unit 3 standards (student pages 19–24) - mentoring minds · 2018-05-02 · a | ee teacher edition...

MATH | LEVEL 3Teacher Edition Sample Page

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Unit 3 Standards (Student pages 19–24)

California Common Core State Standards for Mathematical Content: 3.OA.A.3

Domain Operations and Algebraic ThinkingCluster Represent and solve problems involving multiplication and division. (Major Cluster)Standard 3.OA.A.3

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Other Standards Addressed in this Unit3.OA.A.1, 3.OA.A.2, 3.OA.A.4, 3.OA.B.5, 3.OA.B.6, 3.OA.C.7

Common Core State Standards for Mathematical Practice Addressed in this UnitMP.1 Make sense of problems and persevere in solving them.MP.2 Reason abstractly and quantitatively.MP.4 Model with mathematics.MP.6 Attend to precision.MP.7 Look for and make use of structure.

Unpacking the StandardsIn grade 2, students used repeated addition to find the total number of objects arranged in rectangular arrays, forming a foundation for multiplication and division. In grade 3, students apply multiplication (up to 10 × 10 ) and division to solve word problems, using a variety of representations including equal groups, arrays, and measurement quantities. Students should be familiar with a problem-solving process as well as applying various strategies to solve word problems. Strategies may include acting out a problem, using real objects or manipulatives, drawing a representational picture, writing an equation, looking for a pattern, etc.

Unit 3

Standard 3.OA.A.3Solve Word Problems: Multiplication and Division


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Getting Started

Introduction ActivityThe teacher reads the book Divide and Ride: Dividing by Stuart J. Murphy and provides counters for student pairs to represent the action in the story. Students create charts showing the carnival rides, the size of groups for each ride, and a division equation representing the number of groups on each ride.

(DOK 2, Bloom’s Level: Application/Apply)

Suggested Formative AssessmentStudents work with partners to discuss the charts they made in the Introduction Activity. Students explain their thinking and share strategies.

The teacher reviews the charts to assess student understanding of the concept of division. The teacher uses results from the Introduction Activity to plan instruction and intervention activities as needed.


Children’s Literature Connections

Amanda Bean’s Amazing Dream: A Mathematical Story – Cindy Neuschwander

The Best of Times: Math Strategies that Multiply – Greg Tang

Divide and Ride: Dividing – Stuart J. Murphy

Each Orange Had 8 Slices: A Counting Book – Paul Giganti, Jr.

The Great Divide: A Mathematical Marathon – Dayle Ann Dodds

The Hershey’s® Milk Chocolate Multiplication Book – Jerry Pallotta

Minnie’s Diner: A Multiplying Menu – Dayle Ann Dodds

Six-Dinner Sid – Inga Moore

One Hundred Hungry Ants – Elinor J. Pinczes

Unit 3



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Vocabulary Focus

The following are essential vocabulary terms for this unit.

array divisor multiply

divide equation product

dividend factor quotient

division multiplication

Vocabulary ActivityTic-Tac-Toe

The teacher displays a large Tic-Tac-Toe grid with a vocabulary word written in each square as shown.

The class divides into two teams, Team X and Team O. After determining the starting team, the first person on that team selects a word on the grid and states the definition of the word. If correct, that team claims the square with their letter, and play passes to the other team. The first team with three marks in a row wins the game.

(DOK 1, Bloom’s Level: Comprehension/Understand)

Suggested Formative Vocabulary AssessmentAfter completing the Vocabulary Activity, the teacher provides index cards on which two statements are printed. Students record the unit vocabulary words below the appropriate statement.

I understand what these words mean.

I still have a dif�cult time understandingthese words.

Based on student responses, the teacher plans additional vocabulary instruction.

(DOK 1, Bloom’s Level: Comprehension/Understand)

Unit 3


array divide dividend

divisor equation factor

multiply product quotient


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Suggested Instructional Activities

1. Students work with partners to find examples of arrays or equal groups in the real world (e.g., desks in rows, date squares on calendars, egg cartons, muffin tins, floor tiles). Students draw pictures or use advertising circulars, catalogs, magazines, or Internet resources to locate pictures of the real-life arrays and/or equal groups. Student pairs create a product, such as a slide show, poster, or booklet, that shows pictures of real-life arrays/equal groups and the multiplication/division equations that the pictures represent. Students then write original word problems to match each picture.

(DOK 3, Bloom’s Level: Synthesis/Create)

2. The teacher creates index cards with a multiplication or division word problem written on each card and distributes the cards to groups of students. Each group gathers the needed materials and determines how to act out the solution to the problem. Groups present word problems to the class. Observers record the appropriate equations on individual dry erase boards. The teacher asks follow-up questions.


3. Students work in pairs to write multiplication word problems involving arrays of items (e.g., a garden with four rows of 8 tomato plants each) or equal groups of items. Students exchange problems and model the array or arrangement, using counters to find the solutions.


4. Students use die-cut shapes or stickers to create pictorial models of multiplication and division situations. Dot labels are an inexpensive way for students to create pictorial representations of word problems. Students may participate in a brainstorming session to generate ideas for “What could a dot label be?” Students use pencils or markers to add details to one-half-inch dot labels to create balloons, cats, cookies, apples, owls, candies, ice cream cones, etc.

Students use the ideas generated to create pictures, write word problems represented by the pictures, and exchange the pictures and problems with other students. Students then solve each other’s word problems and record the equations they used to solve the problems.


Suggested Formative AssessmentThe class discusses various strategies they used to solve multiplication and division word problems (e.g., act it out, draw a picture, look for a pattern, use manipulatives, write an equation). The teacher provides a word problem and directs students to use two different strategies to solve the problem. The teacher observes selected strategies and asks probing questions to assess student proficiency with problem-solving strategies.


Unit 3



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Suggested Reflection/Closure Activity

Students complete a 3-2-1 reflection prompt such as the one below.

Three problem-solving strategies I used today. . .1.2.3.

Two things I found interesting. . .1.2.

One question I still have. . .1.


Suggested Formative AssessmentAfter students complete the Reflection/Closure Activity, the teacher places students in groups of 3–4. Students discuss the third section of the reflection prompt, “One question I still have.” In turn, each student in the group presents his/her question, and the other students in the group provide clarifications or suggestions. Students turn the cards over and record information they think helps them better understand the individual areas of confusion. The teacher monitors student discussions and provides additional input. The teacher then reviews student responses on the 3-2-1 reflection prompts and adjusts instruction and/or provides interventions.


Interventions

1. Students act out problems and talk through the action. As necessary, students and real objects are used to depict the action of the word problem.


2. In small groups, students translate words to pictures by sketching representational pictures (as opposed to illustrating the problem). Students use stick figures, circles, and rectangles to represent objects and actions in word problems.


3. Students draw or find pictures of rectangular arrays (seats in an auditorium, plants in rows). Students use the pictures to create and solve multiplication and division word problems.


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4. The teacher facilitates small group discussions as students work together and discuss various ways a word problem might be solved. Hearing how others think and explaining personal thinking are powerful components of comprehension.


5. Students solve a problem without numbers. This allows students to focus more on the processes and strategies that could be used to find a solution rather than simply manipulating numbers.

Marty and his mom bake cookies. They place the same number of balls of dough on each of the cookie sheets. After the cookies bake, Marty shares them equally among some friends. How many cookies does each friend receive?

The teacher notes that the underlined words in the problem indicate where numbers have been omitted and guides students through the procedures needed to solve each step of the problem, asking probing questions.

• Which operation is needed to find the total number of cookies baked?

• What numbers can be substituted for the underlined words?

• What equation can be used to solve the first step of this problem?

• Which operation is needed to find how many cookies each friend receives?

• What equation can be used to solve this step of the problem?

Students explain their reasoning for each step, supply possible numbers, and solve the problem. The activity may be repeated with similar problems.


Suggested Formative AssessmentThe teacher provides a word problem without numbers to each student in the intervention group. Students individually determine the operations needed based on the words and actions in the problem. Students explain the steps in finding the solution in a one-on-one diagnostic interview with the teacher.

(DOK 3, Bloom’s Level: Analysis/Analyze)

Extending Student Thinking

Students create original board games in which players match multiplication and division word problems with the appropriate equations. Students demonstrate the games to the class, and classmates play the games.

Note: Many board game templates are available at no cost on the Internet.

Note: Teachers should preview Internet websites for appropriate content to ensure that each website meets the instructional goals of the lesson and complies with district/campus guidelines for acceptable use.


Unit 3



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Answer Key and Codings

Page Question Answer DOK Level Bloom’s Original/Revised

19

1 3 × 5 = 15 or 5 x 3 = 15 1 Comprehension/Understand

2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6 × 2 = 12 feet

1 Application/Apply

3 36 ÷ 4 = 9 almonds 1 Comprehension/Understand

4

Answers may vary. Students should draw a picture to represent 30 light bulbs placed in �ve boxes of 6.

30 ÷ 6 = 5 boxes

1 Application/Apply

5 3 × 6 = 18 apples; 18 ÷ 2 = 9 people 2 Application/Apply

20

1 A 1 Comprehension/Understand

2 B and D 2 Application/Apply

3 B 1 Comprehension/Understand

4 C 1 Comprehension/Understand

5 C 2 Application/Apply

21

1 A, B, and C 2 Comprehension/Understand

2 D 1 Comprehension/Understand

3 A 2 Comprehension/Understand


5 A and D 2 Application/Apply

Unit 3



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Answer Key and Codings

Page Question Answer DOK Level Bloom’s Original/Revised

22


2 B, C, D, and F 2 Comprehension/Understand

3 B 2 Application/Apply

4 D 1 Comprehension/Understand

5 4 × 6 = 24 bottles; 24 ÷ 3 = 8 tables 2 Application/Apply

23

1 6 cupcakes 2 Application/Apply

27 rows of 9 = 7 × 9 = 63 cookies63 ÷ 7 = 9 or 63 ÷ 9 = 7

3 Analysis/Analyze

Journal

Answers may vary. Students explain that a factor in a multiplication problem may become the divisor in a division problem.3 × 6 = 18 and 18 ÷ 6 = 3. In the example, the number 6 is a factor in the multiplication fact and a divisor in the division fact.

3 Analysis/Analyze

24Motivation

Station

Results and answers may vary.Students may explain that using multiplication and division facts helps them �nd the relationship between the “You Say” and the “I Say” numbers to discover the secret rule.

3 Application/Apply

Unit 3


MATH | LEVEL 3Student Edition Sample Page

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Name __________________________________________


Standard 3.OA.A.3

1. Bianca organizes her seashell collection in this array.

Write the multiplication equation that represents Bianca’s array.

Answer:

2. Samantha’s frog, Croaker, moves two feet forward each time he hops. Use the number line to show how far Croaker travels in six hops.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

What equation can be used to describe the total distance Croaker travels?

Answer:

3. Anton, Matt, Craig, and Devon equally share the nuts in a can of almonds. The can contains 36 almonds. Write the equation that shows how many almonds each boy receives.

Answer:

4. Two workers at Wiley Light Bulb Company pack 30 light bulbs in boxes. They place six bulbs in each box. Draw a picture to show how many boxes the workers fill.

Write a division equation that describes your picture.

Answer:

5. Marissa purchases three bags of apples. There are six apples in each bag. How many apples does Marissa purchase? Write and solve an equation to find the answer.

Answer:

Marissa then gives two apples to each person in her dance class and has no apples left over. How many people are in Marissa’s dance class? Write and solve an equation to find the answer.

Answer:

Unit 3 Introduction

array division factor product

divide divisor multiplication quotient

dividend equation multiply

Words for the Wise


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Name __________________________________________


Standard 3.OA.A.3

1. Shonda cuts a large pizza into 16 slices. She and her three brothers share the slices equally.

Which equation shows how many slices of pizza each person receives?

A 16 ÷ = 4

B ÷ 4 = 16

C 15 ÷ 3 =

D 16 × 3 =

2. Which two problems can be solved with this equation?

54 ÷ 9 = ?

A There are 54 automobiles and nine trucks on a used car lot. How many vehicles are on the used car lot?

B Tisha needs $54 to purchase a game. She saves $9 each week. How many weeks does Tisha need to save to buy the game?

C The third-grade students take a trip to the science museum in nine buses. Each bus carries 54 students. How many students are on the trip?

D The YMCA forms teams for basketball. Each team has nine players. If 54 children sign up to play, how many teams are formed?

3. At Brooks Grocery Store, there are six types of canned vegetables for sale. There are five rows of canned corn with seven cans in each row as shown in this picture.

Which equation correctly shows how to find the total number of cans of corn for sale?

A 6 × 5 = 30

B 5 × 7 = 35

C 5 × 8 = 40

D 6 × 7 = 42

4. Zack and eight friends are fishing. Each boy catches two fish. How many total fish do Zack and his friends catch?

A 16 C 18

B 17 D 19

5. Emilio makes six short bookmarks and five long bookmarks from a spool of ribbon. The short bookmarks are 6 inches long, and the long bookmarks are 8 inches long. How much ribbon does Emilio use for the short bookmarks?

A 12 in C 36 in

B 25 in D 48 in

Unit 3 Partner Practice


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Name __________________________________________


Standard 3.OA.A.3

1. Armand plays a game. He measures and finds that he can move forward three feet when he takes a giant step. Armand takes several giant steps as shown on this number line.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Select all the equations that can be used to represent the information on the number line.

A 4 × = 12

B 12 ÷ = 3

C 12 ÷ 3 =

D ÷ 4 = 12

E 3 × 12 =

2. Robby has 21 dimes.

He sorts the dimes into seven equal stacks. Which equation shows how many dimes are in each stack?

A 10 × 7 = 70

B 21 + 7 = 28

C 21 − 7 = 14

D 21 ÷ 7 = 3

3. Raymond has 24 flutes and three kazoos. He wants to place the flutes in boxes with four flutes in each box. Which equation shows how many boxes Raymond needs for the flutes?

A 24 ÷ 4 = 6

B 24 ÷ 3 = 8

C 3 × 4 = 12

D 23 + 3 + 4 = 30

4. Helen has five boxes of dog treats. Each box has eight treats and weighs six ounces. How many dog treats does Helen have?

A 19

B 30

C 40

D 48

5. Which two of these problems can be solved using this equation?

72 ÷ 9 =

A There are 72 students in third grade. Coach Stinson puts the students in teams with nine students on each team. How many teams does Coach Stinson form?

B Angela gives each of the 72 students in third grade nine gumdrops. How many total gumdrops does Angela give away?

C Sylvia has 72 baseball cards. She gives nine cards to her brother. How many cards does Sylvia have now?

D Miguel has 72 coins in his collection. He places nine coins on each page of his coin album. How many pages are in Miguel’s coin album?

Unit 3 Independent Practice


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Name __________________________________________


Standard 3.OA.A.3

5. Jenell purchases four cartons of juice with six bottles of juice in each carton. Write an equation that shows how many bottles of juice Jenell purchases.

Answer:

Jenell then shares the juice with her class. She places three bottles of juice on each table and has no bottles left over. Write an equation that can be used to find how many tables are in Jenell’s class.

Answer:

1. Adrian’s scout troop takes a nature hike to the park. They collect 45 leaves and 36 rocks to share equally among nine scouts. Which equation shows how many leaves each scout receives?

A 45 + 36 = 81

B 45 − 36 = 9

C 45 ÷ 9 = 5

D 36 ÷ 9 = 4

2. Taye sets a goal to read a total of 63 books during the 9 months of the school year. He wants to read the same number of books each month.

Select all the equations Taye can use to find the number of books he must read each month in order to meet his goal.

A 9 + 63 =

B 63 ÷ 9 =

C × 9 = 63

D 63 ÷ = 9

E − 9 = 63

F 9 × = 63

3. Which problem can be solved with this equation?

56 ÷ 7 =

A Ariel sells candy bars to raise money for band. She starts with 56 candy bars and sells all but seven bars. How many bars does Ariel sell?

B Mrs. Sorenson has 56 grapes. She shares the grapes equally among her seven children. How many grapes does each child receive?

C In his daily exercise program, Roger completes 56 sit-ups each day. How many sit-ups does Roger complete in seven days?

D On Tuesday morning, 56 animals are at the animal shelter. That afternoon, seven more animals arrive at the shelter. How many animals are at the shelter now?

4. Elroy has a sheet of stickers containing four rows of stickers with eight stickers in each row.

Which equation shows the total number of stickers on the sheet?

A 8 ÷ 4 = 2 C 4 + 8 = 12

B 8 − 4 = 4 D 4 × 8 = 32

Unit 3 Assessment


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Name __________________________________________


Standard 3.OA.A.3 Unit 3 Critical Thinking

1. Camila, Toffer, and Ron bake cupcakes for the bake sale. Ron bakes 9 cupcakes. Toffer bakes twice as many as Ron. The number of cupcakes Toffer bakes is three times as many as Camila bakes. How many cupcakes does Camila bake?

Answer:

2. Shirley makes sugar cookies. She plans to decorate the cookies with icing. Shirley arranges the cookies in five rows of eight cookies to cool as shown.

When Shirley removes the next batch of cookies from the oven, she adds two more rows and one more column to the array of cookies that are cooling. How many cookies are cooling when the new batch is added?

Answer:

Write a division equation that is shown by the new array.

Application

Apply

Analysis

Analyze

How are factors and divisors alike?

________________________________________________________________________________________

________________________________________________________________________________________

________________________________________________________________________________________

Journal Analysis

Analyze


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Name __________________________________________


Standard 3.OA.A.3Unit 3 Motivation Station

You Say, I Say

Play “You Say, I Say” with a partner. Decide which player is player 1 and which is player 2 . In round 1 , player 1 decides on a “secret rule” and records it on a scratch piece of paper so that player 2 cannot see the rule. The rule must be to multiply or divide using a secret number. Player 2 then says and writes a number in the round 1 table in the “You Say” column. Player 1 applies the secret rule to the number and says and writes the resulting number in the “I Say” column. Player 2 then says another number and player 1 responds. Play continues in this manner for up to 5 numbers. At any point, player 2 may try to guess the secret rule. If the first guess is correct, player 2 scores 10 points. If the guess is incorrect, play continues. The next guess is worth 5 points. If player 2 has not identified the rule in five guesses, player 1 reveals the rule and scores 10 points. Players then trade roles for round 2 .

You Say I SayRound 1

I think the secret rule is _____________ .

You Say I SayRound 2

I think the secret rule is _____________ .

You said 7 and I said 56. Do you know my secret rule?

I think I do!Is it multiply

by 8?

How does knowing multiplication and division help you identify the secret rule?

________________________________________________________________________________________

1. Use everyday opportunities such as ordering a pizza to help your child think mathematically. Ask questions such as “If each member of the family eats three slices of pizza, how many slices do we need? There are eight slices per pizza. How many pizzas do we need to buy?”

2. Take advantage of displays in stores to point out multiplication. For example, a card of buttons could have three rows of buttons with two buttons in each row. Help your child see that three rows of buttons times two buttons in each row equals a total of six buttons.

3. Discuss words such as “double,” “twice,” “triple,” “half,” and “third” and how they apply to multiplication and division.

Parent Activities

unit 3 standards (student pages 19–24) - mentoring minds · 2018-05-02 · a | ee teacher edition...

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