Web viewFourth Grade Unit 2: Multiplication and Division of Whole Numbers. 9 weeks. In this unit students will: solve multi-step problems using the four operations . use

Fourth Grade Unit 2: Multiplication and Division of Whole Numbers9 weeksIn this unit students will: solve multi-step problems using the four operations use estimation to solve multiplication and division problems find factors and multiples identify prime and composite numbers generate patterns

Unit 1 Overview video Parent Letter Number Talks Resources Vocabulary Cards Prerequisite Skills Assessment Sample Posttest

Topic 1: MultiplicationBig Ideas/Enduring Understandings: Multiplication may be used to find the total number of objects when objects are arranged in equal groups. One of the factors in multiplication indicates the number of objects in a group and the other factor indicates the number of groups. Products may be calculated using invented strategies. Unfamiliar multiplication problems may be solved by using known multiplication facts and properties of multiplication and division. For example, 8 x 7 = (8 x 2) + (8

x 5) and 18 x 7 = (10 x 7) + (8 x 7). The properties of multiplication and division help us solve computation problems easily and provide reasoning for choices we make in problem solving. Multiplication may be represented by rectangular arrays/area models. Estimation is a helpful tool when finding the products of a 2- digit number multiplied by a 2-digit number. Multiplication may be used in problem contexts involving equal groups, rectangular arrays/area models, or rate. Multiply up to a 4-digit number by a 1-digit number using strategies.Essential Questions (Select a few questions based on the needs of your students): How will diagrams help us determine and show the products of two-digit numbers? What patterns do I notice when I am multiplying whole numbers that can help me multiply more efficiently? What is a sensible answer to a real problem? How can I ensure my answer is reasonable? How are multiplication and division related to each other? What are some simple methods for solving multiplication and division problems? What patterns of multiplication and division can assist us in problem solving?Student Relevance: Purchasing Creating goody bagsContent StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that

4th Grade Quarter 2 1 2015-2016

exist among mathematical topics.Use the four operations with whole numbers to solve problems MGSE4.OA.1 Understand that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity.

a. 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.b. Represent verbal statements of multiplicative comparisons as multiplication equations.

MGSE4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison. Use drawings and equations with a symbol or letter for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Use place value understanding and properties of operations to perform multi-digit arithmetic MGSE4.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 .Vertical Articulation

Third Grade Multiplication StandardsRepresent and solve problems involving multiplication and division MGSE3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the

total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

MGSE3.OA.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.12

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations, 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?.

Understand properties of multiplication and the relationship between multiplication and division MGSE3.OA.5 Apply properties of operations as strategies to multiply and

divide.13 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Multiply and divide within 100

Fifth Grade Multiplication StandardsPerform operations with multi-digit whole numbers and with decimals and hundredths MGSE5.NBT.5 Fluently multiply multi-digit whole numbers using the standard

algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.

MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.


MGSE3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Instructional StrategiesStudents need to solve word problems involving multiplicative comparison (product unknown, partition unknown) using multiplication or division. They should use drawings or equations with a symbol for the unknown number to represent the problem. Students need to be able to distinguish whether a word problem involves multiplicative comparison or additive comparison (solved when adding and subtracting in Grades 1 and 2).

Standard OA.1In standard OA.1, students develop understanding that a multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity. A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times. Students should be given opportunities to write and identify equations and statements for multiplicative comparisons.Examples:5 x 8 = 40: Sally is five years old. Her mom is eight times older. How old is Sally’s Mom?5 x 5 = 25: Sally has five times as many pencils as Mary. If Mary has 5 pencils, how many does Sally have?

Standard OA.2Standard OA.2 requires that students multiply and divide to solve word problems involving multiplicative comparisons. Students should use drawings and equations with a symbol or letter to represent the unknown number. This standard calls for students to translate comparative situations into equations with an unknown and solve. Students need many opportunities to solve contextual problems.Examples: Unknown Product: A blue scarf costs $3. A red scarf costs 6 times as much. How much does the red scarf cost? (3 × 6 = p)

Group Size Unknown: A book costs $18. That is 3 times more than a DVD. How much does a DVD cost? (18 ÷ p = 3 or 3 × p = 18)

Number of Groups Unknown: A red scarf costs $18. A blue scarf costs $6. How many times as much does the red scarf cost compared to the blue scarf? (18 ÷ 6 = p or 6 × p = 18)


When distinguishing multiplicative comparison from additive comparison, students should note the following: Additive comparisons focus on the difference between two quantities. For example, Deb has 3 apples and Karen has 5 apples. How many more apples does Karen

have? A simple way to remember this is, “How many more?” Multiplicative comparisons focus on comparing two quantities by showing that one quantity is a specified number of times larger or smaller than the other. For

example, Deb ran 3 miles. Karen ran 5 times as many miles as Deb. How many miles did Karen run? A simple way to remember this is “How many times as much?” or “How many times as many?”

Standard OA.3The focus of standard OA.3 is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. Students need many opportunities solving multistep story problems using all four operations.

Examples: On a vacation, your family travels 267 miles on the first day, 194 miles on the second day and 34 miles on the third day. About how many miles did they travel

total? Some typical estimation strategies for this problem:

Your class is collecting bottled water for a service project. The goal is to collect 300 bottles of water. On the first day, Max brings in 3 packs with 6 bottles in each container. Sarah wheels in 6 packs with 6 bottles in each container. About how many bottles of water still need to be collected?


Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15. How much money did Chris spend on her new school clothes? 3 × $12 + $15 = 𝑎 There are 29 students in one class and 28 students in another class going on a field trip. Each car can hold 5 students. How many cars are needed to get all the

students to the field trip? (12 cars, one possible explanation is 11 cars holding 5 students and the 12th holding the remaining 2 students) 29 + 28 = 11 × 5 + 2

Estimation skills include identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or determining the reasonableness of situations using various estimation strategies. Estimation strategies include, but are not limited to: front-end estimation with adjusting (using the highest place value and estimating from the front end, making adjustments to the estimate by taking into account

the remaining amounts), clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate), rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values), using friendly or compatible numbers such as factors (students seek to fit numbers together - e.g., rounding to factors and grouping numbers together that have

round sums like 100 or 1000), using benchmark numbers that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate).

Standard NBT.5In Standard NBT.5, students 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. Students who develop flexibility in breaking numbers apart have a better understanding of the importance of place value and the distributive property in multi-digit multiplication. Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and diagrams to explain their thinking. They use the terms factor and product when communicating their reasoning.

Standard NBT.5 calls for students to multiply numbers using a variety of strategies. Multiple strategies enable students to develop fluency with multiplication and transfer that understanding to division. Use of the standard algorithm for multiplication is an expectation in the 5th grade.

Examples: There are 25 dozen cookies in the bakery. What is the total number of cookies at the bakery?


What would an array area model of 74 x 38 look like?

The area model to the right shows the partial products for 14 x 16 = 224. Using the area model, students verbalize their understanding:

o 10 × 10 is 100o 4 × 10 is 40, or 4 tenso 10 × 6 is 60, or 6 tenso 4 × 6 is 24o 100 + 40 + 60 + 24 = 224

Examples: To illustrate 154 × 6, students can use base 10 blocks or use drawings to show 154 six times. Seeing 154 six times will lead them to understand the distributive

property shown below.

Illustrating 25 x 24 can also be completed with base ten blocks or drawings to show 25 twenty four times. The distributive property is shown below.

OR

Common MisconceptionsOA.1 - Students may have “overspecialized” their knowledge of multiplication or division facts and have restricted it to “fact tests” or one particular format. For example they may think of Multiplicative comparisons, unknown product or partition unknown. For example students complete multiplication fact assessments


satisfactorily but cannot apply knowledge to problem solving situations.Evidence of LearningStudents are able to: solve multi-step problems using the four operations use estimation to solve multiplication and division problemsDifferentiation-Increase the RigorStandard OA.1 Show students two rectangles (one of which is three times longer than the other). How do the sizes of the two rectangles compare? (multiplicative comparison is

when one quantity (factor) is described by a multiple of the other, different than repeated addition and arrays) Martin and Kate used star stickers in a picture of the night sky. Kate used four times as many stars as Martin. How many stars could they have each used? Is there

another possible answer? A plant was 2 inches tall on Day 1, it was measured at 10 inches on Day 12. How can you describe the relationship between the two quantities using multiplicative

reasoning. Mark’s recipe calls for three times as many potatoes as carrots. If Mark uses two cups carrots, how many cups of potatoes will he use? Anna is 8 years old. Her mom is five times older than she is and her grandmother is eight times older than Anna. What multiplication sentences can be written to

represent the relationship between Anna’s age and her mom’s age? between Anna’s age and her grandmother’s age? How old are Anna’s mother and grandmother?

What multiplication equation could you write to match the picture of the pencils?

Standard OA.2 Kamari builds a tower that is 18 inches high. Kamari’s tower is three times taller than his brother’s tower. How tall is his brother’s tower? Show a model, draw a

picture or write an equation to support your answer. What could a story problem, using multiplicative comparison, be for the equation 3 x 8? Kim had 4 taco shells. Her sister Shelly brought three times as many taco shells. (so 12 plus Kim’s 4 = 16) Seven family members will eat tacos. If Kim gives

everyone the same number of taco shells, how many will each person get? As shirt costs $15. A pair of sneakers costs four times as much. How much does the pair of sneakers cost? A hat is half as much as the sneakers, so how much does

the hat cost? If Ken buys one hat, one pair of sneakers and two shirts, how much has he spent? Mr. Hill has 17 marbles in his classroom. Ms. Rice has twice as many marbles as Mr. Hill. Mr. Hill borrowed all of Ms. Rice’s marbles so his students can play a

game. Each student needs 4 marbles to play the game. How many students will be able to play the game?

Standard OA.3 There are 583 students in Suzy’s school. 99 third grade students left the school on a field trip. There are about 20 students in each class. How many classrooms are

being used today? Explain your answer. The school bought apples to give to students. They have 30 boxes with 8 apples in each box and they have 20 boxes with 10 apples in each box. Each student

needs 3 apples for the week. How many students can the school feed? Why is it important to consider the remainder when answering a problem? Give a real-life example of when it is important to drop the remainder? Give a real-life

example of when you need to round the remainder.4th Grade Quarter 2 7 2015-2016

Zoe is having a wedding. She has 178 guests attending. The party location can set up tables with 10 at each table OR tables with 8 at each table. How many tables will Zoe need under each situation?

Write a division problem that has 15 R2 as the quotient. Barry’s family donated 11 cases of tomato soup to the local food kitchen. Each case has 12 cans of soup. The shelter already has 16 cans of tomato soup. How

many cans of tomato soup does the food kitchen have now? The food kitchen uses 20 cans of tomato soup each week. How many weeks will go by before the food kitchen needs more tomato soup?

Standard NBT.5 How many different ways can you solve 289 x 8? 94 x 64? What two factors can be multiplied to result in a product of 126? Create two multiplication sentences that could create a product between 200 and 500? How does the order of the digits in the factors impact the product? (e.g. 452 x 7 compared to 425 x 7) Is the product of 29 x 34 over or under 900? Explain how you know. Think of an example in life when you might multiply two numbers? An example when you might multiply two two-digit numbers? Or a three-digit number by a one

digit number?

Adopted ResourcesMy MathChapter 3: Understand Multiplication and Division3.1 Relate Multiplication and Division3.2 Relate Division and Subtraction3.3 Multiplication as Comparison3.4 Compare to Solve Problems3.5 Multiplication Properties and Division Rules3.6 The Associative Property of Multiplication3.7 Factors and Multiples3.8 Problem-Solving InvestigationChapter 4: Multiply with One-Digit Numbers4.1 Multiples of 10, 100, and 1,0004.2 Round to Estimate Products4.3 Hands On: Use Place Value to Multiply4.4 Hands On: Use Models to Multiply4.5 Multiply by a Two-Digit Number4.7 The Distributive Property4.10 Problem-Solving InvestigationChapter 5: Multiply with Two-Digit Numbers5.1 Multiply by Tens

Adopted Online Resourceshttp://connected.mcgrawhill.com/connected/

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Teacher User ID: ccsde0(enumber)Password: cobbmath1Student User ID: ccsd(student ID)Password: cobbmath1

http://www.exemplarslibrary.com/

User: Cobb EmailPassword: First Name

Bobsled BlunderA Broken Gumball MachineA ChallengeHot Dogs for a PicnicJeff's Marble CollectionLetter PatternsLunch at the Hot Dog Cart

Think MathChapter 2: Multiplication2.1 Introducing Arrays2.2 Separating Arrays2.3 Adding Array Sections2.4 Exploring a Multiplication Shortcut2.5 Using a Multiplication Shortcut2.6 Connecting Multiplication and DivisionChapter 6: Multi-Digit Multiplication6.1 Multiplication Puzzles6.2 Multiples of 10 and 1006.3 Using Arrays to Model Multiplication6.4 Splitting Larger Arrays6.5 Choosing Simpler Problems6.8 Checking for Reasonable Answers



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5.2 Estimate Products5.3 Use the Distributive Property to Multiply5.4 Solve Multi-Step Word Problems5.5 Problem-Solving Investigation: Make a Table

*These lessons are not to be completed in consecutive days as it is too much material. They are designed to help support you as you teach your standards.

Raising ChickensCarpet CaperDominoesFilling the Pool

Additional ResourcesK-5 Math Teaching Resources http://www.k-5mathteachingresources.com/4th-grade-number-activities.html

Illustrative Mathematics (Tasks listed below) https://www.illustrativemathematics.org/content-standards/4/NBT/A

*Press CTRL + Click the link to access each of the Illustrative Mathematics task:

Everyday Math E-Tool Kit http://media.emgames.com/em-v2/eToolkit/eTools_v1.swf

National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html

Khan Academy (Press CTRL + Click the link to view the tutorials):Multiplying: Understanding by Using Area ModelsMultiplying: Using an Area ModelMultiplication, Division Word Problems: How many pieces of pizzas?

Learn Zillion (Press CTRL + Click the link to view the tutorials):Solve Multiplication Problems (partial products and area models)Multiply Multi-Digit Whole NumbersSuggested Manipulativescolor tilesgraph papertwo-color countersdice

Vocabularyestimatefactorsproduct

Suggested LiteratureThings that Come in 2’s, 3’s & 4’sAmanda Bean’s Amazing DreamMy Full Moon is SquareToo Many Kangaroo Things to Do


Tasks for Standard OA.1Threatened and EndangeredThousands and Millions of Fourth GradersComparing Growth, Variation 1Comparing Growth, Variation 2

Tasks for Standard OA.2Comparing Money Raised

Tasks for Standard OA.3Karl's GardenCarnival Tickets

Tasks for Standard NBT.5Thousands and Millions of Fourth Graders

https://learnzillion.com/resources/73077-multiply-multi-digit-whole-numbers-4-nbt-b-5

https://learnzillion.com/resources/72267-solve-multiplication-problems

https://www.khanacademy.org/math/arithmetic/multiplication-division/advanced-mult-div-word-problems/v/multi-step-word-problems-with-whole-numbers-exercise-t2?utm_campaign=embed

https://www.khanacademy.org/math/arithmetic/multiplication-division/area-models-multiplication/v/area-model-for-multiplication?utm_campaign=embed

https://www.khanacademy.org/math/arithmetic/multiplication-division/area-models-multiplication/v/understanding-multiplication-through-area-models?utm_campaign=embed

http://nlvm.usu.edu/en/nav/vlibrary.html

http://media.emgames.com/em-v2/eToolkit/eTools_v1.swf

https://www.illustrativemathematics.org/illustrations/357








https://www.illustrativemathematics.org/content-standards/4/NBT/A

http://www.k-5mathteachingresources.com/4th-grade-number-activities.html

hundreds chartmultiplication chartbase-ten blockssnap cubesnumber line

The Best of TimesThe Doorbell RangEach Orange Had Eight SlicesTwo of Everything Spunky Monkeys On Parade One Hundred Hungry Ants Bats on Parade

Topic 2: Factors, Multiples, & Number PatternsBig Ideas/Enduring Understandings: A whole number is a multiple of each of its factors Whole numbers can be prime, composite, or neither Find the factor pairs for a whole number in the range 1-100 Generate a number or shape pattern that follows a given rule Identify features of a pattern that are not explicit in the rule itselfEssential Questions: What does it mean to factor? What is the difference between a prime and a composite number? What are multiples? How is skip counting related to identifying multiples? What is the difference between a factor and a product? How do we know if a number is prime or composite? How can we use patterns to solve problems?Student Relevance: Multiples of objects Fair shareContent StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics.Gain familiarity with factors and multiples MGSE4.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.

Generalize and understand patterns MGSE4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

Explain informally why the pattern will continue to develop in this way. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.


Instructional StrategiesStandard OA.4Standard OA.4 requires students to demonstrate understanding of factors and multiples of whole numbers. This standard also refers to prime and composite numbers. Prime numbers have exactly two factors, the number one and their own number. For example, the number 17 has the factors of 1 and 17. Composite numbers have more than two factors. For example, 8 has the factors 1, 2, 4, and 8.

Prime vs. Composite: A prime number is a number greater than 1 that has only 2 factors, 1 and itself. Composite numbers have more than 2 factors.Students investigate whether numbers are prime or composite by: Building rectangles (arrays) with the given area and finding which numbers have more than two rectangles (e.g., 7 can be made into only 2 rectangles, 1 × 7 and 7

× 1, therefore it is a prime number). Finding factors of the number.

Students should understand the process of finding factor pairs so they can do this for any number 1-100.Example: Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12.

Multiples:Multiples are products of any given whole number and another whole number. They can also be thought of as the result of skip counting by each of the factors. When skip counting, students should be able to identify the number of factors counted e.g., 5, 10, 15, 20 (there are 4 fives in 20).

Example: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Multiples of 24: 24, 48, 72, 96, 120……

Multiples of the factors of 24:1, 2, 3, 4, 5, … , 24 (24 is the 24th multiple of one.)2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 (24 is the 12th multiple of two.)3, 6, 9, 12, 15, 15, 21, 24 (24 is the 8th multiple of three.)4, 8, 12, 16, 20, 24 (24 is the 6th multiple of four.)8, 16, 24 (24 is the 3rd multiple of eight.)12, 24 (24 is the 2nd multiple of twelve.)24 (24 is the 1st multiple of 24.)

Here are some helpful hints to determine if a number between 1-100 is a multiple of a given one-digit number: All even numbers are multiples of 2.


All even numbers that can be halved twice (with a whole number result) are multiples of 4. All numbers ending in 0 or 5 are multiples of 5.Students need to develop an understanding of the concepts of number theory such as prime numbers and composite numbers. This includes the relationship of factors and multiples. Multiplication and division are used to develop concepts of factors and multiples. Division problems resulting in remainders are used as counter-examples of factors.

Review vocabulary so that students have an understanding of terms such as factor, product, multiples, and odd and even numbers.

Students need to develop strategies for determining if a number is prime or composite, in other words, if a number has a whole number factor that is not one or itself. Starting with a number chart of 1 to 20, use multiples of prime numbers to eliminate later numbers in the chart. For example, 2 is prime but 4, 6, 8, 10, 12 . . . are composite.

After working with the numbers 1 to 20, consider using a hundreds chart and have the students color code multiples of numbers. The color will help students see emerging patterns which they can discuss.

Encourage the development of rules that can be used to aid in the determination of composite numbers. For example, other than 2, if a number ends in an even number (0, 2, 4, 6 and 8), it is a composite number.

Using area models will also enable students to analyze numbers and arrive at an understanding of whether a number is prime or composite. Have students construct rectangles with an area equal to a given number.

They should see an association between the number of rectangles and the given number for the area as to whether this number is a prime or composite number.

Definitions of prime and composite numbers should not be provided, but determined after many strategies have been used in finding all possible factors of a number.

Provide students with counters to find the factors of numbers. Have them find ways to separate the counters into equal subsets. For example, have them find several factors of 10, 14, 25 or 32, and write multiplication expressions for the numbers.

Another way to find the factor of a number is to use arrays from square tiles or drawn on grid papers. Have students build rectangles that have the given number of squares. For example if you have 16 squares:

The idea that a product of any two whole numbers is a common multiple of those two numbers is a difficult concept to understand. For example, 5 x 8 is 40; the table below shows the multiples of each factor.


Ask students what they notice about the number 40 in each set of multiples; 40 is the 8th multiple of 5, and the 5 th multiple of 8.

Knowing how to determine factors and multiples is the foundation for finding common multiples and factors in Grade 6.

Writing multiplication expressions for numbers with several factors and for numbers with a few factors will help students in making conjectures about the numbers. Students need to look for commonalities among the numbers.

Standard OA.5In Standard OA.5, students generate a number or shape pattern that follows a given rule. Patterns involving numbers or symbols either repeat or grow. Students need multiple opportunities creating and extending number and shape patterns. Numerical patterns allow students to reinforce facts and develop fluency with operations.

Patterns and rules are related. A pattern is a sequence that repeats the same process over and over. A rule dictates what that process will look like. Students investigate different patterns to find rules, identify features in the patterns, and justify the reason for those features.Example:After students have identified rules and features from patterns, they need to generate a numerical or shape pattern from a given rule.

Example:Rule: Starting at 1, create a pattern that starts at 1 and multiplies each number by 3. Stop when you have 6 numbers. Students write 1, 3, 9, 27, 81, 243. Students notice that all the numbers are odd and that the sums of the digits of the 2 digit numbers are each 9. Some students

might investigate this beyond 6 numbers. Another feature to investigate is the patterns in the differences of the numbers (3 – 1 = 2, 9 – 3 = 6, 27 – 9 = 18, etc.).

Standard OA.5 calls for students to describe features of an arithmetic number pattern or shape pattern by identifying the rule, and features that are not explicit in the rule. A t-chart is a tool to help students see number patterns.


Example: There are 4 beans in the jar. Each day 3 beans are added. How many beans are in the jar for each of the first 5 days?

In order for students to be successful later in the formal study of algebra, their algebraic thinking needs to be developed. Understanding patterns is fundamental to algebraic thinking. Students have experience in identifying arithmetic patterns, especially those included in addition and multiplication tables. Contexts familiar to students are helpful in developing students’ algebraic thinking.Students should generate numerical or geometric patterns that follow a given rule. They should look for relationships in the patterns and be able to describe and make generalizations.

As students generate numeric patterns for rules, they should be able to “undo” the pattern to determine if the rule works with all of the numbers generated. For example, given the rule, “Add 4” starting with the number 1, the pattern 1, 5, 9, 13, 17, … is generated. In analyzing the pattern, students need to determine how to get from one term to the next term. Teachers can ask students, “How is a number in the sequence related to the one that came before it?”, and “If they started at the end of the pattern, will this relationship be the same?” Students can use this type of questioning in analyzing numbers patterns to determine the rule.

Students should also determine if there are other relationships in the patterns. In the numeric pattern generated above, students should observe that the numbers are all odd numbers.Provide patterns that involve shapes so that students can determine the rule for the pattern. For example,

Students may state that the rule is to multiply the previous number of squares by 3.Common MisconceptionsOA.4 - A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite. Another common misconception is that all prime numbers are odd numbers. This is not true, since the number 2 has only 2 factors, 1 and 2, and is also an even number.

When listing multiples of numbers, students may not list the number itself. Emphasize that the smallest multiple is the number itself. Also, having students write multiples of a number by consecutive factors beginning with one can clear up this misconception.

Some students may think that larger numbers have more factors. Having students share all factor pairs and how they found them will clear up this misconception.4th Grade Quarter 2 14 2015-2016

When listing multiples of numbers, students may not list the number itself. Emphasize that the smallest multiple is the number itself.

OA.5 - Students think that results are random. There is no pattern. Another common misconception when students are working with repeating patterns is that they will often repeat what is given rather than looking at what “chunks” or part of the pattern is actually being repeated. Example: Given the pattern 6,9,12,6,9,12,6,9,… If the student is asked “what is the next number in the pattern”, they may respond with “6” because they are returning to the beginning of the given pattern and repeat it from there. Students should be encouraged to look for the repeating “set”.Differentiation-Increase the RigorStandard OA.4 What are possible multiples that could go in the Venn Diagram? Place at least three numbers in each section of the Venn. Jacob said that all prime numbers have to be odd? Do you agree with him? Justify your answer. How are the terms “factors” and “multiples” related? Use examples to support your answer. Linda says that 33 is prime because it is odd. Is she correct? Explain why or why not. What products could have a factor of 4? How many of those products exist in the numbers 1-100? What are they? Name three prime numbers greater than 12? What is the greatest prime number in the number set 1-100? Use the digits 0-9 to form five prime numbers.

Standard OA.5 Create 2 patterns that have the same rule. How can you use a multiplication chart to show the patterns in created by the distributive property? Do basic fact strategies (i.e. double plus one) work with all addends? We might think of multiplying by 9 as 1 group less than a number x 10. Does this work with 2-digit numbers? How do you know? How would you describe the difference between a repeating pattern and a growing pattern?

Evidence of LearningStudents are able to: find factors and multiples identify prime and composite numbers generate patternsAdopted ResourcesMy MathChapter 7: Patterns and Sequences7.1 Nonnumeric Patterns7.2 Numeric Patterns7.3 Sequences7.4 Problem Solving Investigation

Adopted Online Resourceshttp://connected.mcgrawhill.com/connected/

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Think Math







Follow My Lead Letter Patterns Playing Checkers






Learn Zillion (Press CTRL + Click the link to access the tutorials):Find and understand factors and determine if a number is a multiple of a given number for whole numbers 0-100Generate number or shape patterns that follow a given rule and identifying pattern featuresSuggested Manipulativescolor tilesgraph papertwo-color countersdicehundreds chartmultiplication chartbase-ten blocks

Vocabularycompositefactorsmultiplesprimeproduct

Suggested LiteratureThings that Come in 2’s, 3’s & 4’sAmanda Bean’s Amazing DreamMy Full Moon is SquareToo Many Kangaroo Things to DoThe Best of TimesThe Doorbell RangEach Orange Had Eight Slices


Tasks for Standard OA.4The Locker GameIdentifying MultiplesNumbers in a Multiplication TableMultiples of 3, 6, and 7

Tasks for Standard OA.5Double Plus OneMultiples of nineMultiples of 3, 6, and 7

https://learnzillion.com/resources/72543-generate-number-or-shape-patterns-that-follow-a-given-rule-and-identifying-pattern-features-4-oa-c-5

https://learnzillion.com/resources/72576-find-and-understand-factors-and-determine-if-a-number-is-a-multiple-of-a-given-number-for-whole-numbers-0-100-4-oa-b-4












snap cubesnumber line

Two of Everything Spunky Monkeys On Parade One Hundred Hungry Ants Bats on Parade

Topic 3: DivisionBig Ideas/Enduring Understandings: There are two common situations where division may be used: fair sharing (given the total amount and the number of equal groups, determine how many/much

in each group) and measurement (given the total amount and the amount in a group, determine how many groups of the same size can be created). Some division situations will produce a remainder, but the remainder will always be less than the divisor. If the remainder is greater than the divisor, that means at

least one more can be given to each group (fair sharing) or at least one more group of the given size (the dividend) may be created. How the remainder is explained depends on the problem situation. Multiplication and division can be represented using a rectangular area model. The dividend, divisor, quotient, and remainder are related in the following manner: dividend = divisor x quotient + remainder. The quotient remains unchanged when both the dividend and the divisor are multiplied or divided by the same number. Divide whole-numbers quotients and remainders with up to four-digit dividends and remainders with up to four-digit dividends and one-digit divisors.Essential Questions (Select a few questions based on the needs of your students): What effect does a remainder have on a quotient? How can I mentally compute a division problem? What are compatible numbers and how do they aid in dividing whole numbers? What happens in division when there are zeroes in both the divisor and the dividend? How are remainders and divisors related? What is the meaning of a remainder in a division problem? How can we use clues and reasoning to find an unknown number? How can we determine the relationships between numbers? How do multiplication, division, and estimation help us solve real world problems? How can we organize our work when solving a multi-step word problem?Student Relevance: Equal sharesContent StandardsContent standards are interwoven and should be addressed throughout the year in as many different units and activities as possible in order to emphasize the natural connections that exist among mathematical topics. MGSE4.OA.3 Solve multistep word problems 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 symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

MGSE4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


Vertical ArticulationThird Grade Division StandardsRepresent and solve problems involving multiplication and division MGSE3.OA.2 Interpret whole number quotients of whole numbers, e.g.,

interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.OA.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.12

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations, 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?.

Understand properties of multiplication and the relationship between multiplication and division MGSE3.OA.5 Apply properties of operations as strategies to multiply and

divide.13 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

MGSE3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Multiply and divide within 100 MGSE3.OA.7 Fluently multiply and divide within 100, using strategies such as

the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Fifth Grade Division StandardsPerform operations with multi-digit whole numbers and with decimals and hundredths MGSE5.NBT.6 Fluently divide up to 4-digit dividends and 2-digit divisors by

using at least one of the following methods: strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations or concrete models. (e.g., rectangular arrays, area models)

MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Instructional StrategiesStudents need experiences that allow them to connect mathematical statements and number sentences or equations. This allows for an effective transition to formal algebraic concepts. They represent an unknown number in a word problem with a symbol. Word problems which require multiplication or division are solved by using drawings and equations.


Present multistep word problems with whole numbers and whole-number answers using the four operations. Students should know which operations are needed to solve the problem. Drawing pictures or using models will help students understand what the problem is asking. They should check the reasonableness of their answer using mental computation and estimation strategies.

Standard OA.3The focus of standard OA.3 is to have students use and discuss various strategies. It refers to estimation strategies, including using compatible numbers (numbers that sum to 10 or 100) or rounding. Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. Students need many opportunities solving multistep story problems using all four operations.

This standard (OA.3) references interpreting remainders. Remainders should be put into context for interpretation. Ways to address remainders: Remain as a left over Partitioned into fractions or decimals Discarded leaving only the whole number answer Increase the whole number answer by one Round to the nearest whole number for an approximate result

Examples: Mary had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches did she fill?

Answer: 44 ÷ 6 = p; p = 7 r 2. Mary can fill 7 pouches completely.

Mary had 44 pencils. Six pencils fit into each of her pencil pouches. How many pouches could she fill and how many pencils would she have left?Answer: 44 ÷ 6 = p; p = 7 r 2; Mary can fill 7 pouches and have 2 pencils left over.

Mary had 44 pencils. Six pencils fit into each of her pencil pouches. What is the fewest number of pouches she would need in order to hold all of her pencils?Answer: 44 ÷ 6 = p; p = 7 r 2; Mary needs 8 pouches to hold all of the pencils.

Mary had 44 pencils. She divided them equally among her friends before giving one of the leftovers to each of her friends. How many pencils could her friends have received?Answer: 44 ÷ 6 = p; p = 7 r 2; Some of her friends received 7 pencils. Two friends received 8 pencils.

Mary had 44 pencils and put six pencils in each pouch. What fraction represents the number of pouches that Mary filled?

Answer: 44 ÷ 6 = p; p = 726 ; Mary filled 7

26pencil pouches.

There are 128 students going on a field trip. If each bus held 30 students, how many buses are needed? (128 ÷ 30 = b; b = 4 R 8; they will need 5 buses because 4 buses would not hold all of the students). Students need to realize in problems, such as the example above, that an extra bus is needed for the 8 students that are


left over.

In division problems, the remainder is the whole number left over when as large a multiple of the divisor as possible has been subtracted.

Kim is making candy bags. There will be 5 pieces of candy in each bag. She had 53 pieces of candy. She ate 14 pieces of candy. How many candy bags can Kim make now? (7 bags with 4 leftover)

Estimation skills include identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or determining the reasonableness of situations using various estimation strategies. Estimation strategies include, but are not limited to: front-end estimation with adjusting (using the highest place value and estimating from the front end, making adjustments to the estimate by taking into account

the remaining amounts), clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate), rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values), using friendly or compatible numbers such as factors (students seek to fit numbers together - e.g., rounding to factors and grouping numbers together that have

round sums like 100 or 1000), using benchmark numbers that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate).

Standard NBT.6In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context.

Standard NBT.6 requires that students find whole number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. In fourth grade, students build on their third grade work with division within 100. Students need opportunities to develop their understandings by using problems in and out of context.Example: A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants to put the pencils in the boxes so that each box has the same number of pencils.

How many pencils will there be in each box?

This standard calls for students to explore division through various strategies. Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups. Some students may need to trade the 2 hundreds for 20

tens but others may easily recognize that 200 divided by 4 is 50.

Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4) = 50 + 15 = 65

Using Multiplication: 4 × 50 = 200, 4 × 10 = 40, 4 × 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65

Examples:


There are 592 students participating in Field Day. They are put into teams of 8 for the competition. How many teams are created?

Using an Open Array or Area ModelAfter developing an understanding of using arrays to divide, students begin to use a more abstract model for division. This model connects to a recording process that will be formalized in the 5th grade.

Students make a rectangle and write 6 on one of its sides. They express their understanding that they need to think of the rectangle as representing a total of 150.

1. Students think, 6 times what number is a number close to 150? They recognize that 6 x 10 is 60 so they record 10 as a factor and partition the rectangle into 2 rectangles and label the area aligned to the factor of 10 with 60. They express that they have only used 60 of the 150 so they have 90 left.

2. Recognizing that there is another 60 in what is left they repeat the process above. They express that they have used 120 of the 150 so they have 30 left.3. Knowing that 6 x 5 is 30. They write 30 in the bottom area of the rectangle and record 5 as a factor.4. Students express their calculations in various ways:


Common Misconceptions

OA.3 - Students apply a procedure that results in remainders that are expressed as r or R for ALL situations, even for those for which the result does not make sense. For example when a student is asked to solve the following problem, the student responds to the problem—there are 32 students in a class canoe trip. They plan to have 3 students in each canoe. How many canoes will they need so that everyone can participate? And the student answers of “10𝑟2 canoes”.


Differentiation-Increase the RigorStandard OA.3 There are 583 students in Suzy’s school. 99 third grade students left the school on a field trip. There are about 20 students in each class. How many classrooms are

being used today? Explain your answer. The school bought apples to give to students. They have 30 boxes with 8 apples in each box and they have 20 boxes with 10 apples in each box. Each student

needs 3 apples for the week. How many students can the school feed? Why is it important to consider the remainder when answering a problem? Give a real-life example of when it is important to drop the remainder? Give a real-life

example of when you need to round the remainder. Zoe is having a wedding. She has 178 guests attending. The party location can set up tables with 10 at each table OR tables with 8 at each table. How many tables

will Zoe need under each situation? Write a division problem that has 15 R2 as the quotient. Barry’s family donated 11 cases of tomato soup to the local food kitchen. Each case has 12 cans of soup. The shelter already has 16 cans of tomato soup. How

many cans of tomato soup does the food kitchen have now? The food kitchen uses 20 cans of tomato soup each week. How many weeks will go by before the food kitchen needs more tomato soup?

Standard NBT.6 What is the relationship between multiplication and division? Provide examples to show your thinking. How does knowing 5 x 5 help you to solve 75 ÷ 5? Explain. How many different ways can you solve 84 ÷ 6? If the quotient is 15, what could your possible dividend and divisor be? How does changing the value of your divisor affect the quotient? (e.g. 350 ÷ 5 vs. 350 ÷ 50?) Using the digits 4, 9, 7, and 5, create a division sentence with the greatest possible quotient? Which division strategy (partial quotients, rectangular array, area model) do you think is best? Justify your answer.

Evidence of LearningStudents are able to: solve multi-step problems using the four operations use estimation to solve multiplication and division problemsAdopted ResourcesMy Math:Chapter 3: Understand Multiplication and Division3.1 Relate Multiplication and Division3.2 Relate Division and Subtraction3.3 Multiplication as Comparison3.4 Compare to Solve Problems3.5 Multiplication Properties and Division Rules3.6 The Associative Property of Multiplication

Adopted Online Resources



Think MathChapter 2: Multiplication2.6 Connecting Multiplication and Division2.7 Arrays with Leftovers2.8 Working with Remainders2.9 Solve a Simpler ProblemChapter 13: Division13.1 Finding Missing Dimensions13.2 Finding Missing Factors



3.7 Factors and Multiples3.8 Problem-Solving InvestigationChapter 6: Divide by a One-Digit Number6.1 Divide by Multiples of 10, 100, and 1,0006.2 Estimate Quotients6.3 Hands On: Use Place Value to Divide6.4 Problem-Solving Investigation: Make a Model6.5 Divide with Remainders6.6 Interpret Remainders6.8 Distributive Property and Partial Quotients6.11 Solve Multi-Step Word Problems




Equal Snacks What is Fair? The Beaver Olympics

13.3 Finding Missing Factors More Efficiently13.4 Estimating Missing Factors and Quotients13.6 Completing Division SentencesChapter 15: Estimation15.1 Estimation Strategies






Khan Academy (Select CTRL + Click the link to view the tutorials):Partial Quotient Method of DivisionMultiplication, Division Word Problems: How many pieces of pizzas?

Learn Zillion (Press CTRL + Click the link to access the tutorials):Find whole number quotients and remainders with up to four-digit dividendsSuggested Manipulatives Vocabulary Suggested Literature


Tasks for Standard OA.3Karl's GardenCarnival Tickets

Tasks for Standard NBT.5Mental Division Strategy

https://learnzillion.com/resources/72478-find-whole-number-quotients-and-remainders-with-up-to-four-digit-dividends-4-nbt-b-6

https://www.khanacademy.org/math/arithmetic/multiplication-division/advanced-mult-div-word-problems/v/multi-step-word-problems-with-whole-numbers-exercise-t2?utm_campaign=embed

https://www.khanacademy.org/math/arithmetic/multiplication-division/partial_quotient_division/v/partial-quotient-division?utm_campaign=embed


http://media.emgames.com/em-v2/eToolkit/eTools_v1.swf







color tilesgraph papertwo-color countersdicehundreds chartmultiplication chartbase-ten blockssnap cubesnumber line

dividenddivisordivision (repeated subtraction)estimatepartition division (fair-sharing)quotientremainder

Things that Come in 2’s, 3’s & 4’sAmanda Bean’s Amazing DreamMy Full Moon is SquareToo Many Kangaroo Things to DoThe Best of TimesThe Doorbell RangEach Orange Had Eight SlicesTwo of Everything Spunky Monkeys On Parade One Hundred Hungry Ants Bats on Parade

GA Framework TasksTask Descriptions

Task Name Task Type/Grouping Strategy

Content Addressed Standard(s) Description of Task

Factor Findings Scaffolding TaskPartner Task

Finding Factors MGSE4.OA.4 Students will create a factor poster with array illustrations and factor rainbows.

My Son is Naughty Constructing TaskPartner Task

Finding Factors MGSE4.OA.4 Students solve a problem involving finding factors of a number and addends of another number.

Investigating Prime and Composite

Scaffolding TaskPartner Task

Prime and Composite Numbers

MGSE4.OA.4 Students learn about prime and composite by making arrays with color tiles.

Prime vs. Composite Practice TaskIndividual Task


MGSE4.OA.4 Students list factors for numbers and determine whether the numbers are prime or composite given the list of factors.


Scaffolding Task Task that build up to the learning task.Constructing Task Task in which students are constructing understanding through deep/rich contextualized problem solvingPractice Task Task that provide students opportunities to practice skills and concepts.Culminating Task Task designed to require students to use several concepts learned during the unit to answer a new or unique situation.Formative Assessment Lesson (FAL)

Lessons that support teachers in formative assessment which both reveal and develop students’ understanding of key mathematical ideas and applications.

3-Act Task Whole-group mathematical task consisting of 3 distinct parts: an engaging and perplexing Act One, an information and solution seeking Act Two, and a solution discussion and solution revealing Act Three.

Factor Trail Game Practice TaskIndividual/Partner Task

Determining factor pairs MGSE4.OA.4 Students earn points in the game Factor Trail as they practice finding all factors in a selected number.

The Sieve of Eratosthenes

Practice TaskIndividual/Partner Task

Determining prime numbers less than 100

MGSE4.OA.4 Students will find all the prime numbers between 0-100 using colored pencils and a hundreds chart.

The Factor Game Practice TaskIndividual/Partner Task

Recognizing factors as prime and composite numbers

MGSE4.OA.4 Students play a partner game by coloring in numbers and their factors on a hundreds chart.

Cicadas, Brood X Constructing TaskPartner Task


MGSE4.OA.4 Students learn that cicadas have a prime number of years in their life cycle which helps them survive.

Finding Multiples Scaffolding TaskIndividual Task

Finding Multiples MGSE4.OA.4 Students color in multiples of various one digit numbers on the hundreds chart and discuss numbers that are and are not multiples of the number colored in.

Finding Products Constructing TaskIndividual/Partner Task

Understanding multiplicative comparisons with factors

MGSE4.OA.1 MGSE4.OA.4

Students will use intersection models to learn about multiplicative comparisons.

At the Circus Constructing TaskIndividual/ Partner Task

Using Partial Products to Multiply

MGSE4.OA.2 MGSE4.NBT.5MGSE4.OA.3

Students solve circus word problems to practice

School Store Constructing TaskIndividual/ Partner Task

Using Properties of Multiplication to Multiply

MGSE4.OA.1MGSE4.OA.2MGSE4.OA.3MGSE4.NBT.5

Students apply what they know about multiplication to invent ways to multiply larger numbers.

Compatible Numbers to

Estimate

Constructing TaskIndividual/Partner Task

Using compatible numbers to divide

MGSE4.OA.3MGSE4.NBT.6

Students will learn about compatible numbers and how to use them to make reasonable estimates for division problems.

Brain Only ScaffoldingIndividual/Partner Task

Patterns in Multiplication and Division

MGSE4.OA.2MGSE4.NBT.5MGSE4.NBT.6

Students use compare and contrast two problems in order to discover relationships between the dividend, divisor and quotient.

What is 2500 ÷ 300? ConstructingIndividual/Partner Task

Dividing with zeros MGSE4.OA.2MGSE4.OA.3MGSE4.OA.5MGSE4.NBT.6

Students learn about dividing when zeroes are involved in the calculation. Students also learn why a quotient is undefined when the divisor is zero.


Boxes and Rolls 3 Act TaskIndividual/Partner Task

Multiplying Two Digit Whole Numbers, DividingWhole Numbers

MGSE4.NBT.5MGSE4.NBT.6

Students multiply and divide whole numbers to determine how many pennies are equivalent to the amount of money shown in an image.

Number Riddles Constructing TaskIndividual/Partner Task

Factors and Multiples MGSE4.OA.4 Students solve riddles to apply knowledge of factors, multiples and place value.

Earth Day Project Constructing TaskIndividual/Partner Task

Generating Rules MGSE4.OA.5 Students solve a real world problem involving patterns as students collect cans for a recycling project at school.

Culminating Task:School Newspaper

Performance TaskIndividual Task

Multiplication, Division and Rounding

MGSE4.OA.1MGSE4.OA.2MGSE4.OA.3MGSE4.OA.5MGSE4.NBT.5MGSE4.NBT.6

Students plan how much paper to purchase in order to stay within a budget when producing a school newspaper.

Websites from GA Frameworks Tasks:


Website Corresponding Framework Task Standard(s)Factor Game (NCTM Illuminations) Factor Finding 4.OA.4

Learnzillion Factor Finding 4.OA.4

Primes and Composites My Son is Naughty 4.OA.4

Fruit Shoot Investigating Prime and Composite Numbers 4.OA.4

Prime and Composite Area Model Investigating Prime and Composite Numbers 4.OA.4

Sieve of Eratosthenes Investigating Prime and Composite Numbers 4.OA.4

Larger Prime Numbers Prime vs. Composite 4.OA.4

Making Your Own Product Game Finding Multiples 4.OA.4

Finding Products Finding Multiples 4.OA.4

Product Game Finding Multiples 4.OA.4

Documents

Web viewFourth Grade Unit 2: Multiplication and Division of Whole Numbers. 9 weeks. In this unit students will: solve multi-step problems using the four operations . use