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Grade 4

Mathematics

Unit 2: Performing Multi-Digit Whole Number Addition and Multiplication

Time Frame: Approximately six weeks

Unit Description

This unit develops a more complete understanding of the operations of addition and multiplication. Students learn the multiplication algorithm for up to 4-digit by 1-digit numbers and for 2-digit by 2-digit numbers. This understanding builds on the concepts of place value, multiplication facts, the distributive property and the general concept of multiplication.

Student Understandings

Students will use place value, repeated addition with equal groups, and area to develop a basis for mastery of basic multiplication facts and the standard algorithms for addition and multiplication. Students will use factor pairs and tables to identify and differentiate between prime and composite numbers. Students will solve multiplication problems up to 4-digit by 1-digit numbers and 2-digit by 2-digit numbers. Their work will be based on the concept of multiplication and will use base-ten blocks to model the distributive property. Students will also determine the difference between addition and multiplication problem situations.

Guiding Questions

1. Can students model and represent addition and multiplication with objects and verbal situations?

2. Can students show mastery of the basic facts for multiplication through 12×12 including recognizing the factor pairs of a whole number?

3. Can students identify prime and composite numbers?

4. Can students solve simple whole number sentences having whole number solutions related to the facts?

5. Can students determine the difference between additive comparison and multiplicative comparison types of problems?

6. Can students model multiplication of 2-digit by 1-digit and 2-digit by 2-digit numbers?

7. Can students write a number sentence containing a variable for multiplication?

8. Can students use the multiplication algorithm to solve problems involving up to 4-digit by 1-digit numbers and 2-digit by 2-digit numbers?

9. Can students rewrite products as the sum of two products to illustrate the distributive property of multiplication over addition?

10. Can students identify the different types of addition and multiplication problem situations?

Unit 2 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)

|Grade-Level Expectations |

|GLE # |GLE Text and Benchmarks |

|Number and Number Relations |

|10. |Solve multiplication and division number sentences including interpreting remainders (N-4-E) (A-3-E) |

|Algebra |

|15. |Write number sentences or formulas containing a variable to represent real-life problems (A-1-E) |

|17. |Use manipulatives to represent the distributive property of multiplication over addition to explain |

| |multiplying numbers (A-1-E) (A-2-E) |

|19. |Solve one-step equations with whole number solutions (A-2-E) (N-4-E) |

|Measurement |

|25. |Use estimates and measurements to calculate perimeter and area of |

| |rectangular objects (including squares) in U.S. (including square feet |

| |and metric units (M-3-E) |

|Data Analysis, Probability, and Discrete Math |

|36. |Analyze, describe, interpret, and construct various types of charts and graphs using appropriate titles, |

| |axis labels, scales, and legends (D-2-E) (D-1-E) |

|CCSS for Mathematical Content |

|CCSS # |CCSS Text |

|Operations and Algebraic Thinking |

|4.OA.1 |Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 |

| |times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as |

| |multiplication equations. |

|4.OA.2 |Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and |

| |equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative |

| |comparison from additive comparison |

|4.OA.3 |Solve multistep word problems posed with whole numbers and having whole-number answers using the four |

| |operations, including problems in which remainders must be interpreted. Represent these problems using |

| |equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental|

| |computation and estimation strategies including rounding. |

|4.OA.4 |Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of |

| |each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given |

| |one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. |

|Number and Operations in Base Ten |

|4.NBT.3 |Use place value understanding to round multi-digit whole numbers to any place. |

|4.NBT.4 |Fluently add and subtract multi-digit whole numbers using the standard algorithm. |

|4.NBT.5 |Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit |

| |numbers, using strategies based on place value and the properties of operations. Illustrate and explain the |

| |calculation by using equations, rectangular arrays, and/or area models. |

|ELA CCSS |

|CCSS # |CCSS Text |

|Writing Standards |

|W.4.2 |Write informative/explanatory texts to examine a topic and convey ideas and information clearly. |

| |d. Use precise language and domain-specific vocabulary to inform about or explain the topic. |

|Speaking and Listening Standards |

|SL.4.1 |Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with |

| |diverse partners on grade 5 topics and texts, building on others’ ideas and expressing their own clearly. |

| |Follow agreed-upon rules for discussions and carry out assigned roles. |

| |Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on|

| |the remarks of others. |

| |Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the |

| |discussions. |

Sample Activities

Activity 1: Multiplication Vocabulary Bingo (CCSS: W.4.2d)

Materials List: paper, pencil, index cards, zip lock bag or envelope for the vocabulary cards.

Have students create multiplication vocabulary cards, (view literacy strategy descriptions) for the following terms: addend, sum, factor, product, multiple, array, multiplication, area, distributive property, property of zero, and identity property. Vocabulary cards will help students learn the content-specific terminology necessary for higher order understanding. Each vocabulary card has four parts: the definition, characteristics, an example, and an illustration. These vocabulary cards will be used to play Addition and Multiplication Vocabulary Bingo as well as to serve as future reference cards to deepen the understanding of multiplication.

Vocabulary card example:

|an arrangement a rectangular picture |

|of objects in used to show a |

|rows and columns multiplication problem |

|problem |

|array |

|6 columns |

|( “array”ngement) |

|an arrangement that 3 rows |

|shows multiplication. |

| |

| |

|This is an array for 3 ( 6 = 18. |

To play Addition and Multiplication Bingo:

o Have the students fold a sheet of paper into eighths. Have them choose any of the addition or multiplication vocabulary cards and write one vocabulary word on each space on their paper to create their own bingo card. State the definitions or examples of a vocabulary word. Have the student cross out the corresponding vocabulary word on their card. The first person to cross out their entire bingo card wins.

2013 - 2014

Activity 2: Addition Standard Algorithm (CCSS: 4.NBT.4, SL.4.1b, SL.4.1c)

Materials List: base-ten blocks, pencil, paper

Students will use their knowledge of place value to add 2-digit numbers. Provide the students with base-ten blocks. Begin with 2-digit plus 2-digit problems such as 25 + 18 = n. Have the students write the problem with the variable, n, standing for the unknown sum. Explain to students that a variable is used to stand for an unknown number when solving a number sentence. Model for the students how base-ten blocks can be used in an addition problem. An example of a model for 25 + 18 = n is below:

1. Ask students where they would start to add the problem. Most students will say that eight ones plus five ones is thirteen ones. Ask students when writing the answer if 13 ones can be left in the ones column? (No, thirteen is 1 ten and three ones.) Ask, what should be done? (Exchange ten ones for one ten.) Tell students that the base-ten blocks will be the same as the written answer, 13 = 1 ten + 3 ones.

2. Ask students what they should do with the 13 or 1 ten and 3 ones. (Write a three in the ones place because only one digit can be written in the ones place. The one ten will be placed above the tens place because that is the place value of tens.)

3. Ask students what they should do next. (Add the tens. One tens plus two tens plus one tens is four tens. They will write four tens in the tens place.)

4. Ask the students what is the sum of 25 + 18. (43) Ask, What is the value of the unknown or variable, n? (43) Tell students that they have solved the equation 25 + 18 = n.

Have the students work in pairs to solve 37 + 25 = n using base-ten blocks and paper and pencil. Have each pair orally explain to another pair how they got their answer.

Extend the activity by modeling 3-digit plus 3-digit and 4-digit plus 4-digit problems. Have students work in pairs to solve the problems. Gradually have students work only with pencil and paper and take away the base-ten blocks so they have to rely on their knowledge of place value to explain how they solved the problem.

Activity 3: Talking Calculators (CCSS: 4.OA.4)

Materials List: calculator, pencil, paper

Have students use calculators to find multiples of 2 by pressing 0 + 2 =. Have them record the number on the display bar. Have students continue to hit the = key for 20 more times, each time recording the number in the display bar. Have the students look at the numbers they recorded and make observations. (Possible answers: All the numbers are even. Every number ends in a 2, 4, 6, 8, or 0. You’re counting by 2s.) Discuss how multiplication is the same as repeated addition.

After all observations are made, have students try larger numbers that are even and divide them by 2 on the calculator. Help them discover that all even numbers are divisible by 2. Tell students that the numbers on the display of the calculator were all multiples of 2, that all of those numbers were divisible by 2, and that 2 is a factor of all of those numbers. Repeat this activity for +5 =, +10 =, and +3 =. Remind students that the numbers that appear on the display are the multiples of the number entered.

Example:

|Input for +2 |Output (after pressing =) |

|1 (1 time of pressing = after| 2 |

|+2 was put in) | |

|2 (times of pressing =) | 4 |

|3 | 6 |

Activity 4: Prime and Composite Numbers (GLE: 36; CCSS: 4.OA.4)

Materials List: Prime and Composite Numbers Chart BLM, paper, pencil

Tell students that when any whole numbers are multiplied to create a product, they are called factors of the product. Ask students which numbers are factors of 1. (1 because only 1 ( 1 = 1). Ask students which numbers are factors of 2 (2 and 1 because only 2 ( 1 = 2 and 1 ( 2 = 2). Tell students that if a factor is repeated, it is only counted once. For example for 1, 1 ( 1 = 1, but it has only 1 factor. For 2, 2 ( 1 = 2 and 1 ( 2 = 2, but it has only 1 and 2 as factors. Make sure that students realize that they should not say that 2 has 4 factors. Repeat this process with numbers up to 10. Discuss with students any patterns they see. Do they see that 1 only has 1 factor? Do they see that 2, 3, 5, and 7 have only 2 factors? Do they see that 9 has more than 2 factors even though it is odd? Etc.

Provide students with the Prime and Composite Numbers Chart BLM. Explain to students that this chart organizes frequencies of numbers. In this chart, the numbers at the top represent the number of factors of each whole number. The numbers on the left side are the whole numbers under investigation. Have students use their knowledge of factors to mark the number of factors each whole number has for the numbers 1 – 24.

Have students investigate the chart. Ask questions such as these: What patterns do you see? Which numbers have exactly two factors? (2, 3, 5, 7, 11, 13, 17, 19, 23) Tell students that these numbers are called prime numbers because they have exactly two factors: 1 and the number itself. Which numbers have more than two factors? (4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24) Tell students that these numbers are called composite numbers because they have more than two factors. Are there any numbers that do not fit these criteria? (1) Why does 1 not fit? (1 times itself is itself. 1 has only one factor. In order to be a prime number, a number must have 2 factors, 1 and the number itself.) Are there any patterns with prime numbers? (All prime numbers are odd, except 2, which is even.)

Over the next few days, extend the activity to 100. Ask the same questions about prime, composite, and odd and even numbers.

Activity 5: Additive and Multiplicative Comparison Problems (GLE: 10; CCSS: 4.OA.1, 4OA.2, SL.4.1b, SL.4.1c)

Materials List: paper, pencil, chart paper, markers

Give the students the following two problems:

1. Jack bought a blue hat for $5. Lucy bought a red hat that cost $3 more than Jack’s. How much did Lucy’s hat cost?

2. Jack bought a blue hat for $5. Lucy bought a red hat that cost 3 times more than Jack’s. How much did Lucy’s hat cost?

Ask students questions and chart their answers about both problems. What is each problem asking you? What are the numbers and units you are working with in each problem? What is the difference between the two questions? Have the students create a drawing to represent each problem with a variable for the unknown number.

For example:

Lucy

1.

Jack

$5 + $3 = n

2. Lucy

Jack

$5 ( 3 = n

Discuss with the students the difference between the two drawings. Ask which operation would solve each problem? What part of the problem led you to think that you should use that operation? Tell students that question 1 involves additive comparison. Additive comparison is when a question focuses on the difference between two quantities. In question 1, the focus is the difference between the cost of the blue hat and the red hat. Tell students that question 2 involves multiplicative comparison. Multiplicative comparison focuses on comparing two quantities by showing that one quantity is a specific number of times larger than the other quantity. In this example, the red hat is 3 times as expensive as the blue hat.

Ask students to identify and verbalize which quantity is being multiplied and which number tells how many times. Discuss the difference between the two and why it is important to understand the difference even though the product will be same regardless of the order in which students multiply the factors (The products of 5 times 3 and 3 times 5 are both 15). Give students other sets of questions and go through the same process.

Activity 6: Writing Multiplicative Comparison Problems (CCSS: 4.OA.1, 4.OA.2)

Materials List: paper, pencils

Give the students the following problem:

Zander has 6 markers. His teacher, Ms. Diaz, has 8 times as many markers as Zander. How many markers does Ms. Diaz have?

Review with students what multiplicative comparison is. Have students identify which quantity is being multiplied (Zander’s 6 markers) and which number tells how many times (8 times). Have students write a number sentence to match the word problem. (7 ( 8 = n)

Give the students the following information: The quantity being multiplied is 7 and the number that tells how many times is 3. Have students work in pairs to write a word problem that matches the criteria. Have the students share their word problems with the class. Listen to see if the students matched the numbers to the criteria correctly.

Give the students other criteria to write their own word problems. Have the pairs give their problems to other groups. Have the groups identify which quantity is being multiplied and which number tells how many times. Have the students write a number sentence to match the word problem.

Activity 7: Multiplication Strategies (CCSS: 4.OA.4, NBT.5)

Materials List: chart paper, markers

Have students brainstorm (view literacy strategy descriptions) strategies that help with multiplication. Example: Multiplying by two’s is the same as doubling a number. Use the minute hand on the clock to help you multiply by five. Display the multiplication strategy chart in the room as an easy reference when students are having difficulty. Students should be able to come up with ideas similar to these:

Multiplication Strategies

( 0---Any number multiplied by 0 is 0. Example: 435 ( 0 = 0

( 1---Any number multiplied by 1 is that number. Example: 64 ( 1 = 64

( 2---Any number multiplied by two: just double that number.

Example: 7 ( 2 = (7 + 7 = 14)

or Skip count by 2’s that many times.

Example: 4 ( 2 = (2, 4, 6, 8)

( 3 Any number multiplied by 3: double the factor to be multiplied by three and add that factor to the product. Example: 3 ( 7 = (2 ( 7 = 14 so 14 + 7 = 21)

( 4---Any number multiplied by 4: double the number and double it again.

Example: 4 ( 6 = (You think 2 ( 6 = 12 so 4 ( 6 = 12 + 12 which is 24 because 4 x 6 is the same as 2 ( 6 + 2 ( 6)

( 5---To multiply by five, use the minute hand on the clock.

Example: 8 ( 5 = 40 (The minute hand is on the 8 so it is 40 minutes past the hour.) or Skip count by 5’s that many times.

Example: 8 ( 5 = (5, 10, 15, 20, 25, 30, 35, 40)

( 6--- multiply the factor by 5 instead of 6 and add one more of that factor to the product.

Example: 6 ( 7= (Think 5 ( 7 = 35 so 35 + 7 = 42)

( 7---You only have to learn 7 ( 7 = 49 and 7 ( 8 = 56 All other multiplication facts for 7 you already know. (Because of the commutative property)

( 8---You only have to learn 8 ( 8 = 64 All other multiplication facts for 8 you already know. (Because of the commutative property) Use this poem to help you---8 ( 8 Open the door because I know it’s 64.

( 9---The digits add up to 9 Example: 6 ( 9 = (Think 1 less than 6 is 5. Write 5 down. Now think “What number can I add to 5 to get 9”? (4) Write 4 behind the 5. The answer is 6 ( 9 = 54 (Because 5 + 4 = 9)

or

Hand jive---Place your hands on a flat surface. Look at the multiplication sentence, example 4 ( 9. Start with your pinky and count the number that is being multiplied by nine (4). Fold your fourth finger under. Count the number of fingers in front of your fourth finger (3); put that number in the tens place. Count the number of fingers behind your fourth finger (6); that number is in the ones place so 4 ( 9 = 36

or

Think Ten ---Example: 6 ( 9 = (Think 6 ( 10 = 60 so 60 – 6 = 54)

( 10---Add a 0 behind the number you are multiplying. Ex.: 6 x 10 = 6 with a 0 behind it. (60) Think of 10 as a dime and count the number of dimes you are multiplying 10 by. Example: 4 ( 10 = 4 dimes

Activity 8: Multiplication Wheels (GLEs: 19; CCSS: 4.OA.4)

Materials List: Multiplication Wheels BLM (2 pages), scissors, dry erase markers, glue

Laminate the two pages of the Multiplication Wheels BLM: a large circle and a medium-sized circle. Use a different color of construction paper for each circle. Have students cut out the two circles. Have students write the numbers 0 through 12 along the edge of the medium circle (as if on a clock). Have them glue the medium circle on top of the large circle. When the circles are ready to use, tell students to write a number (factor) in the small center circle with an erasable marker. Have students complete their wheels by writing the product of the two factors on the outer segment of the wheel. Example: The student puts a 6 in the middle circle, thinks 6 ( 9, and writes 54 in the outer circle. Have students erase the numbers from the circle. Give the students another number to write in the small center circle and repeat the process.

Activity 9: Domino Games (CCSS: 4.OA.4)

Materials List: dominoes or make dominoes on card stock (a template can be found at this site: ), manipulatives (beans, cubes, chips), calculator, pencil, paper

Use dominoes in a variety of games to practice multiplication facts. The two numbers on the domino tiles will be the factors. Have students draw a tile and state the product. The person having the largest product gets a point. Have students write the number sentence and record the points in a chart. An incorrect answer causes a person to lose his/her turn. If the other person can state the correct answer, he steals that point and then takes his regular turn. Make sure that manipulatives such as cubes, beans, or chips are available for students to use to determine the products, if needed. A calculator should also be made available to check answers when there is a disagreement. The student who has the most points when time is up wins.

2013-14

Activity 10: Multiplication Stories (CCSS: 4.OA.3, W.4.2d)

Materials List: Each Orange Has Eight Slices, paper, pencils, crayons (for illustrating books)

Read the story, Each Orange Has Eight Slices by Paul Giganti, Jr., or a similar book. Discuss the different multiplication stories from the book along with other real-life multiplication stories. Have students work in groups of four to construct their own multiplication text chain (view literacy strategy descriptions) using the book Each Orange Has Eight Slices as a model. The first person will write the first page, and then pass it on to the next person to add a page. They will continue taking turns writing a page until the book is complete. Have each group choose a topic to write about before beginning their text chain to ensure a variety of stories. Have each group share their book with the class and then place them in a center for students to read again and again. The real-world application of multiplication shown in the text chains will help to give relevance to multiplication.

For example, one group might write the following page, and then pass it on to another group to write the next page in the text chain:

Student 1. When I went into the classroom, I saw 4 table groups.

Student 2. Each table group had 6 desks.

Student 3. Each desk had 3 books.

Student 4 would write the questions: How many table groups are there? How many desks are there in all? How many books are there in all?

Activity 11: Understanding Multiplication I (GLEs: 17; CCSS: 4.NBT.5)

Materials List: pencil, paper, Grid Paper BLM

Provide students with the Grid paper BLM on which to draw arrays. Have students create an array for the expression, 3 × 12. Have students break the arrays along place value lines.

For example 3 × 12 would look like the following:

10 + 2

* * * * * * * * * * |* *

3 * * * * * * * * * * |* *

* * * * * * * * * * |* *

Tell students that in the array, the tens are to the left of the vertical lines and the ones are to the right. There are three rows since the multiplier is 3. Help students to see that 3 × 12 = 3 × (10 + 2) = 3 × 10 + 3 × 2 = 30 + 6 = 36. Note that the arrays could be broken in other ways. For example, instead of the array 3 × (10 + 2), 3 × (7 + 5) could have been used. A discussion could ensue about why it is easier to break the arrays along place value lines using tens. Repeat this activity with other 2-digit by 1-digit multiplication problems.

o Students, along with the teacher, will create a chart to help them better understand multiplication. Give students a chart with plenty of rows and columns. Have students write the important terms in the columns. Once the chart is formed, have the students suggest 2-digit by 1-digit multiplication problems to be used in the grid. Students can continue to build the multiplication problems using the base-10 blocks or draw the corresponding array on grid paper, if needed.

o Have students look at both factors of the expression. Have students break down each of the factors into expanded form so that it will be easier for them to see how the factors are distributed. Once the grid is completed, allow time for students to review the newly learned concepts individually and with a partner. This review should be done in preparation for other class activities and quizzes.

Example:

|Multiplication problem |Break down the factor on the|Break down the factor on |Write the expression so that all |

| |left into expanded form |the right into expanded |of the numbers on both sides are |

| | |form |multiplied together. |

|5 ( 26 |5 |20 + 6 |(5 ( 20) + (5 ( 6) |

|8 ( 12 |8 |10 + 2 |(8 ( 10) + (8 ( 2) |

|15 ( 6 |10 + 5 |6 |(10 ( 6) + (5 ( 6) |

Activity 12: Understanding Multiplication II (GLE: 17; CCSS: 4.NBT.5)

Materials List: base 10 blocks or Grid Paper BLM, pencil, paper

Extend Activity 11 to 3-digit by 1-digit and 2-digit by 2-digit multiplication problems. Instead of dot arrays, have students draw rectangles or use base 10 blocks to show the problems. Make sure the rectangles are broken along place value lines for both numbers. Repeat this activity several times with various multiplication problems. Notice the use of the distributive property: Think of 11 as 10 + 1 and 52 as 50 + 2. Multiply 10 × 50 and 10 × 2. Then multiply 1 × 50 and 1 × 2. Add the partial products together to get the final product. Give students many opportunities for continued practice.

For example, 11 × 52 would be represented as:

[pic]

Show the students that the following algorithm can also represent their work:

52

( 11

2

50

20

500

--------

572

Give students additional problems to solve using this method.

Activity 13: Rectangular Sections Multiplication (GLEs: 10; CCSS: 4.NBT.5, W.4.2d)

Materials List: pencil, paper

Give students the problem 25 ( 24 = n. Model for students how to solve this problem using rectangular sections multiplication instead of the traditional multiplication algorithm. Have students practice this process with additional multi-digit number sentences.

For example:

Tell students the following: Start by multiplying 20 ( 20. Put the product (400) in the corresponding box. Continue to multiply the rest of the rows and columns. When the products have been placed in each box, add up each row. (400 + 100 = 500; 80 + 20 = 100) Alternatively, each of the columns can be added. (400 + 80 = 480; 100 + 20 = 120) Complete the problem by adding the sums of each row or each column. (500 + 100 = 600 or 480 + 120 = 600). 25 ( 24 = 600. n = 600)

20 5

20 400 100 500

4 80 20 100

480 + 120 600

When students become proficient at using this form of multiplication, have students participate in RAFT writing (view literacy strategy descriptions). RAFT writing gives students an additional opportunity to extend their understandings. Students express their understandings of the content from a unique perspective. From these perspectives, students explain processes for solving a problem. Students’ writing should be both creative and informative. Explain to students what the acronyms of RAFT stands for:

R – Role; A – Audience: F – Form; T – Topic. For this assignment, the RAFT will be:

R – The Rectangular Sections Model

A – The Standard Multiplication Algorithm

F – Letter

T – Why am I, the rectangular sections model, easier to use? How do you use me?

Have students work individually or with partners to write their RAFT explaining to the standard multiplication algorithm how to use the matrix model and why it is easier to use for multi-digit factors. When they finish, have students share their RAFTs with a group or the whole class. Have students listen for accuracy and logic. Listen to your students’ thoughts on the RAFT’s being read to assess the students’ understanding of the topic.

Activity 14: Higher or Lower? (GLEs: 10; CCSS: 4.NBT.3, 4.NBT.5, SL.4.1b, SL.4.1c; SL.4.1d)

Materials List: index cards with multiplication problems, calculators, paper, pencil

Prepare several multiplication problems using 2-digit by 1-digit, 2-digit by 2-digit, 3-digit by 1-digit, or 4-digit by 1-digit number sentences on index cards. Have students draw number lines to show how they will round in order to estimate the product. Have them write their estimated product on the card. Then choose one student to come up to be the “Professor” to play professor know-it-all (view literacy strategy descriptions). Professor know-it-all is a strategy that makes students the “experts” on topics to inform their peers. It allows the students to challenge and hold the “expert” accountable for the material. It also teaches the other students to ask a variety of questions and actively participate in the review process.

Have the “Professor” draw a card and write the multiplication problem on the board. Have the student explain how they rounded and estimated on the card. Have him/her say if the given answer is higher or lower than the exact answer. Have the class use paper/pencil, mental math, or the calculator to check for the correctness of this answer. Include several cards where the exact answer can be found using mental math strategies and several where the computation strategy would require using a calculator. Have students compare the strategies. Engage students in a discussion about when the appropriate calculation strategy may be a calculator, mental math, or paper/pencil. (This game should be played more than once.)

For example, The “Professor” pulls the following card:

| |

|345 |

|( 23 |

| |

|Answer: 600 |

“The Professor” writes the problem on the board and says, “The estimated product is 600 on the card. I think that answer is lower than the exact answer because 300 ( 20 would be 600. 345 is closer to 300 than 400 on the number line so I rounded to 300. 345 is more than 300 and 23 is more than 20, so the exact answer is higher.”

2013-14

Activity 15: Types of Addition and Multiplication Problems (CCSS: 4.OA.3)

Materials List: Types of Addition and Multiplication Problems BLM, paper, pencils,

Using the Types of Addition and Multiplication Problems BLM, have students complete a modified word grid (view literacy strategy descriptions) for a variety of addition and multiplication problems. Discuss the differences among the problems. Ask students what the questions are asking and what the different methods are for answering the questions. Work together with students to complete the word grid so that students will better understand addition and multiplication problems. Have students write the equation for the question in the appropriate box. Once the word grid is formed, give the students other problems. Have students draw models of the problems, write an equation describing the problem, solve them, and mark on their word grid which type of problem each problem was. In this way, the completed grid can serve as a review tool for students in preparation for quizzes and other assignments.

Activity 16: Area of a Rectangle (GLEs: 25)

Materials list: Grid Paper BLM, base-ten blocks, pencils

In this activity, have students explore how to find area. Have the students work in groups and provide each group with base-ten blocks and several sheets of the Grid Paper BLM.

Give the students the following problem: With all of the new cell phones on the market, you want to find the one with the biggest screen. One of the phones has a screen that is 7 centimeters long and 9 centimeters wide. What is the area of the screen? (63 square centimeters)

Discuss with students how an area problem is like an array problem. Have students use the base-ten blocks or the grid paper to construct or draw what they think the new screen will look like. Some may show a 7 by 9 array with base-ten blocks or some may draw a 7 by 9 rectangle. Discuss how their demonstrations represent the area of the screen. Ask them what mathematical expression they could use to represent this problem (7 cm ( 9 cm) Tell them that the formula for the area of a rectangle is Length x Width = Area. Discussion of the process and the results is critical. Give other real-life problems to find the area. Limit your lengths to 30 units if students are using base-ten blocks. At this point, give the students a few problems that use units other than centimeters. Explain that the grid paper can be used for other units as long as students use a key to represent that one cube equals whatever square unit the problem calls for. Challenge students to use both the base-ten blocks and the grid paper to create the expressions and find the area. Discuss the strategies students used throughout the lesson.

Activity 17: Turn the Table (GLE: 10; CCSS: 4.NBT. 5, W.4.2d)

Materials List: index cards with scenarios and multiplication problems, paper, pencil,

Student groups will create a math text chain (view literacy strategy descriptions) that can be solved by the given multiplication problems. Put students into cooperative groups of three students. Give each group a selection of multiplication statements that include 2-digit by 1-digit, 3-digit by 1-digit, 4-digit by 1-digit, and 2-digit by 2-digit problems along with a group scenario. (They may choose to use the scenario and multiplication statements given or they may create their own following the above guidelines.) Have each student write one sentence using one of the multiplication problems and pass the paper to their neighbor. Each sentence should relate to the group’s scenario. Once the stories are created, have groups exchange their problems with other groups and solve the story problems. Solutions should contain the multiplication sentence and the computation technique used (standard algorithm or multiplication matrix). A discussion about the computational method could be held. Groups should also be checking for accuracy and logic in the completed text chain.

Example:

Group 1 is given the scenario that they are putting together a fourth grade party, and they are to incorporate these multiplication statements 48 ( 2 = n, 16 ( 12 = n, 103 ( 50 = n. Student 1 begins by writing, “Two schools will take part in the party. Each school has a total of 48 students. How many fourth graders will participate?”

Student 2 writes, “There are 16 tables. Sam wonders if there will be enough room for everyone to sit down and have some seats leftover for guests. Twelve students can sit at each table. There are 16 tables. Will there be enough room for everyone?”

Student 3 writes “To help pay for the party, each student and teacher collects cans to be recycled. The money received goes towards the party. There are 103 people who will participate. If each of them collects 50 cans, how many cans would they collect?”

Sample Assessments

General Assessments

• Maintain portfolios containing student work.

• Record anecdotal notes on students as they complete tasks.

• Give prompts, such as the one that follows, for students to record their thoughts in their personal math learning logs.

o Ask students to demonstrate comprehension of addition and multiplication concepts in real-world problems.

• Give prompts, such as the ones that follow, and have students record their thoughts in their personal math journals.

o Explain how you can use 10 × 6 to solve 12 × 6.

o Write a story problem that shows it would be easier to multiply than to add.

o Write a story to illustrate the property of multiplication used in class today. (This can be repeated for Distributive Property, Commutative Property, Associative Property, Zero Property, and Identity Property.)

Activity-Specific Assessments

• Activity 10: Have the students create multiplication picture books for younger students (If two wagons each have three puppies in them, how many puppies are there in all?) or real-world word problem books for their peers (The student bought four pencils at 25¢ each and three folders at 50¢ each at the school store. He gave the cashier $5.00. How much change did he get back?).

• Activity 11: Assign each pair of students a large 1-digit by 1-digit multiplication fact to solve. Have the students show how smaller arrays can be used to make it easier to find the product of a more difficult multiplication fact. Display the solution arrays to be used as a reference by other students.

Example: The fact 8 ( 7 could be displayed as:

5 ( 7 = 35

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+ 3 ( 7 = 21

8 ( 7 = 56

• Activity 14: Give the students several 2-digit by 2-digit multiplication problems. Have them determine the estimated answer by using mental math and state if the actual answer is higher or lower. Have students work the problem using paper and pencil. Have them exchange papers and use calculators to check for accuracy.

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xxxxxx

xxxxxx

xxxxxx

$3

$5

$5

$5

$5

54 36

9 6

6

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