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Fourth Grade Math

Domain: Number and Operations in Base Ten

Cluster: Generalize place value understanding for multi-digit whole numbers.

Common Core Standard: 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times

what it represents in the place to its right.

 For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value 

and division

.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

-greater than > -less than < -equal to = -compare -comparisons -round -digit -place value Explicit -tenths place -hundredths place -ten thousands place -hundred thousand place -ten thousands place -millions place

 Identify a given place value.

Identify the value of a number in a given place value.

 Show how a number in a given place value is increased or decreased by multiplying or dividing by multiples of 10.

 Understand place value by multiplying and dividing by multiples of 10. Example:

How is the 2 in the number 582 similar to and different from the 2 in the number 528?

The orecity.k12 resource has some activities that can be completed by students.

Let students know that you’re going to play a game with big numbers today. They will work as a team against you to see who can get closest to a 5-digit target number. Then select a student to roll 5 dice, one at a time. As the dice are rolled, line them up, left to right, to form a 5-digit target number.

(Resource is called Place Value through

Millions on orecity.k12 website.)

Use funbrain website to have students practice identifying the correct place in a number.

Use betterlesson resource on Introduction to place value as a lesson plan to teach place value. Extend on practice numbers to include larger numbers up to millions.

Use several different resources from the right to set up centers that students can complete within about 20 minutes. Rotate centers until all centers have been complete.

http://www.orecity.k12.or.us/ staff/curriculum_resources/ mathematics/fourth_grade

http://

www.superteacherworksheets.co m/place-value.html

http://www.fourthnten.com/ 2012/06/place-value-block-math-craftivity.html

http://www.math-aids.com/ Place_Value/

http://www.math-play.com/4th-grade-math-games.html

http://mrnussbaum.com/ placevaluepirates1/

http://www.funbrain.com/tens/ index.html

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http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following activities and should be referenced to for further explanation and examples. This set of place-value blocks represents a number. The value of this number can be represented in many different ways.

For numbers 1a–1d, choose Yes or No to show whether the value is equivalent to the number represented by the place value blocks.

1a. 200 + 90 + 12 Yes No 1b. Three hundred two Yes No 1c. 1 hundred + 20 tens + 2 ones Yes No 1d. 300 + 12 Yes No All CIS strategies applicable

http://betterlesson.com/lesson/ 7662/introduction-to-place-value

http://betterlesson.com/lesson/ 7663/place-value-to-the-hundreds-place

http://betterlesson.com/lesson/

8075/rounding-real-life-situations

http://betterlesson.com/lesson/ 7818/place-value-to-the-ten-thousands-place

http://

www.teachervision.fen.com/tv/ printables/scottforesman/ Math_4_TTT_3.pdf

http://studyjams.scholastic.com/ studyjams/jams/math/index.htm

http://www.nclack.k12.or.us/ cms/lib6/OR01000992/

Centricity/Domain/115/B4SUP-A3_NumPlVal_0409.pdf is an excellent source for additional activities!!!

Fourth Grade Math

Domain: Number and Operations in Base Ten Cluster: Generalize place value understanding for multi-digit whole numbers.

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expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols

to record the results of comparisons.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

-standard form -expanded form -written form -place value -less than < -greater than > -equal to =

Understand place value

Understand standard form

Understand written form

Understand expanded form

Deconstruct numbers to show all the ways to write that number

Deconstruct numbers to show all the ways to write that number and compare your method with a neighbor

Demonstrate if your method or the method of your neighbor equals the same value of the number

Compare multi-digit numbers using appropriate symbols (‹, ›, =).

The orecity.k12 resource has some activities that can be completed by students.

Use worksheet from superteacherworksheets (2nd resource in list) to have student cut and

paste the correct word form, standard form, and expanded form into the correct place. Use podcast link to the right to have students practice comparing numbers. They may choose to compare numbers up to 100, 1,000, or 10,000.

Use several different resources from the right to set up centers that students can complete within about 20 minutes. Rotate centers until all centers have been complete. Use index cards to create cards to play match. On one card have the standard form, another card should have the word form, and the last card should have the expanded form. Have students match up the numbers.

Have numbers written on construction paper. Give two students a number and have them come to the front of the room. Give a third student a greater than, a less than, and an equal sign. The third student must show the correct symbol.

http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following

http://www.orecity.k12.or.us/ staff/curriculum_resources/ mathematics/fourth_grade

http://

www.superteacherworksheets.co m/place-value/seven-digit-place-value-match.pdf

http://

www.superteacherworksheets.co m/place-value.html

http://podcast.eusd4kids.org/ groups/student_resources/wiki/ e4b96/

http://studyjams.scholastic.com/ studyjams/jams/math/index.htm

http://www.nclack.k12.or.us/ cms/lib6/OR01000992/

(4)

activities and should be referenced to for further explanation and examples. This set of place-value blocks represents a number. The value of this number can be represented in many different ways.

For numbers 1a–1d, choose Yes or No to show whether the value is equivalent to the number represented by the place value blocks.

1a. 200 + 90 + 12 Yes No 1b. Three hundred two Yes No 1c. 1 hundred + 20 tens + 2 ones Yes No 1d. 300 + 12 Yes No All CIS strategies applicable

Fourth Grade Math

Domain: Number and Operations in Base Ten Cluster: Generalize place value understanding for multi-digit whole numbers.

Common Core Standard: 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

 Use rounding with a number line and a

The orecity.k12 resource has some activities that can be completed by students.

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-rounding -estimating -place value

hundreds chart . See example at: http://www.ncpublicschools.org/docs/ acre/standards/common-core-tools/ unpacking/math/4th.pdf

 Use rounding by rounding whole numbers to the greatest place value

 Practice rounding by the greatest place value within a word problem

Example:

I rounded 267 to 300. I rounded 194 to 200. I rounded 34 to 30. When I added 300, 200 and 30, I know my answer will be about 530.

 Use rounding by rounding whole numbers to a given place value

 Practice rounding by a given place value within a word problem

Example

I first thought about 194. It is really close to 200. I also have 2 hundreds in 267. That gives me a total of 4 hundreds. Then I have 67 in 267 and the 34. When I put 67 and 34 together that is really close to 100. When I add that hundred to the 4 hundreds that I already had, I end up with 500

 Use rounding by rounding each number to each place value

 Practice rounding with each number in each place value in a word problem. Example

I first thought about 267 and 34. I noticed that their sum is about 300. Then I knew that 194 is close to 200. When I put 300 and 200 together, I get 500.

Use gvsd link to the right to have students practice rounding numbers. Students have the option of rounding to hundreds, thousands, using number lines, or finding the halfway point between two numbers.

Use several different resources from the right to set up centers that students can complete within about 20 minutes. Rotate centers until all centers have been complete.

Write a number on the board and have students round the number to the specific place you tell them or underline the number you want them to round the number to. Repeat this process until every student has had a turn to successfully round a number. Watch the studyjams video on rounding numbers. There is a short quiz at the end of the video.

http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following activities and should be referenced to for further explanation and examples. A teacher asked her students to use

estimation to decide if the sum of the problem below is closer to 4,000 or 5,000.

496 + 1,404 + 2,605 + 489 =

One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning.

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Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated.

All CIS strategies applicable

Fourth Grade Math

Domain: Number and Operations in Base Ten

Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.

Common Core Standard: 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior -regrouping

-commutative property of addition

-associative property of addition

-distributive property -algorithm

 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

 Fluently add and subtract within

1,000,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.  Justify why the standard algorithm for

addition and subtraction works.  Fluently add and subtract multi-digit

whole numbers using the standard algorithm.

http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following activities and should be referenced to for further explanation and examples.

A

scientist watched a group of squirrels collect acorns. Each squirrel

ate some of the collected acorns and stored the rest of the collected

acorns.

The table below shows data for three squirrels in the group. The

number of acorns each squirrel stored is missing from the table. Fill

http://www.orecity.k12.or.us/ staff/curriculum_resources/ mathematics/fourth_grade

http://

www.mathworksheetsland.com/ 4/9bigaddsub.html

https://

mathcoachinteractive.com/ mathcoach-az/topic.php? AtoZTopicAcronym=SMD

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in the data that are missing from the table.

http://www.busyteacherscafe.com/themes/ add_sub_unit.html  has additional activities  for this standard.  

http://www2.smarttutor.com/ player/swf/STA_Problem %20Solving_Addition%20and %20Subtraction%20with %20Decimals_L4_V1_t3a_1.swf

http://www.nclack.k12.or.us/ cms/lib6/OR01000992/

Centricity/Domain/115/B4SUP-A3_NumPlVal_0409.pdf is an excellent source for additional activities!!!

http://www.k-5mathteachingresources.com/ addition-and-subtraction-activities.html 

http://www.region10ct.org/math/ region10mathsitefaq/

activitiestopractice/ activitiestopractice.html 

Fourth Grade Math

Domain: Number and Operations in Base Ten

Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.

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

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior -algorithm -factor -multiple -product -area models

-commutative property of addition

-associative property of addition

-distributive property

Explicit -partitioning -compensation

 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using, modeling, and drawing visual

representations of base ten blocks.  Multiply a whole number of up to four

digits by a one-digit whole number, and multiply two two-digit numbers using and drawing visual representations of area models, and providing justification of strategy.

 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using and drawing visual representations of partitioning, and providing justification of strategy.

 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers using and drawing visual representations of compensation, and providing

justification of strategy.  Construct other strategies of

multiplication using place value and mathematical properties to justify his/her strategy.

 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

The orecity.k12 resource has some activities that can be completed by students.

Use several different resources from the right to set up centers that students can complete within about 20 minutes. Rotate centers until all centers have been complete. Use studyjams videos to show how about multiplication. The videos even include one about the distributive property. Studyjams even has videos for multiples.

Play multiplication bingo. Partners remove the 12 face cards and the aces. Partners divide the remaining cards between the two of them. They should keep cards face down. At the count of three, they each turn over a card. The first partner to say the

multiplication answer after cards have been turned over gets both cards. Continue until one partner has all cards. (May also use for addition and subtraction for students who need practice on basic facts.)

A group of students can use dice to make a three or four digit number. Then roll one additional die to make the other factor. Students must multiply the numbers.

A group of students can use two dice to make a number and then roll two more dice to make the other factor. Students in group must multiply the number and check to see if everyone in group has the same answer. If

(9)

area models. not, other group members must help student figure out the mistake.

http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following activities and should be referenced to for further explanation and examples.

Mr. Torres sold a total of 30 boxes of sports cards at his store on Monday. These boxes contained only baseball cards and football cards.

• Each box contained 25 sports cards. • He earned $3 for each sports card he sold. • He earned a total of $1134 from the football cards he sold. What amount of money did Mr. Torres earn from the baseball cards he sold? In the space below, use pictures, numbers, and/or words to show how you got your answer.

Another Example

Pablo solved a multiplication problem using two different methods. He made a mistake in either Method W or Method Z.

Identify the method where Pablo made a mistake and explain what he should do to correct it.

Students create a factor tree with numbers between 1 and 100. See website for complete lesson outline.

http://mathlessons.about.com/ od/fourthgradelessons/a/Lesson-Plan-Factor-Trees.htm

Students play the factor game to determine the factors of

numbers and then identify the numbers as either prime or composite. See website for complete lesson outline. http://illuminations.nctm.org/ LessonDetail.aspx?ID=L620

Students use Venn diagrams to represent the relationship between the factors or products of two numbers. See website for complete lesson outline.

http://illuminations.nctm.org/ LessonDetail.aspx?ID=L274

Students watch an online video lesson on how to find factors of numbers. They can then

complete the online practice and teachers can print out the free worksheet for homework. http://www.adaptedmind.com/ p.php?tagId=605#

(10)

Another Example

A multiplication problem is shown below. 17

×12

Which model(s) below could represent the solution to this problem? Click the letter next to all that apply.

A.

B.

C.

(11)+(1 7)+(2 1)+(2 7)

D.

E.

(17 2)+(17 1)

homework.

http://www.adaptedmind.com/ p.php?tagId=681

4.OA.C.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. Students examine a version of Pascal’s triangle and determine the number patterns to fill in the triangle. Free downloadable worksheet.

http://

www.mathmammoth.com/ preview/

Patterns_Pascals_Triangle.pdf

Smart Board lessons that teach both number patterns and shape patterns. Found in Smart

Exchange.

http://exchange.smarttech.com/ search.html?

q=Patterns&subject=Mathematic s&grade=Grade+4&region=en_U S

Several lesson plans for teaching number patterns. Some are online and some have free printable worksheets.

http://www.teachingideas.co.uk/ maths/contents_nopatterns.htm

(11)

F.

All CIS strategies applicable Another Example

Use these base-ten blocks to model 247 x 3

.

What is the product of 247 x 3?

Type your answer in the space provided.

arrangements. The aim of the unit is for students to keep track of the numbers involved by drawing up a table of values. They are then encouraged to look for patterns in the numbers. http://nzmaths.co.nz/resource/ supermarket-displays?

parent_node=

In this unit the students design and construct homes for the three pigs. Each of the homes is made and filled with patterns that we explore.

http://nzmaths.co.nz/resource/ three-pigs?parent_node=

Fourth Grade Math

Domain: Number and Operations in Base Ten Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.

(12)

models.

Essential Vocabulary Task Analysis Learning Activities/Assessments Resources

Prior

-distributive property -algorithm -factor -multiple -product -dividend -divisor -quotient -partitioning -compensation -reason -compare

Divide a whole number of up to four digits by a one-digit whole number modeling and drawing visual

representations of base ten blocks, and providing justification of strategy.

Divide a whole number of up to four

digits by a one-digit whole number modeling and drawing visual representations of place value  principles/distributive property, and providing justification of strategy. Example: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4)  Divide a whole number of up to four

digits by a one-digit whole number modeling and drawing visual

representations of multiplication, and providing justification of strategy. Example:

4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65 

 Divide a whole number of up to four digits by a one-digit whole number modeling and drawing visual

representations of open arrays or area  models, and providing justification of strategy. Example:

150 ÷ 6 =

6 6

10

The orecity.k12 resource has some activities that can be completed by students.

Use several different resources from the right to set up centers that students can complete within about 20 minutes. Rotate centers until all centers have been complete. Watch studyjams video on distributive property.

A group of students can use dice to make a three or four digit number. Then roll one additional die to make the divisor. Students must divide the numbers to get the answer. Students must all come up with same answer. If not members of group must help to find the mistake.

http://dese.mo.gov/divimprove/assess/ documents/asmt-sbac-math-gr4-sample-items.pdf is credited for the following activities and should be referenced to for further explanation and examples.

There are 37 students in a class. Students go to a science lab in groups that contain no more than 7 students. Make a model to show the fewest number of science lab groups that will need to be formed with these 37 students. Click on an oval to make a group. Continue as many times as

necessary to make the correct number of groups. [When an oval is clicked, an oval will be created in the working space.]

(13)

10

 5

10 + 10 + 5 = 25

So 150 ÷ 6 = 25

 Construct other strategies of division using mathematical properties to justify his/her strategy.

 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.

Click on a student and then click on an oval to put the student in a group. Continue as many times as necessary. [When a student icon is clicked and then an oval is clicked, student icons snap to position

in the oval to allow for multiple icons.]

What is the fewest number of science lab groups that will need

to be formed with these 37 students?

lab groups

All CIS strategies applicable

division

http://www.education.com/ activity/article/Bulls_Eye/

http://pinterest.com/source/ sims4392.blogspot.ca/

http://www.nclack.k12.or.us/ cms/lib6/OR01000992/

Centricity/Domain/115/B4SUP-A3_NumPlVal_0409.pdf is an excellent source for additional activities!!!

Students create a factor tree with numbers between 1 and 100. See website for complete lesson outline.

http://mathlessons.about.com/ od/fourthgradelessons/a/Lesson-Plan-Factor-Trees.htm

Students play the factor game to determine the factors of numbers and then identify the numbers as either prime or composite. See website for complete lesson outline.

http://illuminations.nctm.org/ LessonDetail.aspx?ID=L620

Students use Venn diagrams to represent the relationship between the factors or products of two numbers. See website for complete lesson outline.

(14)

Students watch an online video lesson on how to find factors of numbers. They can then

complete the online practice and teachers can print out the free worksheet for homework. http://www.adaptedmind.com/ p.php?tagId=605#

Students watch an online video lesson on how to determine if a number is prime or composite. They can then complete the online practice and teachers can print out the free worksheet for homework.

http://www.adaptedmind.com/ p.php?tagId=681

4.OA.C.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. Students examine a version of Pascal’s triangle and determine the number patterns to fill in the triangle. Free downloadable worksheet.

http://

www.mathmammoth.com/ preview/

Patterns_Pascals_Triangle.pdf

Smart Board lessons that teach both number patterns and shape patterns. Found in Smart

Exchange.

(15)

search.html?

q=Patterns&subject=Mathematic s&grade=Grade+4&region=en_US

Several lesson plans for teaching number patterns. Some are online and some have free printable worksheets.

http://www.teachingideas.co.uk/ maths/contents_nopatterns.htm

In this unit the students look at the number patterns created when tins are stacked in different arrangements. The aim of the unit is for students to keep track of the numbers involved by drawing up a table of values. They are then encouraged to look for patterns in the numbers. http://nzmaths.co.nz/resource/ supermarket-displays?

parent_node=

In this unit the students design and construct homes for the three pigs. Each of the homes is made and filled with patterns that we explore.

(16)

References

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