 3 ? 5 = ?; Solution: 15 miles per week.

3. Known numbers: Juan spent 48? on gumballs; he bought 8 gumballs; Unknown numbers: amount he spent on each gumball; Division equation: 48 ? 8 = ?; Multiplication equation: ? ? 8 = 48 or 8 ? ? = 48; Solution: 6? per gumball.

? 2020, 2013 Learning Plus Associates

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