Mathematics Pacing Resource Document
4.AT.2
Standard: 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship
between multiplication and division to solve real-world and other mathematical problems.
Teacher Background Information:
http://www.learner.org/resources/series171.html Annenberg Video on Demand: These 26-minute video segments are free professional development that
stream to your computer. Scroll down and select Video 4: Meanings and Models for Operations.
http://www.eduplace.com/math/hmm/background/3/08/te_3_08_overview.html Relating Multiplication and Division Overview
http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/primary/unit_6_multiplication_and_division.pdf Several teaching strategies
Lesson Plans/Print Activities:
Web-based Practice:
Math Expressions:
o Fluency Plan (FP) Lesson 3
o FP Lesson 5
o FP Lesson 9
o U7 Lesson 1
http://www.aaaknow.com/div34cx2.htm AAA Math: relationship
between multiplication and division
http://www.worksheetsplus.com/Multiplication%20and%20Division%20Relatio
nship%20Worksheet.html Worksheets with visuals
http://www.aaamath.com/pro34cx2.htm
Smartboard math activities that are divided into grade levels. Click
on LEARN, PRACTICE, PLAY or EXPLORE.
http://mathsolutions.com/wp-content/uploads/0-590-30012-1_L.pdf Lesson
plan: Amanda Bean’s Amazing Dream
http://www.aaamath.com/g2_39_x1.htm AAA Math: Relationship
between division and subtraction
http://www.ezschool.com/Games/Math/MultiplyDivide/FactFamily2.html Fact
Family Practice (division and multiplication)
http://illuminations.nctm.org/Lesson.aspx?id=2520 NCTM Illuminations Factor
Trail Game
http://illuminations.nctm.org/Lesson.aspx?id=3280 NCTM Illuminations Factor
Findings
http://www.snappymaths.com/mixed/multdivrelate/multdivrelate.htm
Printable activity sheets
http://www.mathplayground.com/tb_multiplication/thinking_blocks_multiplic
ation_division.html Math Playground Thinking Blocks
http://donnayoung.org/math/tricards.htm Printable triangular flashcards
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.AT.2
Item Bank:
1) Elana made the two models shown below. Each model represents the same math problem. [Examview Test Generator, 2004] Answer: C
Which of the following equations does not match Elana’s math problem?
A. 30 ÷ 6 = 5
C. 6 = 5 × 30
B. 6 × 5 = 30
D. 30 ÷ 5 = 6
2) Amanda wrote the number sentence shown below.
56 ÷ 7 = 8
Which number sentence could Amanda use to check her work? [Massachusetts Dept. of Education] Answer: A
A. 8 × 7 =
B. 8 ÷ 7 =
C. 56 × 7 =
D. 56 + 8 =
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
3) Which equation below is true? [IPS C&I] Answer: B
A. 3 + 3 + 3 + 3 + 3 + 3 + 3 = 7 × 7
C. 4 × 9 = 4 + 4 + 4 + 4
B. 5 + 5 + 5 + 5 + 5 + 5 = 6 × 5
D. 2 × 8 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8
4) Jessica and Suzanne have a bag of 108 candies. They want to find the greatest number of candies to put into 12 bags so that each bag will have the same
amount. Sharon says they should see how many times they can subtract 12 from 108. Jessica says they should divide 108 by 12. Who is correct? Sharon,
Jessica, both, or neither? How do you know? [Modified from Mathematics Assessment Sampler, 2005] Answer: Both are correct. Students might show the
actual computation to support their answer.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Companion
4.AT.3
Standard: 4.AT.3: 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.
Teacher Background Information:
Repeated addition and arrays are two ways of thinking about multiplication. Multiplication can also be thought about as multiple comparison problems that
involve a comparison of two quantities in which one is described as a multiple of the other. The relation between quantities is described in terms of how
many times larger one is than the other. An example of multiplicative comparison is a 10-foot alligator is five times longer than a 2-foot alligator. (Howard
County Public Schools, Maryland)
Lesson Plans/Print Activities:
Web-based Practice:
Math Expressions:
o U1 Lesson 4
o U3 Lesson 6
http://www.mathplayground.com/ThinkingBlocks/thinking_blocks_modeling
%20_tool.html Thinking Blocks modeling tool. View the video tutorial before
starting.
http://www.k-5mathteachingresources.com/support-files/representingmultiplicative-comparison-problems.pdf Practice examples
http://www.orglib.com/4.oa.1-worksheetviewTestQuestions_0d1520c2bb_034fc28cb55c40eabc3cf79cb87fd2f9_287.ht
ml Org Lib math assessments and student response system
http://www.khanacademy.org/math/cc-fourth-grade-math/cc-4th-mult-div-topic/cc4th-mult-comparing/e/comparing-with-multiplication Khan Academy comparing with
multiplication
https://learnzillion.com/lessons/2543-see-multiplication-as-a-comparison-usingnumber-sentences Learn Zillion video lesson
http://www.insidemathematics.org/problems-of-the-month/pommeasuringmammals.pdf Inside Mathematics Measuring Mammals lesson plans
https://www.illustrativemathematics.org/illustrations/357 Illustrative Mathematics
Comparing Growth, Variation 2
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Companion
4.AT.3
Item Bank:
1) Select the correct choices for interpreting the following multiplication: [www.orglib.com] Answer: C and E
6=3x2
A. 6 is 3 times as many as 3
B. 6 is 2 times as many as 2
C. 6 is 3 times as many as 2
D. 6 is 2 times as many as 6
E. 6 is 2 times as many as 3
F. 6 is 3 times as many as 30
2) Joyce bought 3 pounds of apples. She also bought 4 times as many pounds bananas as pounds of apples. How many pounds of bananas did she buy?
[www.engageny.org] Answer: 12 pounds
3) This month I saved four times as much as last month. Last month I saved $9.00. How much did I save this month? [IPS C&I] Answer: $36.00
4) A dishwasher uses 11 liters of water for each cycle. A washing machine uses 5 times as much water as a dishwasher uses for each load. Combined, how
many milliliters of water are used for 1 cycle of each machine? [www.engageny.org] Answer: 66,000 ml
Illustrative Mathematics Performance Assessments: https://www.illustrativemathematics.org/illustrations/1809 Threatened and Endangered
https://www.illustrativemathematics.org/illustrations/1808 Thousands and Millions of Fourth Graders
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.1
Standard:
4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach.
Teacher Background Information:
http://www.learner.org/courses/learningmath/number/session4/part_a/index.html Annenberg Learner: Meanings and Relationships of the Operations
https://grade4commoncoremath.wikispaces.hcpss.org/4.NBT.4 Ideas for increasing the rigor of this standard.
Lesson Plans/Print Activities:
Math Expressions
o Unit 3 Lesson 11
o U3 Lesson 12
o U3 Lesson 14
o U3 Lesson 15
o U3 Lesson 16
o U3 Lesson 12
o U3 Lesson 18
o U3 Lesson 19
o U3 Lesson 20
Web-based Practice:
http://www.dositey.com/2008/addsub/add3dig.htm
Step-by-Step Addition
http://mrnussbaum.com/draggablemain/index3/
Drag and Drop Math
http://nlvm.usu.edu/en/nav/frames_asid_155_g_2_t_1.html?from=category_g_2_t_1.html National Library of Virtual
Manipulatives: Subtraction with Regrouping
http://nlvm.usu.edu/en/nav/frames_asid_154_g_2_t_1.html?from=category_g_2_t_1.html National Library of Virtual
Manipulatives: Addition
E-Lab addition with regrouping (base ten blocks)
https://learnzillion.com/lessons/3057-add-using-an-open-number-line Learn Zillion lessons
https://grade4commoncoremath.wikispaces.hcpss.org/file/view/4.NBT.4_3_2_RealityChecking.pdf/457297674/4.NBT.4_3_2_R
ealityChecking.pdf Reality Checking lesson
https://www.illustrativemathematics.org/illustrations/1189 Illustrative Mathematics To Regroup or Not to Regroup
https://grade4commoncoremath.wikispaces.hcpss.org/file/view/Making%20Sense%20of%20the%20Algorithm.pdf/402793860/
Making%20Sense%20of%20the%20Algorithm.pdf Georgia Dept. of Education lesson: Making Sense of the Algorithm
https://grade4commoncoremath.wikispaces.hcpss.org/Creating+Sums+and+Differences+Activities Lesson extensions
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Item Bank:
1) Write a subtraction problem for which the difference equals 1,557. Show your work below. [Howard County Public Schools, Maryland]
Sample Answer: 2,269 – 712
2) Kendra solved a math problem this way: [Howard County Public Schools, Maryland] Sample Answer: Kendra is incorrect. She subtracted 2 ones from 8 ones
instead of the other way around. She also subtracted 3 tens from 7 tens instead of subtracting 7 tens from 2 tens (since you would have regrouped tens to ones).
Also there would have only been 5 hundreds to subtract 1 hundred from once all of the regrouping was done.
Is her answer correct or incorrect?
Use pictures, numbers, and words to show your reasoning
3) Select 3 numbers below that have a sum of 233: [www.orglib.com] Answer: A, B, and C or B, D, and E
A) 120
B) 13
C) 100
D) 150
E) 70
F) 400
4) [Delaware Dept. of Education] Answer: A
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.2
Standard: 4.C.2: 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. Describe the strategy and explain the reasoning.
Teacher Background Information:
http://www.learner.org/courses/learningmath/number/session4/part_a/multiplication.html Annenberg Learner mini course
http://www.helpingwithmath.com/by_subject/multiplication/mul-area-method-4nbt5.htm Many students find the area model helpful when trying to
understand multi-digit multiplication.
Lesson Plans/Print Activities:
Math Expressions
o U5 Lesson 1
o U5 Lesson 3
o U5 Lesson 5
o U5 Lesson 6
o U7 Lesson 7
Web-based Practice:
http://mrnussbaum.com/draggablemain/index2/ Draggable Math
http://www.dositey.com/muldiv/mul1ml1.htm Dositey mini lesson
http://www.iknowthat.com/com/App?File=EarlyMathWorkbench.htm&Type=D&App=Early
MathWorkbench&Topic=Mult Arithmetic Workshop (When asked to register, click “Click here to start your activity.”
Math Solutions The Game of Target 300
“Block it to Multiply” Indiana Framework Lesson: IPS Online>4th Grade ISTEP
PREP Group Math>Grade 4 Lessons>4.2.5
http://www.factmonster.com/math/knowledgebox/player.html?movie=sfw50645
Crack the Code Multiplication: Video and game (more difficult for students that need a
challenge)
https://learnzillion.com/search?query=4.nbt.5&page=1&models%5B%5D=Le
ssonSet&models%5B%5D=Resource Learn Zillion lessons
http://www.khanacademy.org/math/arithmetic/multiplicationdivision/multi_digit_multiplication/v/2-digit-times-1-digit-example Khan
Academy video
https://www.khanacademy.org/math/arithmetic/multiplicationdivision/lattice_multiplication/v/why-lattice-multiplication-works Khan
Academy: Why Lattice Multiplication Works
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Item Bank:
1) Write a multiplication problem with one 3-digit factor and one 1-digit factor with a resulting product that falls between 4,000 and 5,000. Show your work.
2)[Delaware Dept. of Education] Answer: A
3) http://www.insidemathematics.org/assets/common-core-math-tasks/the%20baker.pdf Inside Mathematics task: The Baker
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.4
Standard:
4.C.4: Multiply fluently within 100
Teacher Background Information:
“Mastery of a basic fact means that a child can give a quick response (in about 3 seconds) without resorting to nonefficient means, such as counting.” Elementary and Middle School Mathematics: Teaching Developmentally, John A. Van de Walle , 2004
Students who struggle with the memorization of these math facts may not have a solid understanding of the concepts of multiplication and division
and the number relationships among the operations. Use of the Math Expressions strategy cards (found in the individual student manipulative bags) is
encouraged to support these connections.
Lesson Plans/Print Activities:
Math Expressions:
Fluency Plan (FP) Lesson 2
FP Lesson 3
FP Lesson 4
FP Lesson 5
FP Lesson 6
FP Lesson 7
FP Lesson 8
FP Lesson 9
FP Lesson 10
FP Lesson 11
FP Lesson 12
FP Lesson 13
FP Lesson 14
FP Lesson 15
FP Lesson 17
Blackout game (Math Expressions TRB p. M25-M26)
Product Cards are provided in each student’s manipulative kit. Those on Activity Workbook p. 8-12 may be sent home to be cut out and used for
practice.
http://illuminations.nctm.org/LessonDetail.aspx?id=L620 NCTM
Illuminations: The Factor Game
Indianapolis Public Schools
Web-based Practice:
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/multiplication/timestabl
es/index.shtml Factsheets, tests and games for multiplication
http://www.eduplace.com/kids/mw/swfs/manip/manipulative.swf?tm=/kids/mw/s
wfs/manip/tables_mult.swf Interactive Times Tables
http://www.multiplication.com/interactive_games.htm several interactive games
http://www.mathplayground.com/multiples.html Pumpkin Multiples
http://www.amblesideprimary.com/ambleweb/mentalmaths/tabletrees.html
Table Trees
http://www.prongo.com/lemon/game.html Lemonade Larry
http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html
Division Machine
http://www.sums.co.uk/playground/c3a/playground.htm Division Factory
http://www.multiplication.com/flashgames/GrannyPrix.htm Granny Prix: online
multiplication practice by tables (4s, etc.)
Curriculum and Instruction
Mathematics Pacing Resource Document
http://illuminations.nctm.org/LessonDetail.aspx?id=U100 NCTM
Illuminations: The Product Game
http://www.donnayoung.org/math/tricards.htm Printable triangular flash
cards
http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/multrock.html
Multiplication Rock
Item Bank:
http://www.worksheetworks.com/math/basic-operations/drills/multiplication-division-drill.html Create multiplication and division drills
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.C.7
Standard: 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication
(associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the
distributive property.
Teacher Background Information:
http://www.icoachmath.com/math_dictionary/Commutative_Property_of_Multiplication.html commutative property of multiplication: video definition
http://www.icoachmath.com/math_dictionary/associative_property.html associative property of multiplication: video definition
http://investigations.terc.edu/library/curric-math/multdiv_2ed.pdf Investigation in Number, Data and Space
http://www.eduplace.com/math/mw/models/overview/4_4_2.html Houghton Mifflin Math Teaching Models
The distributive property is used in the traditional multiplication and division algorithms (Ex. When multiplying 53 42, we first multiply 53 2 and then
multiply 53 40.) The distributive property is also useful in making mental math calculations easier. (Buying 2 notebooks that each cost $1.98 can be done
by multiplying 2 $2.00 and then subtracting 2 2¢.) Connect students’ prior knowledge with these processes to the step-by-step procedure in the
distributive property.
The rectangle sections model for multiplication used in Math Expressions is based on the distributive property. Support provided at
http://www.eduplace.com/math/mthexp/g4/algorithms/pdf/aa_g4_06.pdf
http://my.hrw.com/math06_07/nsmedia/homework_help/msm1/msm1_ch01_05_homeworkhelp.html Video help and practice problems
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Lesson Plans/Print Activities:
Web-based Practice:
Math Expressions
o Fluency Plan (FP) Lesson 3
o FP Lesson 16
http://www.ixl.com/math/grade-4/properties-of-multiplication
http://www.aaamath.com/pro74bx2.htm definitions and examples of commutative,
associative, distributive properties
http://reviewgamezone.com/game.php?id=2646
http://www.studyzone.org/mtestprep/math8/e/multprop_6p.cfm
http://www.math-aids.com/Properties/Property_Identifying.html question generator
http://www.glencoe.com/sec/math/brainpops/00112039/00112039.html
BrainPop Scroll down to “Chapter 1” and click on Commutative Property
http://www.lessonplanspage.com/MathArtCommutativeProperty35.htm lesson plan
BrainPop Click on ”Distributive Property” under Chapter 1.
http://illuminations.nctm.org/Lesson.aspx?id=1820 NCTM Illuminations:
Commutative Rectangle
http://www.glencoe.com/sec/math/brainpops/00112040/00112040.html
BrainPop Scroll down to “Chapter 1” and click on Associative Property
http://studyjams.scholastic.com/studyjams/jams/math/multiplicationdivision/distrib-property.htm Scholastic online tutorial and quiz
Harcourt School E-lab with visual models
http://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-andmultiples/cc-6th-distributive-property/v/the-distributive-property Khan Academy
videos
http://learnzillion.com/lessons/1877-use-an-area-model-to-multiply-a-three-digitnumber-by-a-one-digit-number Learn Zillion lesson (multiplication with an area
model)
https://www.mathscore.com/math/practice/Distributive%20Property/
Distributive property practice online
http://www.quia.com/ba/15357.html Battleship
http://www.quia.com/pages/jspicer/page22 online quizzes
Item Bank:
1) Choose the number that makes the number sentence true. [IPS C&I] Answer: D
1 × (3 × 5) = (1 × 3) × ____
A. 1
B. 3
C. 4
D. 5
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
2) Suppose you are finding 6 × 2 × 5 mentally. Which number sentence correctly shows another way to arrange the numbers to make the mental math easier?
[IPS C&I] Answer: C
A. 6 × 2 + 5 = 17
C. 5 × 2 × 6 = 60
B. 2 × 6 × 5 = 50
D. 6 + 2 × 5 = 16
3) Which number replaces the ? to make the equation true? [IPS C&I] Answer: A
7 × (5 + 3) = (7 × ?) + (7 × 3)
A. 5
B. 7
Indianapolis Public Schools
C. 8
D. 35
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.1
Standard: 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show
equivalent forms of whole numbers up to 1,000,000.
Teacher Background Information:
http://www.learner.org/courses/learningmath/number/session1/index.html Annenberg Learner What is a Number System?
http://www.learner.org/courses/learningmath/number/session2/index.html Annenberg Learner Number Sets, Infinity, and Zero
Utilize hundred charts, number lines, base ten blocks, dot grid on the back of the Grade 4 Math board, and other models to represent forms of numbers.
Avoid using the word “and” when reading whole numbers. “And” is used to signify the transition between whole numbers and decimals when reading those numbers. (Ex:
2.31 is two and thirty-one hundredths)
We use a decimal place value system (based on ten) where there are different symbols for the natural numbers 1 to 9, and a symbol for 0 which is used as a placeholder.
There are patterns in the way that numbers are formed, for example, each decade has a symbolic pattern that is reflective of the symbols 1 to 9 (e.g. 21, 31, 41, 51, 61, 71,
81, 91, etc.).
The position of digits in numbers determines what they represent. The lowest value digits are on the right and the value of each digit is 10 times the value of the digits on its
immediate right.
0 has a double function. Sometimes it represents ‘nothing’ and so represents no objects and as such makes no difference when it is added to another number. At other
times it represents a placeholder, for example, in the number 208 it indicates that there are no tens and forces the 2 into the hundred place.
Science connections: 4.3.14 (fossil fuels), 4.5.1 (multi-digit numbers), 4.4.8 (artifacts), 4.4.1(cells). Some of these science concepts are paced at the end of the year, which
may serve as a nice review of number and place value.
Lesson Plans/Print Activities:
Math Expressions
o Unit 3 Lesson 8
o Unit 3 Lesson 10
http://illuminations.nctm.org/Lesson.aspx?id=4018 NCTM Illuminations: Making Your
First Million
Web-based Practice:
https://learnzillion.com/search?query=4.nbt.2&page=1&models%5B%5D=Less
onSet&models%5B%5D=Resource Learn Zillion videos
Read and Write Numbers in Numeric Form Video Lesson
Read and Write Numbers with Zeros Video Lesson
Read and Write Numbers in Word Form Video Lesson
http://www.funbrain.com/numwords/index.html Fun Brain: Cookie Dough
IPS Online>Community Group Elementary Math K-6>Indiana Standards Resources for
Mathematics> Grade 4>4.1.1 A Thousand Thousands
Indianapolis Public Schools
http://www.mathcats.com/explore/reallybignumbers.html Math Cats:
Reading Really Big Numbers
Curriculum and Instruction
Mathematics Pacing Resource Document
http://nrich.maths.org/public/viewer.php?obj_id=1288 Calculator BINGO
http://www.studyzone.org/mtestprep/math8/d/million5l.cfm Study Zone
http://www.learnnc.org/lp/pages/3013 Exploring place value with M&Ms
Getting Ready for ISTEP+ workbook Page 39-40
Math Diagnosis and Intervention System in Scott Foresman—Lesson page 19, Activity
page 88
http://www.eduplace.com/cgibin/template/kids/hmm/practice/templates/rules.thtml?ID=hmm07_ep/gr4/0
104&GRADE=4&UNIT=1&CHAPTER=1&LESSON=4&UNIT_TITLE=Place%20Valu
e Eduplace Online
http://www.emaonline.org.uk/ema/client_files/resources_ftp/netmedia/digit
wize/english/index.htm Digit-wize
http://www.toonuniversity.com/flash.asp?err=503&engine=15 Place Value to
Thousands
http://www.funbrain.com/tens/index.html Funbrain Place Value Puzzler
http://education.jlab.org/placevalue/index.html Place Value Game
http://www.ixl.com/math/grade-4/place-values Place Value Models
http://www.ixl.com/math/grade-4/convert-between-place-values Convert
between place values
http://www.starrmatica.com/standalone/starrMaticaplaveValueMysteryNum
bers.swf Place Value Mystery Number
Item Bank:
1. Write the following number in standard form: [Examview Test Generator, 2004] Answer: 484,502
4 hundred thousands 8 ten thousands 4 thousands 5 hundreds 2 ones
2. Which choice below shows 992,459 in word form? [Examview Test Generator, 2004] Answer: C
A. nine hundred thousand, four hundred fifty-nine
B. nine hundred twenty thousand, four hundred fifty-nine
C. nine hundred ninety-two thousand, four hundred fifty-nine
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
D. nine hundred ninety-two million, four hundred fifty-nine thousand
3. By how much would the value of 5,647 be decreased if the 5 were replaced by a 2? [NAEP, 1990] Answer: C
A. 3
B. 300
C. 3,000
D. 30,000
4.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.2
Standard: 4.NS.2: Compare two whole numbers up to 1,000,000 using >, =, and < symbols.
Teacher Background Information:
Students having difficulty with this skill can be directed to write the numbers one on top of the other in order to compare place values.
Continue to use place value language as students work to master this skill.
Lesson Plans/Print Activities:
Math Expressions
o Unit 3 Lesson 1
o Unit 3 Lesson 9
IPS Online Indiana Standards and Resources for Mathematics
Go to IPS Online > Community Group Elementary Math K-6 > Indiana Standards
Resources for Mathematics > Grade 4 > 4.1.3 More or Less
Optional Scrimmage 3: Questions 4, 5, and 6 (IPS Online, Elementary Math K-6
Community Group, Optional Math Scrimmage Folder)
http://learnzillion.com/lessons/521-compare-numbers-using-the-symbols-and- Learn
Zillion lesson
Web-based Practice:
http://www.funbrain.com/ofm/index.html One False Move
http://www.khanacademy.org/math/arithmetic/applying-math-reasoningtopic/greater-than-less-than/v/greater-than-and-less-than-symbols Khan
Academy
http://www.ictgames.com/caterpillar_slider.html Counting Caterpillar
(numbers 1,000-9,000)
http://www.free-training-tutorial.com/place-value/greaterthan.html
Speedboats (numbers 1,000-9,999)
http://www.free-training-tutorial.com/place-value/clickthehighest.html UFOs
in Space (numbers 100-9,999)
http://bridges1.mathlearningcenter.org/media/Bridges_Gr4_OnlineSupplement/B4SU
P-A3_NumPlVal_0409.pdf Bridges in Mathematics Grade 4 Supplement
Item Bank:
1) Compare the two multi-digit numbers 5,160 and 5,167. Which of the following statements is FALSE? [www.orglib.com] Answer: D
A. Both numbers have the same value of thousands.
B. Both numbers have the same value of hundreds.
C. Both numbers have the same value of tens.
D. Both numbers have the same value of ones.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
2) The chart gives the number of books in some city libraries. [Examview Test Generator modified, 2004] Answer D
TRASH CANS IN THE CITY
City
Smithville
Number of Trash Cans
1,047,689
Dingo City
1,349,045
Jonesburg
1,298,034
Chalkland
1,030,405
Eco Beach
1,003,607
Which city has more trash cans, Smithville or Eco Beach?
What number sentence shows the comparison?
A.
B.
C.
D.
Eco Beach;
Eco Beach;
Smithville;
Smithville;
1,003,607 > 1,047,689
1,003,607 < 1,047,689
1,003,607 > 1,047,689
1,003,607 < 1,047,689
3) Circle the number below with the largest value. [Howard County Maryland] Answer: 876,359 is the largest and 867,359 has the smallest value.
Underline the number below with the smallest value.
869,735
873,965
867,953
876,359
4) Complete the numbers to make each sentence true.
14,765 > 14, _ 75
Indianapolis Public Schools
26,243 < _6,243
345,679 = 3_5,679
972,_01 < 972,401
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.8
Standard: 4.NS.8: 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.
Teacher Background Information:
This standard does not include the concept of prime and composite numbers, which has moved to 6th grade.
http://www.learner.org/courses/learningmath/number/session5/index.html Annenberg Learner mini course.
Lesson Plans/Print Activities:
Web-based Practice:
Amanda Bean’s Amazing Dream: A Mathematical Story by Cindy Newschwander is included in
your literature library.
https://learnzillion.com/student/lessons/785-find-all-factor-pairs-of-anumber-using-a-tchart Learn Zillion videos
Complete Going Further and Differentiated Instruction Card
http://www.helpingwithmath.com/resources/games/target_factors01/
not_factor.html “Not a Factor” game
(Challenge) TE p. 734-735
http://illuminations.nctm.org/LessonDetail.aspx?id=L620 NCTM Illuminations: The Factor
Game
http://illuminations.nctm.org/unit.aspx?id=6087 NCTM Illuminations: The Product Game
http://studyjams.scholastic.com/studyjams/jams/math/multiplicationdivision/divisibility-rules.htm Divisibility Rules from Study Jams
http://illuminations.nctm.org/Lesson.aspx?id=3726 NCTM Illuminations: Chocolate FACTORy
http://www.mathplayground.com/howto_divisibility.html Divisibility
Rules from Math Playground
http://illuminations.nctm.org/Lesson.aspx?id=3697 NCTM Illuminations: Times Square:
Reinforcing Multiplication Skills Using Times Square and Strategy
http://www.vectorkids.com/vkdivisible.htm Divisibility Rules practice
http://illuminations.nctm.org/Activity.aspx?id=3511 Factorize (finding factors of a given
number by creating arrays)
https://www.engageny.org/resource/grade-4-mathematics-module-3-topic-f-lesson-24
Engage NY: Determine whether a whole number is a multiple of another number
https://www.engageny.org/resource/grade-4-mathematics-module-3-topic-f-lesson-23
Engage NY: Use division and the associative property to test for factors and observe patterns
https://www.engageny.org/resource/grade-4-mathematics-module-3-topic-f-lesson-22
Engage NY: Find factor pairs of numbers to 100 (understanding of prime and composite
numbers is not required until 6th grade according to the IAS 2014.)
http://illuminations.nctm.org/Lesson.aspx?id=2520 Factor Trail game
http://www.donnayoung.org/math/tricards.htm Printable triangular flash cards
http://faculty.kutztown.edu/schaeffe/Mnemonics/MultRock/multrock.html Multiplication
Rock
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.8
Item Bank:
1) Circle the whole number factors of 24. [www.orglib.com modified] Answer: A, B, D, F
A. 1 × 35
B. 2 × 12
C. 3 × 3
D. 4 × 6
E. 6 × 6
F. 8 × 3
2) Jack is 36 years old. He went to a birthday party for someone in his family named Alicia. When he was there, he realized that his age is a multiple of Alicia’s age. Find all the possible ages that Alicia could be. Show your work in the space below, and then write your answers on the lines.
3) Jason and Laura were at the soccer game. Jason told Laura that his two daughters, Penny and Lily, were celebrating birthdays that week. He didn’t tell Laura how old they were. Instead, he gave Laura these clues about their ages: [Howard County Maryland] See below for scoring notes.
• Each of their ages is a factor of 24
• 36 is a multiple of both Penny’s age and Lily’s age.
• 30 is a multiple of Lily’s age, but not Penny’s age.
• The sum of their ages is 14.
Use Jason’s clues, the chart, and the space below to help figure what Penny and Lily’s ages are.
Penny
Indianapolis Public Schools
Lily
SUM
Curriculum and Instruction
Mathematics Pacing Resource Document
Teacher notes:
• Students may do calculations on the paper, either to solve or to check their work. You may also choose to give students extra paper on which they can do their work.
• The target concept of this task is described in 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.
• For this task, students should ultimately indicate that Penny is 12 and Lily is 2.
• Common errors for this task would be for students to identify a pair of ages that meets some but not all of the given criteria. For example, they might select 10 for Lily’s age and 4 for Penny’s age. These ages would meet some
of the criteria (sum of 14, 30 is a multiple of 10 but not 4, 36 is a multiple of 4, 4 is a factor of 24) but not others (10
is not a factor of 24, 36 is not a multiple of 10). When scoring a task for a student who selects such numbers, it may
be helpful to consider each number in the context of all the clues to see how many clues each answer meets. You
may rate the student to indicate that he or she “got” the target concept if the numebrs meet many, but not all, of the clues.
• In addition, you may choose to use the level of student work to distinguish between a 3 and a 2 or a 2 and a 1
when scoring this task. If you decide to account for the student’s work when grading, it is important to make sure the students know in advance of working that the task will be graded based on the correct answers and their work.
• The students’ work can be helpful in determining whether students have a plan or strategy for finding factors (i.e., finding them in pairs or beginning with a low number and working up) or if students seem to be using a more
random, guess-and-check style method.
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4) The Locker Game Performance Task: The 20 students in Mr. Wolf’s 4th Grade Class are playing a game in a hallway that is lined with 20 lockers in a row.
www.smarterbalanced.org (See website for scoring guide.)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
The 1st student starts with the first locker and goes down the hallway and OPENS ALL the lockers.
The 2nd student starts with the second locker and goes down the hallway and SHUTS EVERY OTHER locker.
The 3rd student stops at every third locker and opens the locker if it is closed AND closes the locker if it is open.
The 4th student stops at every fourth locker and opens the locker if it is closed AND closes the locker if is open.
This process continues until all 20 students in the class have passed through the hallway.
Questions:
1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only 2 students? Explain your reasoning.
3. Which lockers were touched by only 3 students? Explain your reasoning.
4. Which lockers were touched the most?
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
4.NS.9
Standard: 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value.
Teacher Background Information:
Students should have knowledge of place value of a given digit up to and including a four-digit numeral and have had a chance to practice and understand
the concept of place value. They should have understanding of numbers and number sense. Students should be taught specific vocabulary relating to the
lesson before you begin. This should include: numeral, digit, and place value.
Provide students with opportunities to round numbers like 9,825 to the nearest ten and hundred, not just to the nearest thousand.
Students often round simply through rote procedure and memorization. They have difficulty understanding why numbers are rounded and why this is
helpful. This standard should be connected to adding and subtracting whole numbers and other estimation activities. Experiencing estimating helps develop
a sense of purpose for rounding. [Howard County Public Schools, Maryland]
https://grade4commoncoremath.wikispaces.hcpss.org/4.NBT.3 Rounding background information and ideas to increase the rigor.
Lesson Plans/Print Activities:
Math Expressions:
o U3 Lesson 8
o U3 Lesson 13
Math Expressions Differentiated Cards 3-8 (Intervention, On Level, Challenge)
Optional Scrimmage 4: Questions 1, 2, and 3 (IPS Online, Elementary Math K-6 Community
Group, Optional Math Scrimmage Folder)
http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=102
5 Explore Learning Gizmo: Cannonball Clown (register for a free trial)
https://www.engageny.org/resource/grade-4-mathematics-module-1-topic-c-lesson-7
Engage NY: Round numbers to the nearest 1,000 using a vertical number line
https://www.engageny.org/resource/grade-4-mathematics-module-1-topic-c-lesson-8
Engage NY: Round numbers using a vertical number line
https://www.engageny.org/resource/grade-4-mathematics-module-1-topic-c-lesson-9
Engage NY: Use place value understanding to round numbers
Indianapolis Public Schools
Web-based Practice:
http://www.funbrain.com/cgi-bin/tens.cgi?A1=s&A2=4 Fun Brain Place
Value Puzzler
http://mrnussbaum.com/halfcourt Half Court Rounding
http://www.aplusmath.com/Flashcards/rounding.html A Plus Math
flash cards
http://www.wmnet.org.uk/resources/gordon/Dart%20Board%20%20rounding.swf Dartboard Rounding
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_r
esources/848/rounding.swf Rounding Bingo
http://mrnussbaum.com/rounding-2 Rounding Games
http://www.softschools.com/math/practice/rounding_numbers.jsp
Rounding Numbers Generator
http://studyjams.scholastic.com/studyjams/jams/math/problemsolving/psestimate-whole-numbers.htm Study Jams rounding numbers
Curriculum and Instruction
Mathematics Pacing Resource Document
https://www.engageny.org/resource/grade-4-mathematics-module-1-topic-c-lesson-10
Engage NY: Use place value understanding to round numbers to any place value using realworld applications
http://www.bbc.co.uk/skillswise/topic/rounding-and-estimating Fact sheet, worksheet and
online quiz
http://teachers.net/lessons/posts/113.html Fruity Place Value: kinesthetic learner activity
IPS Online Indiana Standards and Resources for Mathematics
Go to IPS Online > Community Group Elementary Math K-6 > Indiana Standards Resources for
Mathematics > Grade 4 > 4.1.3 More or Less
https://learnzillion.com/lessonsets/239 Learn Zillion lessons
https://grade4commoncoremath.wikispaces.hcpss.org/file/view/4.NBT.3_BackToSchoolPlace
ValueRoundingBlasttoFREEBIE.pdf/447813690/4.NBT.3_BackToSchoolPlaceValueRoundingBl
asttoFREEBIE.pdf Back to School Blast (rounding card game)
Item Bank:
1) The capacity of Lucas Oil Stadium 62,421 people. What is the capacity rounded to the nearest thousand? [IPS C&1] Answer: 62,000
2) Place 1,525 on the number line below. [Howard County Public Schools, Maryland] Answer: 1,525 rounds to 1,000 when rounding to the nearest thousand
since it is closer to 1,000 than it is to 2,000.
1,000
2,000
Round 1,525 to the nearest thousand.
__________________________________________________________________
Indianapolis Public Schools
Curriculum and Instruction
Mathematics Pacing Resource Document
Explain your reasoning.
__________________________________________________________________________________________________________________
__________________________________________________________________________________________________________________
3) When rounded to the nearest thousand, an elephant’s weight is 5,000 pounds. What is the least amount that the elephant could weigh? Use pictures,
numbers, and words to represent your thinking. [Howard County Public Schools, Maryland] Answer: To round to 5,000 when rounding to the nearest thousand,
the elephant’s weight could be anywhere from 4,500 to 5,499 pounds. The least it can weigh is 4,500 pounds.
4) Study the table below: [Howard County Public Schools, Maryland] Answer: Megan might be rounding to the nearest 100,000 while Heather might be
rounding to the nearest ten thousand, one thousand, hundred, etc.
Student Enrollment
Montgomery County Schools
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148, 779
107, 033
123, 737
Meghan said, “When I round all of these numbers, I get the same answer.”
Heather said, “I disagree. I get all different numbers.”
Can they both be correct? Explain your reasoning.
Indianapolis Public Schools
Curriculum and Instruction