CURRICULUM MAPPING
Subject: Math
Grade: Fourth
Enrichment Curriculum:
The purpose of this curriculum is to expand, extend, and enrich the regular curriculum, to
motivate and stimulate the academic and creative talents of all students, and to encourage
higher order questioning and critical thinking in the learning process
Mathematically proficient students can:
Apply the mathematics they know to solve problems arising in everyday life,
society, and the workplace. In early grades this might be as simple as writing an addition
equation to describe a situation
Make assumptions and approximations to simplify a complicated situation,
realizing that these may need revision later
Identify important quantities in a practical situation and map their relationships
using such tools as diagrams, two‐way tables, graphs, flowcharts, and formulas
Analyze relationships mathematically to draw conclusions and can interpret their
mathematical results in the context of the situation and reflect on whether the results
make sense, possibly improving the model if it has not served its purpose.
Standards:
The following standards apply to all units of study below:
4.OA.3- Solve multistep word problems posed with whole numbers and having wholenumbers answer using the four operations, including problems in which remainders must
be interpreted. Represent these problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of answers using mental computation and
estimation strategies including rounding.
4.OA-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. 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. Explain informally
why the numbers will continue to alternate in this way.
4.MD.2 Use the four operations to solve word problems involving distances, intervals of
time, liquid volumes, masses of objects, and money, including problems involving simple
fractions or decimals, and problems that require expressing measurements given in a
larger unit in terms of a smaller unit Represent measurement quantities using diagrams
such as number line diagrams that feature a measurement scale.
4.MD.4- Make a line plot to display a data set of measurements in fractions of a unit (1/2,
¼, 1/8). Solve problems involving addition and subtraction of fractions by using
information presented n line plots For example, from a line plot find and interpret the
difference in length between the longest and shortest specimens in an insect collection.
I. Unit - Place Value
A. Content/Essential Questions
Can students identify place value?
Standards:
The following Common Core standards apply to Place Value:
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.
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.
Determine whether a given whole number in the range 1- 100 is prime or
composite.
4.NBT.2- Read and write multi-digit whole numbers using base-ten numerals,
number names, and expanded form. Compare two multi-digit numbers based on
meanings of the digits in each place, using >, =, < symbols to record the results of
comparisons.
4.NBT.3- Use place value understanding to round multi-digit whole numbers to
any place.
4.NBT.5- Multiply a whole number of up to four digits by a one-digit whole
number, and multiply two two-digit numbers, using strategies based on place
value and the properties of operations. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models.
4.NBT.6- Find whole-number quotient 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.
B. Skills
The student will be able to:
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Understand place value
Read and write numbers through hundred millions
Write numbers in expanded form from standard form and vice versa
Use estimation and learn when an estimate is appropriate
Compare and order whole numbers
Recognize halfway points and locate other points on a number line
Make change and find its value
Compare and order money amounts through $99.99
Round whole numbers up to the nearest million and money amounts up
to the nearest ten dollars
Solve problems involving money amounts using place-value skills
Solve problems by using the Make a Table or List strategy
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Investigate the value of each place in the base ten system and recognize
that a digit in one place represents ten times what it represents in the
place to the right
Enrichment Activities/Procedures
Research the distance of the planets and in the solar system from Earth.
Make a chart that lists the planets and their distances in order from the
farthest to the closest.
 Read the book How Much Is a Million? by David M. Schwartz Choose
your own item and calculate how much space it would take to reach a
million.
You have $200 to spend for your birthday party. However, you must feed
and entertain all of your friends for less than $200. Develop a plan for
having your party and staying within the budget.
Using a preselected list of number tiles, explain how you used place value
to help you determine the correct order of the numbers.
Describe a situation when it would be best to round a number to the nearest
thousand.
Compare and contrast the Egyptian number system with our base ten
system. Tell which system you like best and why.
Read and review data from books such as Hottest, Coldest, Highest,
Deepest by Steve Jenkins or Highest, Longest, Deepest by John Malam.
Discuss the numbers and round each number to several different places,
recording the results in a chart.
Create a set of trading cards for each place value. Be creative in the facts
you record about teach.
 Enrichment Resources
 How Much is a Million? David Schwatz
 Sir Cumference and All the Kind’s Tens-A Math Adventure by Cindy
Neuschwander
 A Place for Zero- A Math Adventures by Angeline Sparagna LoPresti
 Egyptian number system
 Really Big Numbers by Richard Evan Schwartz
II. Unit – Addition and Subtraction
A. Content/Essential Questions
Do students know addition and subtraction concepts?
Are students able to do addition and subtraction computation?
Standards:
The following Common Core standards apply to Addition and Subtraction:
4.NBT.4- Fluently add and subtract multi-digit whole numbers using the standard
algorithm.
B. Skills
The student will be able to:
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Understand and use the commutative, identity, and associative properties
of addition
Use strategies to add mentally
Understand the four meanings of subtraction and use subtraction rules
for zero
Identify and write addition and subtraction expressions, using variables
Find missing addends, subtrahends, and minuends
Add and subtract mentally, including the use of compensation and the
breaking apart of numbers
Use rounding to estimate sums and differences
Add and subtract money amounts with no regrouping
Check addition and subtraction examples
Use logical reasoning to solve problems
Solve addition and subtraction problems by choosing from a variety of
problem-solving strategies
Use front end estimation to find sums and differences
Add and subtract 2-, 3-, 4-, and 5-digit whole numbers and money
amounts with regrouping as needed
Find sums of three or more addends with regrouping
Subtract whole numbers and money amounts across zero
Add or subtract whole numbers and money amounts to 5 digits
Solve problems by choosing the correct operation
Choose from a variety of strategies to solve problems
Explain steps involving addition and subtraction problems and use
inverse operations to justify answers
Enrichment Activities/Procedures
 Design a book cover for a book about using addition and subtraction in
everyday lives
 Create a crossword puzzle in which the addition and subtraction clues are
the problems.
 Write a poem or a jingle that shares the steps to solve a math problem
using three or four digit numbers
Complete two Venn diagrams. One will compare and contrast addition and
multiplication and the other will compare and contrast subtraction and
division.
Write a 1-2 page story using numbers, and then write 5 word problems
using information presented in the story. Your problems should be
creative and complex!
Find a mistake in an addition or subtraction problem and explain why it
is incorrect.
After reading Comic Strip Math by Dan Greenberg, design your own
comic strip based on a story you created about a complex addition and
subtraction problem.
iPad app-Sum Stacker
 Enrichment Resources
Eat Your Math Homework by Ann McCallum
Comic Strip Math: Mini-Story Problems by Dan Greenberg
iPad apps
III. Unit - Multiplication
A. Content/Essential Questions
Can students multiply by one and two digits?
Can students identify the properties of multiplication?
Standards:
The following Common Core standards apply to Multiplication:
4.OA.1- Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5
X 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.
Represent verbal statements of multiplicative comparisons as multiplication
equations.
4.OA.2- Multiply or divide to solve word problems involving multiplicative
comparison, e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem, distinguishing multiplicative compassion from
additive comparison. (Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.)
4.OA.4- Find all factor pairs for a whole number in the range 1 -100. Recognize
that a whole number is a multiple of each of its factors. Determine whether a
given whole number in the range 1-100 is a multiple of a given one-digit number.
Determine whether a given whole number in the range 1- 100 is prime or
composite.
4.NBT.5- Multiply a whole number of up to four digits by a one-digit whole
number, and multiply two two-digit numbers, using strategies based on place
value and the properties of operations. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models.
B. Skills
The student will be able to:
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Understand and apply the properties of multiplication
Use models to understand multiplication
Multiply 2-, 3-, and 4-digit numbers and money amounts by 1- and
2-digit multipliers with and without regrouping
Estimate products using front-end estimation
Use patterns to multiply by 10 and by multiples of 10
Use rounding to estimate products
Use the strategy Work Backward to solve problems
Solve problems using a variety of strategies
Explain calculations by using equations, rectangular arrays, and/or area
models.
Enrichment Activities/Procedures
Write an original scenario based on a multiplication comparison reflecting
a real world situation
Make a collage of items that come in equal groups
Write a riddle showing a multiplication comparison and provide clues
that do not name actual numbers. For example: The number of keys on a
piano is 8 times as many as a 1 less than a dozen.
 Enrichment Resources
Motivation Math – Critical Thinking for Life
 The Multiplying Menace Divides by Pam Calvert
The California Gold Rush: Multiplying and Dividing Using Three- And
Four-Digit Numbers by Kerri O'Donnell
 Multiplying Menace: The Revenge of Rumpelstiltskin (A Math
Adventure) by Pam Calvert
The Best of Times: Math Strategies that Multiply by Greg Tang
If I Were a Times Sign by Trisha Speed Shaskan
IV. Unit - Dividing by One Digit
A. Content/Essential Questions
Can students divide by one digit?
Standards:
The following Common Core standards apply to Dividing by One-Digit:
4.OA.2- Multiply or divide to solve word problems involving multiplicative
comparison, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem, distinguishing multiplicative
compassion from additive comparison. (Grade 4 expectations in this domain
are limited to whole numbers less than or equal to 1,000,000.)
4.NBT.6- Find whole-number quotient 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.
B. Skills
The student will be able to:
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Understand the meanings of division and its rules
Understand the relationship between multiplication and division
Find the missing dividends and divisors
Find the value of a variable in a multiplication or a division sentence
Create and extend number patterns
Estimate quotients
Divide 2-, 3-, and 4-digit dividends by 1-digit divisors to find 2-, 3-, and
4-digit quotients with and without remainders using whole numbers and
money
Learn divisibility rules for 2, 3, 5, and 10
Divide and find quotients with zeros
Evaluate numerical expressions using the order of operations
Find the mean of a set of numbers
To solve problems using the strategy Interpret the Remainder
To solve problems using a variety of strategies
Enrichment Activities/Procedures
Choose a word from this list. Draw, explain, or create a model that explains
your answer.
Animals were sharing riddles. Ollie Ostrich said, “Octopus divided by
Donkey equals chicken.” What relationship do you think Ollie’s riddle
shows? Compose a challenging riddle of your own.
Write a division problem that result in a remainder of 2.
Play the card game “”A-maze-ing Division”
Write a skit and film a video of how to divide a 4 digit number by a 1 digit
number
www.mathplayground.com
 Enrichment Resources
Math-terpieces: The Art of Problem-Solving by Greg Tang
A-maze-ing Division-Game board
Cheetah Math by Ann Whitehead Nagda
The Multiplying Menace Divides by Pam Calvert
iPad apps
V. Unit – Measurement
A. Content/Essential Questions
Are students able to use different measurements?
Can students use a ruler to measure accurately?
Can students convert customary units of measurement?
Are students able to use a clock and a calendar to answer problems?
Standards:
The following Common Core standards apply to Measurement:
4.MD.1- Know relative sizes of measurement units within one system of units
including km, m, cm, kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of
measurement, express measurements in a larger unit in terms of a smaller unit.
Record measurement equivalents in a two-column table. For example, now that 1
ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate
a conversion table for feet and inches listing the number pairs (1,12), (2, 24), (3,
36).
4.MD.3- Apply the area and perimeter formulas for rectangles in real world and
mathematical problems For example, find the width or a rectangular room given
the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
B. Skills
The student will be able to:
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Measure length to the nearest inch, half inch, quarter inch, centimeter,
and decimeter
Estimate length to the nearest inch
Rename, compare, add, and subtract customary units of length
Explore, rename, and compare customary units of capacity and weight
Use, rename, and compare metric units of length, mass, and capacity
Estimate and measure lengths to the nearest centimeter and decimeter
Use metric units of measurement to interpret a map
Measure, compare, and compute temperatures
Tell time to the minute
Find elapsed time on a clock and on a calendar
Solve problems using more than one step
Solve problems using a variety of strategies
Enrichment Activities/Procedures
Using a measuring cup, show how it can be used to find equivalent
fractions.
Think about the skills and characteristics that allow students to be
successful in math. Create a recipe for math success using at least 4
ingredients. Use fractions and mixed numbers for each of the
ingredients. (e.g. 2 ¼ cups listening in class)
Imagine that you are giving directions for a new student to travel
from your classroom to the library. Explain how to get to the library
using direction words and degree measurements. (eg. first, turn 45°
to the left, etc.)
Create an acrostic poem that expresses the meaning or critical
attributes of a measurement vocabulary word. The letters in the
word would be the first letter in each lime of your poem. Read your
acrostic poem to the class.
Create an original game or puzzle using measurement conversions.
The game may be a card game, board game, or a puzzle. Write the
rules of play or directions and create all items needed to play the
game. Share the game with your classmates.
 Play Math Charades-Act out a math vocabulary word using
gestures and motions. Guess each other’s words and take turns.
Enrichment Resources
The Librarian who Measured the Earth by Kathryn Lasky
What’s Your Angle, Pythagoras? By Julie Ellis
 Sir Cumference and the Great Knight of Angleland; A Math
Adventure by Cindy Neuschwander
VI. Unit – Statistics and Probability
A. Content/Essential Questions
Are students familiar with statistics and probability?
Are students able to use statistics and probability?
Standards:
B. Skills
The student will be able to:
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Make, read, and interpret pictographs, bar graphs, line graphs, line plots,
and circle graphs
Find the median of a set of data
Use line plots to find mode and range
Conduct a survey and show the results on a line plot
Use tree diagrams or multiplication to find numbers of combinations
Predict the probability of an event
Tell which of two events is more or less likely to occur
Understand that probability changes as the number of possible outcomes
changes
Solve problems by using information in graphs and diagrams
Solve problems using a variety of strategies
Enrichment Activities/Procedures
 Make an argument for which graphing method is the easiest to read: pie
charts, stem-and-leaf plots, bar graphs, or line graphs. Construct a visual
model to show why.
Create a poster that explains how to read both a digital and analog clock
Make a quiz for your classmates that test their ability to plot and recognize
points on a graph.
Compare and contrast line plots and bar graphs.
Find a line graph in a magazine or newspaper. Explain what data is being
presented and what each scale represents. Write three questions that can be
answered using the data in the line graph.
VII. Unit – Fractions
A. Content/Essential Questions
Do students have an understanding of fractions?
Are students able to use fractions?
Standards:
The following Common Core standards apply to Fractions:
4.NF.1- Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by
using visual fraction models, with attention to how the umber and size of he parts
differ even though the two fractions themselves are the same size. Use this
principle to recognize and generate equivalent fractions.
4.NF.2- Compare two fractions with different numerators and different
denominators, e.g., b creating common denominators or numerators, or by
comparing to a benchmark fraction such as 12. Recognize that comparisons are
valid only when the two fractions refer to the same whole. Record the results of
comparison with the symbols >, =, <, and justify the conclusions, e.g., by using a
visual fraction model.
4.NF.3- Understand a fraction a/b with a. 1 as a sum of fraction 1/b.
4.NF.3a- Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
4.NF.3b- Decompose a fraction into a sum of fractions with the same denominator
in more tha one way, recording each decomposition by an equation. Justify
decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 +1/8
+ 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 1/8; = 8/8 + 8/8 + 1/8.
4.NF.3c- Add and subtract mixed numbers with like denominators, e.g., by
replacing each mixed number with an equivalent fraction, and/or by using
properties of operations and the relationship between addition and subtraction.
4.NF.3d- Solve word problems involving addition and subtraction of fractions
referring to the same whole and having like denominators, e.g., by using visual
fraction models and equations to represent the problem.
4.NF.4- Apply and extend previous understandings of multiplication to multiply a
fraction by a whole number.
4.NF.4a- Understand a fraction a/b as a multiple of 1/b. For example, use a visual
fraction model to represent 5/4 as the product of 5 x (1/4), recording the
conclusion by the equation 5/4 = 5 x ¼).
4.NF.4b- Understand a multiple of a/b as a multiple of 1/b, and use this
understanding to multiply a fraction by a whole number. For example, use a
visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as
6/5. (In general, n x (a/b) = (n x a)/b.)
4.NF.4c- Solve word problems involving multiplication of a fraction by a whole
number, e.g., by suing visual fraction models and equations to represent the
problem. For example, if each person at a party will eat 3/8 of a pound of roast
beef, and there will be 5 people at the party, how many pounds of roast beef will
be needed? Between what two whole numbers does your answer lie?
4.NF.5- Express a fraction with denominator 10 as an equivalent fraction with
denominator 100, and use this technique to add two fractions with respective
denominators 10 adn100. (Student who can generate equivalent fractions can
develop strategies for adding fractions with unlike denominators in general. But,
addition and subtraction with unlike denominators inn general is not a
requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 +
4/100 = 34/100.
B. Skills
The student will be able to:
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Write fractions
Identify fractions on a number line
Estimate fractions
Model equivalent fractions
Recognize equivalent fractions
Write equivalent fractions
Determine factors
Reduce fractions to lowest terms
Identify and use mixed numbers
Compare fractions
Order fractions
Use models to add fractions
Add and subtract fractions with like denominators
Recognize and use improper fractions
Estimate with mixed numbers
Add and \subtract mixed numbers
Delineate multiples
Identify and use factor pairs
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Identify prime and composite numbers
Add fractions with denominators of 10 and 100
Add and subtract fractions with unlike denominators
Multiply fractions
Compute probability
Find part of a number
Identify points , lines, and line segments
Determine angle measures
Identify rays and angles
Use unknown angle measures
Identify and use parallel and perpendicular lines
Identify and measure circles. Polygons, quadrilaterals, triangles,
Utilize symmetry
Identify similar figures
Use slides, turns and flips
Use coordinate geometry
Use perimeter and area formulas
Identify and measure solid figures and polygons
Use spatial relationships
Measure volume
Determine division patterns
Use divisors: multiples of ten
Estimate quotients
Use two, three, and four digit dividends
Use trial quotients
Determine greater quotients
Use zeros in quotients
Identify and use greater dividends
Use tenths and hundredths
Identify and use decimals greater than one
Determine decimal place value
Compare, order and round decimals
Estimate with decimals
Add and subtract decimals
Divide with money
Use equations
Find missing numbers
Use functions
Graph equations
Use missing symbols
Use parentheses
Enrichment Activities/Procedures
Create a new way to classify geometric shapes
If you could be any geometric shape, what would it be and why?
Expand on this idea-a square is just another type of rectangle.
Explain why it is important to have a common name for all geometric
shapes.
Write a jingle about geometric shapes.
How many uses can you come up with for a cylinder?
Create as many questions as you can that would have the answer of “square.”
Explain the difference between adding and multiplying fractions.
Describe how people use fractions every day.
Convince a fourth grader that it is a good thing to understand and be able to
use fractions. Give at least 2 specific supports and create a visual example.
Create a fraction riddle. Start with a general clue and end with a specific
clue. Try your riddle out on a friend.
After reading the book Growing Patterns: Fibonacci Numbers in Nature by
Sarah C. Campbell, use library resources to investigate
Leonardo de Pisa, the Italian mathematician also known as Fibonacci.
Discuss and describe the Fibonacci number sequence.
Write a journal entry about either a prime or composite number and its
feelings about its fact families.
Create a rap or song that would help your classmates remember the
difference between prime and composite numbers
Develop a set of manipulatives that you can use to show or teach ordering
fractions.
Make a how-to video that would teach other students how to put fractions
in order from least to greatest.
 Using one of your favorite recipes, convert all the information (including
the ingredient list) into a picture only recipe. You cannot use any words.
 Create a cube with six word problems using fractions. Include three
addition and three subtraction problems.
 Is the number 1 a prime number or a composite number? In your journal,
use words, numbers or pictures to justify your answer.
 Read Full House: An Invitation to Fractions by Dayle Ann Doyle and note
how the fraction concepts are included in the story. Create an original
story in which the characters compare fractional numbers. Record and
illustrate the story. Read your original story to the classroom.
 Go to jeopardylabs.com and build your own Fraction Jeopardy Game
 Enrichment Resources
 Manipulatives
 Motivation Math Level 4
 The Ancient Formula: A Mystery with Fractions (Manga Math
Mysteries) by Melinda Thielbar
 Math Curse by Jon Scieszka
 If You Were a Fraction by Trisha Speed Shaskan
 An Invitation to Fractions by Dayle Ann Doyle
 Piece=Part=Portion by Scott Gifford
 www.jeopardylabs.com
VIII. Unit - Geometry
A. Content/Essential Questions
Are students able to recognize geometry in their surrounding world?
Are students able to use geometry?
Standards:
The following Common Core standards apply to Geometry:
4.MD.3- Apply the area and perimeter formulas for rectangles in real world and
mathematical problems For example, find the width or a rectangular room given
the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
4.MD.5- Recognize angles as geometric shapes that are formed wherever two rays
share a common endpoint, and understand concepts of angle measurement:
4.MD.5a- An angle is measured with reference to a circle with its center at the
common endpoint of the rays, by considering the fraction of the circular arc
between the points where the two rays intersect the circle An angle that turns
through 1/360 of a circle is called a “one-degree angle.” And can be used to
measure angles.
4.MD.5b- AN angle that turns through n one-degree angles is said to have an
angle measure of n degrees.
4.MD.6- Measure angles in whole-number degrees using a protractor. Sketch
angles of specified measure.
4.MD.7- Recognize angle measure as additive. When an angle is decomposed into
non-overlapping parts, the angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction problems to find unknown
angles on a diagram in real world and mathematical problem., e.g., by using an
equation with a symbol for the unknown angle measure.
4.G.1- Draw points, lines, line segments, rays, angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.2- Classify two-dimensional figures based on the presence or absence of
parallel or perpendicular lines, or the presence or absence of angles of a specified
size. Recognize right triangles as a category, and identify right triangles.
4G.3- Recognize a line of symmetry for a two-dimensional figure s a line across
the figure such that the figure can be folded along the line into matching parts.
Identify line symmetric figures and draw lines of symmetry.
B. Skills
The student will be able to:
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Understand points, lines, and line segments
Understand angle measure
Understand how to measure angles
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Understand parallel and perpendicular lines
Recognize and measure circles
Recognize and measure polygons
Recognize and measure quadrilaterals
Recognize and measure triangles
Use symmetry
Use similar figures
Use slides and Flips and Turns
Use coordinate Geometry
Find a Pattern in Problem Solving
Enrichment Activities/Procedures
 Create a complex shape pattern that follows a rule. Explain the rule you
used for the pattern.
Go on a scavenger hunt for angles found in nature. Sketch the angles and
then measure them in the sketches with a protractor.
Write a Haiku poem to describe a right angle or an obtuse angle.
Create a riddle of clues to describe a mystery shape. Explain your
reasoning. Try it out on your classmates.
Use twizzlers, pipe cleanes or flex straws to make different types of
geometry shapes. Discuss their angles.
Design an original game that incorporates concepts about angles, lines
and the attributes of two-dimensional geometric figures. Teach your
classmates how to play your game.
Investigate symmetry in nature using library or internet resources. Create
a display board showing pictures or actual objects with line(s) of
symmetry, including radial symmetry. Share with you classmates and
elaborate on facts learned during your investigation.
Enrichment Resources
The Greedy Triangle by Marilyn Burns
What's Your Angle, Pythagoras? by Julie Ellis
”M” is for Mirror by Duncan Birmingham
Seeing Symmetry by Loreen Leedy
IX. Unit – Perimeter, Area, and Volume
A. Content/Essential Questions
Are students able to determine perimeter, area, and volume?
Standards:
The following Common Core standards apply to Perimeter, Area and Volume
4.MD.3- Apply the area and perimeter formulas for rectangles in real world and
mathematical problems For example, find the width or a rectangular room given
the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
4.MD.5- Recognize angles as geometric shapes that are formed wherever two rays
share a common endpoint, and understand concepts of angle measurement:
4.MD.5a- An angle is measured with reference to a circle with its center at the
common endpoint of the rays, by considering the fraction of the circular arc
between the points where the two rays intersect the circle An angle that turns
through 1/360 of a circle is called a “one-degree angle.” And can be used to
measure angles.
4.MD.5b- AN angle that turns through n one-degree angles is said to have an
angle measure of n degrees.
4.MD.6- Measure angles in whole-number degrees using a protractor. Sketch
angles of specified measure.
4.MD.7- Recognize angle measure as additive. When an angle is decomposed into
non-overlapping parts, the angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction problems to find unknown
angles on a diagram in real world and mathematical problem., e.g., by using an
equation with a symbol for the unknown angle measure.
4.G.1- Draw points, lines, line segments, rays, angles (right, acute, obtuse), and
perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.2- Classify two-dimensional figures based on the presence or absence of
parallel or perpendicular lines, or the presence or absence of angles of a specified
size. Recognize right triangles as a category, and identify right triangles.
4G.3- Recognize a line of symmetry for a two-dimensional figure s a line across
the figure such that the figure can be folded along the line into matching parts.
Identify line symmetric figures and draw lines of symmetry.
B. Skills
The students will be able to:
 Use perimeter and area formulas
 Understand solid figures and polygons
 Spatial Relationships
 Understand Volume
 Use or Draw a model to solve problems
 Apply the formulas and communicate understandings of why the formulas
work in real world and mathematical problems
 Enrichment Activities/Procedures
 After reading the story, Spaghetti and Meatballs for All by Marilyn
Burns, brainstorm methods of finding the areas and perimeters of tables
without using tiles or paper clips. Come up with a formula that you can
share with your classmates.
Create a word web with activities that involve perimeter or area.
Design your own perimeter/area super hero or bot. Calculate the area and
perimeter for each body part.
Create a product to teach an audience of second graders about perimeter
and area. Your must show that you know what each term means, how to
find the value of perimeter and area, how they are measured, why each is
important to daily life (connection to real world), and demonstrate an
understanding of the relationship between perimeter and area. Your
product can be: a song /rap, an illustrated poster for the classroom walls,
or a story book about area and perimeter.
 Volume-Predict the size of a humpback whale. Explain your estimates.
Read Counting on Frank by Rod Clement. Research information about
humpback whales. Calculate how large a box is needed to hold the
average humpback whale. Complete “Getting the Fact” sheet.
Enrichment Resources
Spaghetti and Meatballs for All by Marilyn Burns
Sir Cumference and the Isle of Immeter: A Math Adventure by Cindy
Neuschwander
Perimeter, Area, and Volume: A Monster Book of Dimensions by David
Adler
Counting on Frank by Rod Clement
X. Unit - Divide By Two Digits
A. Content/Essential Questions
Are students able to divide by two-digits?
Standards
The following Common Core standards apply to Divide by Two-Digits
4.OA.2- Multiply or divide to solve word problems involving multiplicative
comparison, e.g., by using drawings and equations with a symbol for the
unknown number to represent the problem, distinguishing multiplicative
compassion from additive comparison. (Grade 4 expectations in this domain are
limited to whole numbers less than or equal to 1,000,000.)
4.NBT.6- Find whole-number quotient 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.
B. Skills
The children will be able to:
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Recognize division patterns
Use divisors that are multiples of ten
Estimate quotients
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Use two and three–digit dividends
Figure out trial quotients
Work with greater quotients
Use four –digit dividends
Know how to use zero in the quotient
Work with greater dividends
Use more than one step in solving word problems
XI. Unit - Decimals
A. Content/Essential Questions
Are students able to use decimals?
Standards:
The following Common Core standards apply to Decimals:
4.NF.6- Use decimal notation for fractions with denominators 10 or 100. For
example, rewrite 0.62 as 62/100; describe the length as 0.62 meters; locate 0.62
on a number line diagram.
4.NF.7- Compare two decimals to hundredths by reasoning about their size.
Recognize that comparisons are valid only when the two decimals refer to the
same whole. Record the results of comparisons with the symbols >, =, <, and
justify the conclusions, e.g., by using a visual model.
B. Skills
The students will be able to:
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Understand tenths and hundredths
Understand decimals greater than one
Understand decimal place value
Compare decimals with models and symbols
Compare decimals
Order decimals
Round decimals
Estimate with decimals
Add and subtract decimals
Divide with money
Use more than one step to solve word problems
Enrichment Activities/Procedures
 Create a flipbook with examples of adding and subtracting decimals on the
flaps with the answers inside.
 Choose a sport of your choice. Prepare a poster that explains how statistics
are calculated for that sport. Share examples in your explanation.
 Write a letter to your family about how decimals are part of our daily life.
Include examples to prove your point.
 Make a Venn diagram comparing decimals and fractions
 Create a poem, song, or rap which direction
 Create a tri-fold display about decimals. One panel should include
information on the use of decimals in the everyday world. Another panel
should show commonly used fractions and their decimal equivalents.
The third panel should provide an explanation of how to use equivalent
fractions to write a common fraction as a decimal number. Include
pictures to support your answers. Share with your classmates.
 Enrichment Resources
The $1.00 Word Riddle Book by Marilyn Burns
Fractions and Decimals Made Easy by Rebecca Wingard-Nelson
XII. Unit - Get Ready for Algebra
A. Content/Essential Questions
Are students familiar with the basic notation of algebra?
Standards:
The following Common Core standards apply to Get Ready for Algebra:
4.OA.2- Multiply or divide to solve word problems involving multiplicative
comparison, e.g., by using drawings and equations with a symbol for the unknown
number to represent the problem, distinguishing multiplicative compassion from
additive comparison. (Grade 4 expectations in this domain are limited to whole
numbers less than or equal to 1,000,000.)
4.NBT.5- Multiply a whole number of up to four digits by a one-digit whole
number, and multiply two two-digit numbers, using strategies based on place
value and the properties of operations. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models.
4.NBT.6- Find whole-number quotient 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.
4.MD.3- Apply the area and perimeter formulas for rectangles in real world and
mathematical problems For example, find the width or a rectangular room given
the area of the flooring and the length, by viewing the area formula as a
multiplication equation with an unknown factor.
B. Skills
The student will be able to:
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Work with equations
Find missing numbers
Understand functions
Graph equations
Find missing symbols
Use parentheses
Discover that there is more than one way to solve a word problem
C. Activities/Procedures
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Direct group instruction
Small group instruction
Independent work
Enrichment papers
Use of Promethean Board
Enrichment Activities/Procedures
Generate a list of math words that have more than one meaning. Create
a slideshow in which you present the word and show its meanings with
words, numbers, or pictures. Words might include: acute, area, angle,
base, formula, line, meter, plot, pound, prime, product, right, square or
yard.
Additional Learning Specialist Activities/Procedures:
 Pre-teach concept
 Reteach concept
 Extra practice of concept
 Facts drill with flash cards
 Mnemonics & rhymes
 Color coding
 Additional practice with games: concentration, dots, connect four,
Eggspert, tic tac toe, matching with manipulatives, math skills dominoes,
student-made manipulatives, Switch, Bingo, Jenga
 Reinforcement with movement: round robin recital, Duck, Duck, Goose
w/math facts, Mother May I?, students make own study guides and facts
lists, Dracula, line up as integers
 Partner drills
D. Resources
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Sadlier-Oxford Progress in Mathematics-Grade 4
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Reading Problems in Mathematics – Continental Press Grade 5
Problem-Driven Math: Grade 4- Creative Publications
Roads to Reasoning: Grade 4 – Creative Publications
Explain It! Grades 4-5 Creative Publications
DynaMath
Harcourt Math – Level 4 Enrichment
Additional Learning Specialist Resources:
 Mad Minute math
 Rulers, playing cards, dice, teacher-made Bingo boards, cubes, items to
divide with knife
 Lined paper
 Money
 Marmaduke Multiply’s
 Gorey Games
 Teacher-made Bingo boards
 Rainbow Fraction Tiles
 Calculators
 Multiplication chart
 Hundreds chart
E. Technology
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Promethean Board
Making graphs
Manipulative shapes
AhaMath.com
SadlierOxford.com
F. Assessment
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Written assessments
Ability to verbally explain solutions to problems
Additional Learning Specialist Assessment:
 work on whiteboards and paper
*All fifth grade students will participate in the Math Olympiads www.moems.org.
This worldwide contest presents students with five competitions a year with the purpose
of:
 Stimulating an enthusiasm and love for Mathematics
 Developing Mathematical concepts
 Teaching strategies for problem solving
 Developing flexibility in solving problems
 Strengthening Mathematical intuition
 Fostering Mathematical creativity and ingenuity
 Providing Satisfaction, joy and thrill of meeting challenges
Revised: December 2014