Summit Public Schools
Summit, New Jersey
Grade Level: Grade 4
Content Area: Math
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.
4.MP.1
Make sense of problems and persevere in solving them.
4.MP.2
Reason abstractly and quantitatively.
4.MP.3
Construct viable arguments and critique the reasoning of others.
4.MP.4
Model with mathematics.
4.MP.5
Use appropriate tools strategically.
4.MP.6
Attend to precision.
4.MP.7
Look for and make use of structure.
4.MP.8
Look for and express regularity in repeated reasoning.
Fourth Grade Scope and Sequence
Please N ote - This scope and sequence is a Fourth Grade Scope and Sequence
Please N ote - This scope and sequence is a general guideline and will vary depending upon the math program teachers are using and the needs of the students.
Summary of the Year
In Grade 4, instructional time should focus on three critical areas: (1)
developing understanding and fluency with multi-digit multiplication, and
developing understanding of dividing to find quotients involving multidigit dividends; (2) developing an understanding of fraction equivalence,
addition and subtraction of fractions with like denominators, and
multiplication of fractions by whole numbers; (3) understanding that
geometric figures can be analyzed and classified based on their properties,
such as having parallel sides, perpendicular sides, particular angle
measures, and symmetry.
Overview
OPERATIONS AND ALGEBRAIC THINKING
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between
multiplication and division.
Multiply and divide within 100.
Solve problems involving four operations, and identify and explain
patterns in arithmetic.
NUMBER AND OPERATIONS IN BASE TEN
Use place value understanding and properties of operations to perform
multi-digit arithmetic.
NUMBER AND OPERATIONS—FRACTIONS
Develop understanding of fractions as numbers.
MEASUREMENT AND DATA
Solve problems involving measurement and estimation of intervals of
time, liquid volumes, and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to
multiplication and to addition.
Geometric measurement: recognize perimeter as an attribute of plane
figures and distinguish between linear and area measures.
GEOMETRY
Reason with shapes and their attributes.
Year-at-a-Glance
Marking Period 1
*Place Value and Operations with Whole Numbers (Units 1-5)
Marking Period 2
*Fractions and Decimals (Units 6-10)
Marking Period 3
*Geometry and Measurement Concepts (Units 11-13)
STANDARDS FOR MATHEMATICAL PRACTICE:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5.Use appropriate tools strategically.
6.Attend to precision.
7.Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Marking
Period
Unit Title/Focus
Resources
Everyday
Math Units
Go Math Units
enVision
Units
Standards
1
Title: Place Value
and Rounding
Lesson: Understand
Relationships between Digits
and Their Place Value:
http://learnzillion.com/lesso
ns/516-understandrelationships-between-digitsand-their-place-value
2.3, 2.4
5.8, 5.9, 5.10
Critical Area 1
Topic 3
CCSS.Math.Content.4.NBT.A.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.
Approximate number of
instructional days: 15
Pre-/Post-Assessment
#2
Place value chart:
http://www.k5mathteachingresources.com/
support-files/place-valuechart.pdf
Place value practice:
http://www.k5mathteachingresources.com/
support-files/place-valueproblems.pdf
Practice reading and writing
multi-digit numbers with
expanded form:
http://www.k5mathteachingresources.com/
support-files/numeral-wordexpanded-form.pdf
Place value triangle game:
http://www.k5mathteachingresources.com/
support-files/place-value-
CCSS.Math.Content.4.NBT.A.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 >, =, and < symbols
to record the results of
comparisons.
CCSS.Math.Content.4.NBT.A.3
Use place value understanding to
round multi-digit whole numbers
to any place.
triangle.pdf
Round to the Nearest Ten
Game:
http://www.k5mathteachingresources.com/
supportfiles/roundtothenearest10gam
e.pdf
Round to the Nearest
Hundred Game:
http://www.k5mathteachingresources.com/
supportfiles/roundtothenearest100ga
me.pdf
1
Title: WholeNumber Addition
and Subtraction
Approximate number of
instructional days: 9
Pre-/Post-Assessment
#2A
Lesson: Solve multi-digit
addition problems by
identifying key phrases
http://learnzillion.com/lesso
ns/1581-solve-addition-wordproblems-by-identifying-keyphrases
Multi-digit Addition and
Subtraction Number Stories
http://www.k5mathteachingresources.com/
support-files/adding-andsubtracting-multi-digit-wholenumbers.pdf
2.7, 2.9
Critical Area 1
Topic 4
CCSS.Math.Content.4.NBT.B.4
Fluently add and subtract multidigit whole numbers using the
standard algorithm.
CCSS.Math.Content.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. 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.
Addition and Subtraction
Number Story Generator
http://www.k5mathteachingresources.com/
supportfiles/additionandsubtractionn
umberstories4nbt4.pdf
1
Title: Multiplying
One-digit Numbers
Approximate number of
instructional days: 16
Pre-/Post-Assessment
#3
Lesson: Use place value
understanding to multiply 3and 4-digit numbers
http://learnzillion.com/lesso
ns/1878-use-place-valueunderstanding-to-multiplythree-and-four-digit-numbers
Problems for Representing
Multiplicative Comparison
(4.OA1)
http://www.k5mathteachingresources.com/
support-files/representingmultiplicative-comparisonproblems.pdf
Multiplicative Comparison
Word Problems (4.OA2)
http://www.k5mathteachingresources.com/
supportfiles/multiplicativecomparison
problems.pdf
Multiplication Strategy:
Doubling and Halving
3.1, 3.2, 3.3, 3.4, Critical Area 1
3.5, 3.8, 3.9,
3.11
Topics 5, 6
CCSS.Math.Content.4.OA.A.1
Interpret a multiplication
equation as a comparison, e.g.,
interpret 35 = 5 × 7 as a
statement that 35 is 5 times as
many as 7 and 7 times as many as
5. Represent verbal statements of
multiplicative comparisons as
multiplication equations.
CCSS.Math.Content.4.OA.A.2
Multiply or divide to solve word
problems involving multiplicative
comparison, e.g., by using
drawings and equations with a
symbol for the unknown number
to represent the problem,
distinguishing multiplicative
comparison from additive
comparison.1
CCSS.Math.Content.4.OA.B.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
http://www.k5mathteachingresources.com/
support-files/multiplicationstrategy-doubling-andhalving.pdf
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.
Partial Products Strategy and
Practice (1-digit)
http://www.k5mathteachingresources.com/
support-files/multiplicationstrategy-partial-products-1.pdf
CCSS.Math.Content.4.NBT.B.5
Multiply a whole number of up to
four digits by a one-digit whole
number, and multiply two twodigit 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.
Breaking Apart a Factor
Strategy
http://www.k5mathteachingresources.com/
supportfiles/breakingapartafactor5.nb
t1.pdf
Multiplication Number Story
Generator:
http://www.k5mathteachingresources.com/
supportfiles/multiplicationnumbersto
ry4nbt5.pdf
Practice/Games with
Factors and Multiples
(4.OA4)
- Finding Multiples
CCSS.Math.Content.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. 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.
http://www.k5mathteachingresources.com/
supportfiles/findingmultiples.pdf
- Prime Number Hunt
http://www.k5mathteachingresources.com/
supportfiles/primenumberhunt.pdf
- Common Multiples
http://www.k5mathteachingresources.com/
supportfiles/commonmultiples.pdf
- Least Common Multiples
http://www.k5mathteachingresources.com/
supportfiles/leastcommonmultiples.p
df
- Find the Factor
http://www.k5mathteachingresources.com/
supportfiles/findthefactor4.oa4.pdf
- Multiplication Bump
(practice multiplying by 100)
http://www.k-
5mathteachingresources.com/
supportfiles/multiplicationbumpx100.
pdf
Square Numbers Pattern
http://www.k5mathteachingresources.com/
support-files/squarenumbers.pdf
Triangular Numbers
http://www.k5mathteachingresources.com/
support-files/triangularnumbers.pdf
1
Title: Multiplying
Two-digit Numbers
Approximate number of
instructional days: 16
Pre-/Post-Assessment
#5
Lesson: Use an area model to
multiply 2-digit by 2-digit
http://learnzillion.com/lesso
ns/1879-use-an-area-modelto-multiply-two-digitnumbers-by-two-digitnumbers
Lesson: Multiply using partial
products strategy
http://learnzillion.com/lesso
ns/529-multiply-multidigitnumbers-using-partialproducts
5.1, 5.2, 5.3, 5.4, Critical Area 1
5.5, 5.6
6.1
Topics 7, 8
CCSS.Math.Content.4.OA.B.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.
CCSS.Math.Content.4.NBT.B.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.
Partial Products Strategy and
Practice (1 and 2-digit)
http://www.k5mathteachingresources.com/
support-files/multiplicationstrategy-partial-products-2.pdf
Make the Largest Product
Game
http://www.k5mathteachingresources.com/
supportfiles/makethelargestproduct.p
df
Make the Smallest Product
Game
http://www.k5mathteachingresources.com/
supportfiles/makethesmallestproduct.
pdf
1
Title: Dividing by
One-Digit Divisors
Approximate number of
instructional days: 16
Pre-/Post-Assessment
#6
Lesson: Divide with threedigit dividends
http://learnzillion.com/lesso
ns/1483-divide-threedigitdividends
Partial quotients strategy and
practice
http://www.k5mathteachingresources.com/
3.5, 6.1, 6.2, 6.3, Critical Area 1
6.4, 6.10
Topics 9, 10
CCSS.Math.Content.4.OA.A.2
Multiply or divide to solve word
problems involving multiplicative
comparison, e.g., by using
drawings and equations with a
symbol for the unknown number
to represent the problem,
distinguishing multiplicative
comparison from additive
comparison.1
support-files/divisionstrategy-partial-quotients1.pdf
Partial quotients strategy and
practice (4-digit dividends)
http://www.k5mathteachingresources.com/
support-files/divisionstrategy-partial-quotients2.pdf
Partition the dividend strategy
and practice
http://www.k5mathteachingresources.com/
support-files/divisionstrategy-partition-thedividend.pdf
Estimate the quotient game
http://www.k5mathteachingresources.com/
support-files/Estimate-theQuotient.pdf
Remainder practice game
http://www.k5mathteachingresources.com/
support-files/remainders.pdf
Multi-step, Multi-operational
Word Problems (4.OA3)
http://www.k5mathteachingresources.com/
support-
CCSS.Math.Content.4.NBT.B.6
Find whole-number quotients
and remainders with up to fourdigit 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.
CCSS.Math.Content.4.OA.A.3
Solve multistep word problems
posed with whole numbers and
having whole-number answers
using the four operations,
including problems in which
remainders must be interpreted.
Represent these problems using
equations with a letter standing
for the unknown quantity. Assess
the reasonableness of answers
using mental computation and
estimation strategies including
rounding.
files/4oa3multistepwordprobl
ems.pdf
CCSS.Math.Content.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. 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.
Interpreting Remainder
Problems (4.OA3)
http://www.k5mathteachingresources.com/
supportfiles/interpretingremainders4.
oa3.pdf
2
Title: Decimal
Concepts (focusing
on tenths,
hundredths - reading,
writing, comparing)
Decimal Riddles (4.NF6)
http://www.k5mathteachingresources.com/
supportfiles/decimalriddles.pdf
Approximate number of
instructional days: 5
Comparing Decimals Chart
Activity (4.NF7)
http://www.k5mathteachingresources.com/
supportfiles/comparingdecimals.pdf
Pre-/Post-Assessment
#4
Lesson: Comparing Decimals
On A Number Line
http://learnzillion.com/lesso
ns/563-compare-decimals-
4.1, 4.2, 4.3, 4.4, Critical Area 2
4.5, 4.7
Topic 3
CCSS.Math.Content.4.NF.C.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 >,
=, or <, and justify the
conclusions, e.g., by using a visual
model.
using-a-number-line
2
Title: Fraction
Equivalence,
Comparing, and
Ordering
Approximate number of
instructional days: 8 Days
Pre-/Post-Assessment
#7
Fraction Equivalence Game
(4.NF1)
http://www.k5mathteachingresources.com/
supportfiles/fractionwallgame.pdf
Practice Comparing Fractions
with Birthday Problems
(4.NF2)
http://www.k5mathteachingresources.com/
support-files/birthdayfractions-4nf2.pdf
Lesson: Ordering Fractions
Using Common
Denominators
http://learnzillion.com/lesso
ns/106-order-fractions-usingcommon-denominators
7.7, 7.8, 7.9
Critical Area 2
Topic 11
CCSS.Math.Content.4.NF.A.1
Explain why a fraction a/b is
equivalent to a fraction (n × a)/(n
× b) by using visual fraction
models, with attention to how the
number and size of the parts
differ even though the two
fractions themselves are the same
size. Use this principle to
recognize and generate equivalent
fractions.
CCSS.Math.Content.4.NF.A.2
Compare two fractions with
different numerators and
different denominators, e.g., by
creating common denominators
or numerators, or by comparing
to a benchmark fraction such as
1/2. Recognize that comparisons
are valid only when the two
fractions refer to the same whole.
Record the results of
comparisons with symbols >, =,
or <, and justify the conclusions,
e.g., by using a visual fraction
model.
2
Title: Adding and
Subtracting Fractions
and Mixd Numbers
with Like
Denominators
Approximate number of
instructional days: 15 Days
Pre-/Post-Assessment
#7A
Adding and Subtracting
Fractions with Like
Denominators Practice
Problems (4.NF3)
http://www.k5mathteachingresources.com/
support-files/adding-andsubtracting-like-fractions.pdf
Fraction Word Problems
(4.NF3)
http://www.k5mathteachingresources.com/
support-files/fraction-wordproblems-likedenominator.pdf
Lesson: Subtracting Fractions
With Like Denominators
http://learnzillion.com/lesso
ns/113-subtract-fractionswith-like-denominatorslabeling-shapes
Lesson: Adding Fractions
With Like Denominators
(using shapes and sets)
http://learnzillion.com/lesso
ns/107-add-fractions-withlike-denominators-usingshapes-and-sets
7.5
Critical Area 2
Topic 12
CCSS.Math.Content.4.NF.B.3
Understand a fraction a/b with a
> 1 as a sum of fractions 1/b.
CCSS.Math.Content.4.NF.B.3a
Understand addition and
subtraction of fractions as joining
and separating parts referring to
the same whole.
CCSS.Math.Content.4.NF.B.3b
Decompose a fraction into a sum
of fractions with the same
denominator in more than 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.
CCSS.Math.Content.4.NF.B.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.
Lesson: Adding Mixed
Numbers
http://learnzillion.com/lesso
ns/852-adding-mixednumbers-using-properties-ofoperations
CCSS.Math.Content.4.NF.B.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.
Lesson: Subtracting Mixed
Numbers
http://learnzillion.com/lesso
ns/853-subtracting-mixednumbers-by-using-propertiesof-operations
2
Title: Extended
Fraction Concepts
(Multiplying
Fractions, Fractions
and Decimals)
Approximate number of
instructional days: 20 Days
Pre-/Post-Assessment
#9
Renaming Fractions as
Decimals Word Problems
(4.NF4)
http://www.k5mathteachingresources.com/
support-files/equivalentfractions-with-a-denominatorof-100-problems.pdf
Lesson: Multiplying Fractions
Using Repeated Addition
http://learnzillion.com/lesso
ns/122-multiply-fractions-bywhole-numbers-usingrepeated-addition
Lesson: Word Problems
Multiplying A Fraction By A
Whole Number
9.1, 9.2, 9.5,
Critical Area 2
Topic 13
CCSS.Math.Content.4.NF.B.4
Apply and extend previous
understandings of multiplication
to multiply a fraction by a whole
number.
CCSS.Math.Content.4.NF.B.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 5 × (1/4), recording the
conclusion by the equation 5/4 = 5 ×
(1/4).
CCSS.Math.Content.4.NF.B.4b
Understand a multiple of a/b as a
multiple of 1/b, and use this
understanding to multiply a
http://learnzillion.com/lesso
ns/1430-solve-wordproblems-involvingmultiplying-a-fraction-by-awhole-number
fraction by a whole number. For
example, use a visual fraction model to
express 3 × (2/5) as 6 × (1/5),
recognizing this product as 6/5. (In
general, n × (a/b) = (n × a)/b.)
Lesson: Compare Decimals
Using Fractions
http://learnzillion.com/lesso
ns/562-compare-decimalsusing-fractions
CCSS.Math.Content.4.NF.B.4c
Solve word problems involving
multiplication of a fraction by a
whole number, e.g., by using
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?
CCSS.Math.Content.4.NF.C.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 and 100.2 For
example, express 3/10 as 30/100,
and add 3/10 + 4/100 = 34/100.
CCSS.Math.Content.4.NF.C.6 Use
decimal notation for fractions
with denominators 10 or 100. For
example, rewrite 0.62 as 62/100;
describe a length as 0.62 meters;
locate 0.62 on a number line
diagram.
CCSS.Math.Content.4.NF.C.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 >,
=, or <, and justify the
conclusions, e.g., by using a visual
model.
3
Title: Measurement
Units and
Conversions
Approximate number of
instructional days: 13 Days
Pre-/Post-Assessment
#11
Measurement Concentration
Game (4.MD1)
http://www.k5mathteachingresources.com/
supportfiles/measurementconcentrati
on4thgd.pdf
Measurement Conversion
Word Problems (4.MD1)
http://www.k5mathteachingresources.com/
supportfiles/conversionwordproblem
s.pdf
11.1, 11.4, 11.7
Critical Area 3
Topic 14
CCSS.Math.Content.4.MD.A.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,
know 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), ...
CCSS.Math.Content.4.MD.A.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.
3
Title: Solving
Measurement
Problems
Approximate number of
instructional days: 10 Days
Pre-/Post-Assessment
#8
Measurement Word Problems
(4.MD2)
http://www.k5mathteachingresources.com/
supportfiles/4thgrademeasproblems.p
df
Seating Arrangement Word
Problem (4.MD3)
http://www.k5mathteachingresources.com/
support-files/how-many-
8.1, 8.2, 8.3, 8.4, Critical Area 3
8.5, 11.5
Topic 15
CCSS.Math.Content.4.MD.B.4
Make a line plot to display a data
set of measurements in fractions
of a unit (1/2, 1/4, 1/8). Solve
problems involving addition and
subtraction of fractions by using
information presented in 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.
tables.pdf
CCSS.Math.Content.4.MD.A.3
Apply the area and perimeter
formulas for rectangles in real
world and mathematical
problems. For example, find the
width of 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.
Zoo Enclosure Area Problem
(4.MD3)
http://www.k5mathteachingresources.com/
supportfiles/designingazooenclosure.
pdf
3
Title: Lines, Angles,
and Shapes
Approximate number of
instructional days: 15 Days
Pre-/Post-Assessment
#6A, 1
Angles In Names Activity
(4.MD5)
http://www.k5mathteachingresources.com/
supportfiles/anglesinnames.pdf
How Many Degrees Activity
(4.MD7)
http://www.k5mathteachingresources.com/
supportfiles/hiwmanydegrees.pdf
6.5, 6.6, 6.7,
10.2, 10.4, 11.2,
Unit 1
Critical Area 3
Topic 16
CCSS.Math.Content.4.MD.C.5
Recognize angles as geometric
shapes that are formed wherever
two rays share a common
endpoint, and understand
concepts of angle measurement:
CCSS.Math.Content.4.MD.C.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.
CCSS.Math.Content.4.MD.C.5b
An angle that turns through n
one-degree angles is said to have
an angle measure of n degrees.
CCSS.Math.Content.4.MD.C.6
Measure angles in whole-number
degrees using a protractor. Sketch
angles of specified measure.
CCSS.Math.Content.4.MD.C.7
Recognize angle measure as
additive. When an angle is
decomposed into nonoverlapping 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
problems, e.g., by using an
equation with a symbol for the
unknown angle measure.
CCSS.Math.Content.4.G.A.1
Draw points, lines, line segments,
rays, angles (right, acute, obtuse),
and perpendicular and parallel
lines. Identify these in twodimensional figures.
CCSS.Math.Content.4.G.A.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.
CCSS.Math.Content.4.G.A.3
Recognize a line of symmetry for
a two-dimensional figure as 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.
Unit Description: Marking Period 1
Standard
Operations and Algebraic Thinking 4.OA
Number and Operations in Base Ten 4.NBT
Measurement and Data 4.MD
Geometry 4.G
Big Ideas: Course Objectives / Content Statement(s)
Operations and Algebraic Thinking 4.OA
• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.
Number and Operations in Base Ten 4.NBT
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Measurement and Data
4.MD
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Represent and interpret data.
Geometry
4.G
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Essential Questions
What provocative questions will foster inquiry,
understanding, and transfer of learning?
• What are properties of whole
numbers?
• How does the position of a digit in
a number affect its value?
• How are geometric properties used
to solve problems in everyday life?
• How is thinking algebraically
different than thinking
arithmetically?
Areas of Focus: Proficiencies
(CCSS)
Students will:
Enduring Understandings
What will students understand about the big ideas?
Students will understand that…
• Numbers can be classified by attributes.
• Grouping (unitizing) is a way to count, measure, and estimate.
• Place value is based on groups of ten.
• Flexible methods of computation involve grouping numbers in strategic ways.
• Patterns can be found in many forms.
• Number patterns and relationships can be represented using variables.
• Objects can be described and compared using their geometric attributes.
Examples, Outcomes, Assessments
Instructional Focus:
Operations and Algebraic Thinking
4.OA
Use the four operations with whole numbers to solve
problems.
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.3
Solve multistep word
problems posed with whole
numbers and having wholenumber answers using the
four operations, including
problems in which
remainders must be
interpreted. Represent these
problems using equations
with a letter standing for the
unknown quantity. Assess
the reasonableness of
answers using mental
computation and estimation
strategies including
rounding.
Gain familiarity with factors and multiples.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Identify and draw line segments, lines, and rays.
Construct angles, triangles, and quadrangles.
Describe properties of and compare quadrangles.
Classify quadrangles based on side and angle properties.
Develop definitions for convex and concave polygons.
Identify types of polygons according to the number of sides.
Extend numerical patterns.
Give equivalent mathematical expressions for whole numbers.
Insert grouping symbols to make number sentences true.
Read and write numbers up to 1,000,000,000; identify the values of digits.
Use and describe patterns to find sums.
Add and subtract multi-digit whole numbers.
Solve open sentences.
Use the partial-sums and column-addition algorithms to solve multi-digit addition
problems; choose an appropriate paper-and-pencil algorithm to solve multi-digit addition
problems.
Create a bar graph.
Ask and answer questions and draw conclusions based on data landmarks and a bar graph.
Use the trade-first and partial-differences algorithms to solve multi-digit subtraction
problems; choose an appropriate paper-and-pencil algorithm to solve multi-digit
subtraction problems.
Solve multiplication and division problems.
Use words and symbols to describe and write rules for functions.
Identify and use patterns in the Multiplication/Division Facts Table.
Find factors and multiples of numbers.
Use multiplication facts to generate related division facts.
Determine whether a number sentence is true or false.
Sample Assessments:
• Exit slips
o Draw and label a line segment.
o Draw and label a right triangle.
o Draw and label an equilateral triangle.
o Write five equivalent names for 42.
o Write the largest number you can, using the digits 4, 2, 7, and 0. Use each digit only
once.
o 736 + 645 = ________
o Fill in the blanks with two three-digit numbers to make a true number sentence:
________ - ________ = 345
o 528 – 263 = ________
o List all of the factors of 18.
Generate and analyze patterns.
o List four multiples of 7.
o List the multiplication/division fact family for the numbers 5, 6, and 30.
4.OA.5
Generate a number or shape
o Write true or false for the following number sentence: 42 – 15 = 27.
pattern that follows a given
o Write true or false for the following number sentence: 114 + 66 = 360/2
rule. Identify apparent
• Game record sheets
features of the pattern that
o Addition Top-It
were not explicit in the rule
o Subtraction Top-It
itself.
o Polygon Pair-Up
Number & Operations in Base Ten 4.NBT
o Name That Number
o Fishing for Digits
Generalize place value understanding for multi-digit
o High-Number Toss
whole numbers.
o Subtraction Target Practice
4.NBT.1 Recognize that in a multi-digit
o Baseball Multiplication
whole number, a digit in one
o Division Arrays
place represents ten times what
o Multiplication Top-It
it represents in the place to its
o Seega
right.
• Student self-assessment
• Writing prompts
4.NBT.2 Read and write multi-digit whole
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.
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 >, =, and <
symbols to record the results of
comparisons.
4.NBT.3
Use place value understanding
to round multi-digit whole
numbers to any place.
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
4.NBT.4
Fluently add and subtract multidigit whole numbers using the
standard algorithm.
4.NBT.6
Find whole-number quotients
and remainders with up to fourdigit 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.
•
•
•
•
•
•
o How is a line segment different than a line?
o Explain why a rhombus would be classified as a quadrilateral.
o Why must you know about parallel lines in order to be able to classify
quadrilaterals?
o What are the defining characteristics of a polygon?
o Lisa was given a “polygon riddle” to solve by her older brother. He told her that
the polygon had four sides, four right angles, and the opposite pairs of sides were
parallel. Lisa said that it was a square, but her brother told her she was wrong. Can
you please explain his reasoning?
o Francesco was solving the following addition problem, using the Partial-Sums
Algorithm:
47 + 84. He got 23 as his answer. Can you please explain his mistake?
o Jenny was asked to list all of the multiples of 4. Can you please explain why this is
impossible? Could she list all of the factors of 4?
o Chang was buying treats for his birthday party. He asked his mom and dad, “How
much is 7 times 7 plus 4?” His mom said “53,” and his dad said “77.” How did
they arrive at different answers? Who is correct?
Math journals/Interactive Student Notebooks
Record sheets
Teacher observation
Beginning, Middle, End-of-Year assessments
Progress check written assessment
Class checklists
Interdisciplinary Connections
• Interactive Student Notebooks
• Reading/writing word problems
• Math literature list (see attached)
Measurement and Data
4.MD
Solve problems involving measurement and
conversion of measurements from a larger unit to a
smaller unit.
4.MD.1
4.MD.2
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.
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.
Represent and interpret data.
•
Suggested Projects:
o Students research the distance each planet is from Earth in a standard unit. Then,
they graph the information, using a bar graph and answer a variety of questions
related to the differences of distances.
o Students create a crayfish, which consists of a series of polygons. Then, they label
its parts as accurately as possible.
o Students create a timeline of the significant events of the Revolutionary War. Using
a scale, they try to space out the events as accurately as possible to show elapsed
time.
Technology Integration
• Steps to Solving Word Problems http://school.nettrekker.com/goExternal?np=/external.ftl&pp=/error.ftl&evlCode=2497
24&productName=school&HOMEPAGE=E
• http://school.nettrekker.com/goExternal?np=/external.ftl&pp=/error.ftl&evlCode=3194
35&productName=school&HOMEPAGE=E
• Use Comic Life to create word problems and word problem how-to sheets.
• Anglemania!
http://school.nettrekker.com/goExternal?np=/external.ftl&pp=/error.ftl&evlCode=5782
33527780793372R3oYQ&productName=school&HOMEPAGE=E
• Everyday Math games
• Funbrain – Tic Tac Toe Squares (Multiplication)
http://www.funbrain.com/cgibin/ttt.cgi?A1=s&A2=13&A3=0&INSTRUCTS=1
• Batter’s Up Baseball
http://www.prongo.com/math/index.html
• PBS Kids – Number Sense
http://pbskids.org/cyberchase/math-games/number
sense/
• Around the World in 80 Seconds!
http://www.missmaggie.org/scholastic/roundtheworld_eng_launcher.html
4.MD.4
Geometry
Make a line plot to display a data
set of measurements in fractions
of a unit (1/2, 1/4, 1/8). Solve
problems involving addition and
subtraction of fractions by using
information presented in line
plots.
4.G
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
4.G.1
4.G.2
Draw points, lines, line
segments, rays, angles (right,
acute, obtuse), and
perpendicular and parallel lines.
Identify these in twodimensional figures.
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.
•
•
Math Goodies – Interactive Factor Tree Games
http://www.mathgoodies.com/factors/prime_factors.htm
Kids Games HQ – Factor Feeder
http://kidsgameshq.com/factor-feeder
Media Literacy Integration
• PBS Kids – Don’t Buy It, Buying Smart
http://pbskids.org/dontbuyit/buyingsmart/hotorsnot.html
• Partnership for 21st Century Skills (p. 22-23)
http://www.p21.org/storage/documents/P21_Math_Map.pdf
Global Perspectives
• Investigate Pascal’s triangle and its origin in France, as well as its significance in
mathematics.
• Investigate monetary equivalences to the U.S. dollar in different countries.
21st Century Skills:
Creativity and Innovation
• Create a song to teach a friend about the Partial-Sums Algorithm or Column Addition.
• Create a song about polygons.
• Create a new shape and name it; calculate its area and perimeter.
Critical Thinking and Problem Solving
• Create a new algorithm for multiplication or division.
Communication and Collaboration
• Addition Top-It
• Subtraction Top-It
• Polygon Pair-Up
• Name That Number
•
•
•
•
•
•
•
Fishing for Digits
High-Number Toss
Subtraction Target Practice
Baseball Multiplication
Division Arrays
Multiplication Top-It
Seega
Information Literacy
Life and Career Skills
• What jobs use these skills?
• How do your parents use these skills?
21st Century Themes (as applies to content area):
Financial, Economic, Business, and
Entrepreneurial Literacy
Civic Literacy
Health Literacy
• Students measure the circumference of their head and then compare it to that of a
classmate’s. They then graph the data and identify landmarks (e.g., mode, mean, minimum,
maximum, and median).
• Students measure their height. They then divide to figure out how many times they would
have to stack themselves to reach the top of the Empire State Building.
Unit Description: Marking Period 2
Standard
Operations and Algebraic Thinking 4.OA
Number and Operations in Base Ten 4.NBT
Number and Operations – Fractions 4.NF
Measurement and Data 4.MD
Geometry 4.G
Big Ideas: Course Objectives / Content Statement(s)
Operations and Algebraic Thinking 4.OA
• Use the four operations with whole numbers to solve problems.
Number and Operations in Base Ten 4.NBT
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations – Fractions 4.NF
• Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
4.MD
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Geometry
4.G
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Essential Questions
What provocative questions will foster inquiry,
understanding, and transfer of learning?
• How do I know which
computational method (mental
math, estimation, paper-and-pencil,
and calculator) to use?
• How important are estimations in
real-life situations?
• How is computation with rational
Enduring Understandings
What will students understand about the big ideas?
Students will understand that…
• The relationships among the operations and their properties promote computational
fluency.
• In certain situations, an estimate is as useful as an exact answer.
• There can be different strategies to solve a problem, but some are more effective and
efficient than others.
• Place value is based on groups of ten.
numbers similar and different to
whole number computation?
Areas of Focus: Proficiencies
(CCSS)
Students will:
Operations and Algebraic Thinking
4.OA
Use the four operations with whole numbers to solve
problems.
4.OA.1
4.OA.2
4.OA.3
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.
Multiply or divide to solve
word problems involving
multiplicative comparison,
e.g., by using drawings and
equations with a symbol for
the unknown number to
represent the problem,
distinguishing multiplicative
comparison from additive
comparison.
Solve multistep word
problems posed with whole
•
•
Decimals express a relationship between two numbers.
Patterns can be found in many forms.
Examples, Outcomes, Assessments
Instructional Focus:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Read and write decimals through thousandths.
Order decimals through thousandths on a number line.
Rename fractions with 10 and 100 in the denominator as decimals.
Estimate sums and differences of decimals; explain the strategies used.
Compare whole numbers and decimals.
Add and subtract decimals to the hundredths place.
Judge the reasonableness of solutions to decimal addition and subtraction problems.
Add and subtract decimals through hundredths in the context of money.
Use extended multiplication facts to convert between metric measurements.
Estimate, without tools, the length of objects or distances in centimeters, decimeters, and
meters.
Measure the lengths of objects or distances in centimeters, decimeters, and meters.
Use a scale to determine actual size.
Describe rules to solve problems involving products of ones and tens and products of tens
and tens.
Solve multi-digit multiplication problems.
Compare appropriate situations for the use of exact answers and estimates.
Estimate whether a product is in the tens, hundreds, thousands, or more.
Use the partial-products algorithm to solve multiplication problems with 1-digit and 2-digit
multipliers.
Use the lattice method to solve multiplication problems with 1-digit and 2-digit multipliers.
Use exponential notation to represent powers of 10.
Round large numbers to a given place.
numbers and having wholenumber answers using the
four operations, including
problems in which
remainders must be
interpreted. Represent these
problems using equations
with a letter standing for the
unknown quantity. Assess
the reasonableness of
answers using mental
computation and estimation
strategies including
rounding.
Sample Assessments:
• Exit slips
o List the following decimals in order from least to greatest: 0.12, 0.012, 0.00012,
0.02, .0124.
o Write the fraction equivalent for 0.7.
o Insert <, =, or > to describe the relationship between the two numbers:
0.3 _____ 0.12
o Insert <, =, or > to describe the relationship between the two numbers:
0.63 _____ 0.9
o Solve: $0.45 - $0.23 = ________
o Please write the following in standard notation:
587 thousandths
o Insert <, =, or > to describe the relationship between the two numbers:
0.073 _____ 0.73
Number & Operations in Base Ten 4.NBT
o How many centimeters are there in 1 meter?
o How many decimeters are there in 1 meter?
Generalize place value understanding for multi-digit
o Measure the length of your name tag to the nearest millimeter.
whole numbers.
o Estimate the following sum:
4.NBT.1 Recognize that in a multi-digit
884 + 631 = __________.
whole number, a digit in one
o 43 x 70 = _________
place represents ten times what
o __________ = 232 x 47
it represents in the place to its
o Write a number between 5,893,652 and 6,000,000.
right.
o Write 10,000 as 10 to a power.
o Round 19,763 to the nearest 1,000.
4.NBT.2 Read and write multi-digit whole
o Write a number that is halfway between 21,000 and 21,500.
numbers using base-ten
numerals, number names, and
• Game record sheets
expanded form. Compare two
o Baseball Multiplication
o Base-10 Exchange
multi-digit numbers based on
meanings of the digits in each
o Product Pile-Up
place, using >, =, and <
o Coin Top-It
symbols to record the results of
comparisons.
4.NBT.3
Use place value understanding
to round multi-digit whole
numbers to any place.
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
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.
Number and Operations – Fractions 4.NF
Understand decimal notation for fractions, and
compare decimal fractions.
4.NF.6
4.NF.7
Use decimal notation for
fractions with denominators 10
or 100.
Compare two decimals to
hundredths by reasoning about
their size. Recognize that
comparisons are valid only
when the two decimals refer to
•
•
o Number Top-It (Decimals)
o Name That Number
o Fishing for Digits
o Beat the Calculator
o Multiplication Top-It
o Multiplication Wrestling
o High-Number Toss
Student self-assessment
Writing prompts
o Greg had 48 pencils that he wanted to share with the 20 students (which included
him) in his class. He divided 48 by 20 and got a quotient of 2.4. Why doesn’t his
answer make sense?
o Arjun thought that 0.4 was less than 0.25. Explain or draw pictures to help Arjun
see that 0.4 is more than 0.25.
o Betty’s mom’s gas tank can hold 12 gallons of gas. When they stopped for gas, her
mom only had enough money to buy 7.6 gallons of gas. About how many more
gallons can her tank hold? Explain how you arrived at your solution.
o Bobby solved: 0.34 + 0.4 and got 0.38 as the sum. Explain the error that he made.
Then, show him how to correct it by solving the problem.
o Tamra and Jackie are arguing over a math problem. Tamra is convinced that 0.73
= 0.073. On the other hand, Jackie argues that 0.73 > 0.073. Who is right? How
do you know?
o 8 packs of gum cost $0.70 each. What is the total cost?
o Jeremiah knows that 7 x 8 = 56. However, he is stuck when his teacher gives him
the following problem to solve for homework: 70 x 80. Can you please help him
use his knowledge of basic facts to solve the problem above?
o If 1 centimeter on a map represents 200 miles, what do 6.5 centimeters represent?
Explain your reasoning.
o Solve the following problem using the Partial-Products Multiplication Algorithm
and the Lattice Method of Multiplication: 37 x 8. Which method do you prefer?
Why?
the same whole. Record the
results of comparisons with
symbols >, =, or <, and justify
the conclusions, e.g., by using a
visual model.
Measurement and Data
4.MD
Solve problems involving measurement and
conversion of measurements from a larger unit to a
smaller unit.
4.MD.1
4.MD.2
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.
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
•
•
•
•
•
•
o When would it be helpful to write a number in exponential notation as opposed to
expanded notation?
Math journals/Interactive Student Notebooks
Record sheets
Teacher observation
Beginning, Middle, End-of-Year assessments
Progress check written assessment
Class checklists
Interdisciplinary Connections
• Interactive Student Notebooks
• Reading/writing word problems
• Math literature list (see attached)
• Suggested Projects:
o Students plan a party for the Super Bowl. They must stay within a certain budget,
based on the number of people they plan on inviting. They will use decimal
addition and/or multiplication in order to compute the total cost.
o Students obtain a bank statement from one of their parents, in which only the
deposits, withdraws, and principal amount of money invested are displayed. They
must add/subtract, using decimals in order to compute how much money is
remaining in their parent’s account.
o Students are given a 10 x 10 blank grid. They must use at least six colors to create a
pattern and/or tessellation on the grid. Then, they will calculate the fraction,
decimal, and percent of each color, displayed on the grid.
o Students are given a menu from a restaurant in Summit. They must compute how
much it would cost their entire family to go out to dinner, including the tip. They
will need to use extended math facts to multiply by .10 and double it, in order to
calculate a 20% tip. (For enrichment: Have students calculate the tax, as well.)
o Students keep track of a baseball player’s batting average over time. Then, they
chart the player’s progress over time by computing the differences, using decimals
quantities using diagrams such
as number line diagrams that
feature a measurement scale.
Geometry
4.G
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
4.G.1
Draw points, lines, line
segments, rays, angles (right,
acute, obtuse), and
perpendicular and parallel lines.
Identify these in twodimensional 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.
to thousandths.
o What difference, if any, does it make if the decimal is placed before the zero, or
after the zero?
o Give at least three examples of jobs, in which employees encounter decimals on a
daily basis.
Technology Integration
• BrainPop – Decimals
• SMART http://school.nettrekker.com/goExternal?np=/external.ftl&pp=/error.ftl&evlCode=3685
65&productName=school&HOMEPAGE=E
• Everyday Math games
• Gamequarium – Death to Decimals
http://www.mrnussbaum.com/deathdecimals.htm
• BBC Education – Builder Ted
http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html
• Fraction/Decimal Match-Up
http://www.hbschool.com/activity/con_math/con_math.html
• Multiplication.com – Flying High
http://www.multiplication.com/games/play/flying-high
• Multiplication.com – Cone Crazy
http://www.multiplication.com/games/play/cone-crazy
Media Literacy Integration
• PBS Kids – Don’t Buy It, Buying Smart
http://pbskids.org/dontbuyit/buyingsmart/hotorsnot.html
• Partnership for 21st Century Skills (p. 22-23)
http://www.p21.org/storage/documents/P21_Math_Map.pdf
Global Perspectives
•
•
Investigate tax systems in other countries (See:
http://en.wikipedia.org/wiki/List_of_countries_by_tax_rates)
Research the use of the metric system as a standard unit of measure in many countries.
21st Century Skills:
Creativity and Innovation
• Create a new unit to add to the metric system. Explain how to make conversions using the
new unit.
• Create a menu for your own restaurant and include reasonable prices for each item. Then,
try to figure out how much revenue you will make over the course of a week if 50 people
eat at your restaurant each day for 7 days.
Critical Thinking and Problem Solving
• Use a Venn diagram to compare/contrast the Partial-Products Algorithm and the Lattice
Method of Multiplication.
• Write a “How To” sheet for the Partial-Products Algorithm and the Lattice Method of
Multiplication, which the teacher can photo-copy for the kids in your class to use for
reference.
Communication and Collaboration
• Baseball Multiplication
• Base-10 Exchange
• Product Pile-Up
• Coin Top-It
• Number Top-It (Decimals)
• Name That Number
• Fishing for Digits
• Beat the Calculator
• Multiplication Top-It
•
•
Multiplication Wrestling
High-Number Toss
Information Literacy
Life and Career Skills
• What jobs use these skills?
• How do your parents use these skills?
21st Century Themes (as applies to content area):
Financial, Economic, Business, and
Entrepreneurial Literacy
Civic Literacy
Health Literacy
• Lesson 5.4 – Estimating Products
(What Do Americans Eat?)
• The U.S. Department of Agriculture conducted a survey, which revealed that the average
American eats about 5.5 pounds of food per day. How much food would a person
consume in a week? A month? A year?
Unit Description: Marking Period 3
Standard
Operations and Algebraic Thinking 4.OA
Number and Operations in Base Ten 4.NBT
Number and Operations – Fractions 4.NF
Measurement and Data 4.MD
Big Ideas: Course Objectives / Content Statement(s)
Operations and Algebraic Thinking 4.OA
• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
Number and Operations in Base Ten 4.NBT
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations – Fractions 4.NF
• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
4.MD
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Represent and interpret data.
• Geometric measurement: understand concepts of angle and measure angles.
Essential Questions
What provocative questions will foster inquiry,
understanding, and transfer of learning?
• How can I use what I know about
repeated subtraction, equal sharing,
and forming equal groups to solve
division problems?
• How do I use concrete materials
Enduring Understandings
What will students understand about the big ideas?
Students will understand that…
• Computation involves taking apart and combining numbers using a variety of approaches.
• Fractions express a relationship between two numbers.
• The expected outcome of an event is a prediction of what might happen in the long run.
• A problem solver understands what has been done, knows why the process was
and drawings to understand and
appropriate, and can support it with reasons and evidence.
show understanding of fractions?
• There are many ways to model and compare fractions.
• How can we use models to compute
fractions with like and unlike
denominators?
Areas of Focus: Proficiencies
Examples, Outcomes, Assessments
(CCSS)
Students will:
Instructional Focus:
Operations and Algebraic Thinking
4.OA
Use the four operations with whole numbers to solve
problems.
4.OA.2
Multiply or divide to solve
word problems involving
multiplicative comparison,
e.g., by using drawings and
equations with a symbol for
the unknown number to
represent the problem,
distinguishing multiplicative
comparison from additive
comparison.
4.OA.3
Solve multistep word
problems posed with whole
numbers and having wholenumber answers using the
four operations, including
problems in which
remainders must be
interpreted. Represent these
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Describe the inverse relationship between multiplication and division.
Solve multiplication and division number stories.
Apply extend multiplication facts to long-division situations.
Solve equal-grouping division number stories.
Solve division number stories and interpret remainders.
Form angles of a given measure.
Rotate objects a given number of degrees.
Investigate the relationship between rotations and degrees.
Draw and measure angles with a full-circle protractor.
Describe a circle as having 360°.
Use reference points to estimate the measures of angles.
Use a half-circle protractor to measure and draw angles.
Classify angles according to their measure.
Identify and use multiples of 10.
Identify fractions and equal parts of a whole or the ONE and solve problems involving
fractional parts of regions.
Identify equivalent fractions and mixed numbers.
Find fractions and mixed numbers on number lines.
Solve problems involving fractional parts of collections.
Identify the whole or the ONE when given the “fraction-of.”
problems using equations
with a letter standing for the
unknown quantity. Assess
the reasonableness of
answers using mental
computation and estimation
strategies including
rounding.
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Express the probability of an event as a fraction.
Find fractional parts of polygonal regions.
Model fraction addition and subtraction with pattern blocks.
Develop a rule for generating equivalent fractions.
Rename fractions with 10 and 100 in the denominator as decimals.
Explain strategies used to compare and order fractions.
Sample Assessments:
• Exit slips
4.OA.4
Find all factor pairs for a
o There are 5 rows of cookies, with 7 cookies in each row. How many cookies in all?
whole number in the range
o 60 x _____ = 540
1-100. Recognize that a
o A box holds 7 crayons. How many boxes are needed to hold 128 crayons?
whole number is a multiple
o How many 7s are in 289?
of each of its factors.
o How many degrees are in a semicircle (1/2 of a circle)?
Determine whether a given
o Use a protractor to draw a 270° angle.
whole number in the range
o Use a half-circle protractor to draw and label an acute angle.
1-100 is a multiple of a given
o Use the Partial-Quotients Division Algorithm to solve: 743 ÷ 14.
one-digit number.
o List the following fractions from least to greatest: 1/6, 2/3, 4/12, 1 ½.
Determine whether a given
o How much is 2/5 of 30 raisins?
whole number in the range
o What is 7/8 of 32?
1-100 is prime or composite.
o There are 6 faces on a die. What fraction of the faces are even numbers?
o 2/3 + 1/6 = ______
Number & Operations in Base Ten 4.NBT
o
o Write 3/10 as a decimal.
Generalize place value understanding for multi-digit
o Barbara made cookies. ¾ of the cookies was 12. How many cookies did she make
whole numbers.
in all?
4.NBT.2 Read and write multi-digit whole
• Game record sheets
numbers using base-ten
o Division Arrays
numerals, number names, and
o High-Number Toss
expanded form. Compare two
o Buzz and Bizz-Buzz
multi-digit numbers based on
Gain familiarity with factors and multiples.
meanings of the digits in each
place, using >, =, and <
symbols to record the results of
comparisons.
4.NBT.3
Use place value understanding
to round multi-digit whole
numbers to any place.
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
4.NBT.6
Find whole-number quotients
and remainders with up to fourdigit 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.
Number and Operations – Fractions 4.NF
Extend understanding of fraction equivalence and
ordering.
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
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o Robot
o Angle Tangle
o Beat the Calculator
o Fraction Of
o Fraction Match
o Fraction Top-It
o Chances Are
Student self-assessment
Writing prompts
o The school custodian is setting up chairs for a parent meeting. There are 58 chairs.
The principal asked the custodian to place 7 chairs in each row. How many rows
of chairs will there be? Please explain your reasoning.
o Mrs. Smith is planning a field trip for her fourth grade class to go to the Liberty
Science Center. The bus will cost $200, and the tickets will cost $175. There are 25
students in her class. If they each pay an equal amount, how much will they each
pay? Explain how you arrived at your solution.
o How can you use multiples to solve division problems? Provide an example.
o Suzy’s birthday is in 131 days. How many weeks until her birthday? How did you
solve the problem?
o Bobby has 28 brownies. He wants to share them with 14 of his friends. Please
explain how each person’s share can be represented as a mixed number.
o When you divide and are left with a remainder, how do you use the context to
decide what to do with it?
o Tessa had 36 cookies. 2/3 of them were chocolate chip. How many of them were
not chocolate chip? Explain how you arrived at your solution.
o What is ¼ of 14? Explain using pictures or a visual fraction model, how you solved
the problem.
o Can the probability of a situation always be represented as a fraction? Why or why
not?
o Johnny solved the following problem: 5/6 – 2/3 and got 3/3 as his answer. Please
explain his mistake as well as how to correct it.
4.NF.2
to how the number and size of
the parts differ even though the
two fractions themselves are the
same size. Use this principle to
recognize and generate
equivalent fractions.
Compare two fractions with
different numerators and
different denominators, e.g., by
creating common denominators
or numerators, or by comparing
to a benchmark fraction such as
1/2. Recognize that
comparisons are valid only
when the two fractions refer to
the same whole. Record the
results of comparisons with
symbols >, =, or <, and justify
the conclusions, e.g., by using a
visual fraction model.
Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
4.NF.3
Understand a fraction a/b with
a >1 as a sum of fractions 1/b.
a. Understand addition and
subtraction of fractions as
joining and separating parts
referring to the same whole.
b. Decompose a fraction into a
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o What is the easiest way to generate an equivalent fraction for ¾? Use the rule you
described to generate at least two equivalent fractions.
o Jimmy wanted to figure out whether he would get more pizza if he ate ¾ of it or
5/8. He figured since 5 is greater than 3 and 8 is greater than 4 that 5/8 of the
same pizza would be more. Can you please explain the flaw in his logic?
Math journals/Interactive Student Notebooks
Record sheets
Teacher observation
Beginning, Middle, End-of-Year assessments
Progress check written assessment
Class checklists
Interdisciplinary Connections
• Interactive Student Notebooks
• Reading/writing word problems
• Math literature list (see attached)
• Suggested Projects:
o Students use their knowledge of angle measures and coordinate grids, in order to
locate specific locations on a map. By plotting the locations, it will lead them to a
final destination. (http://www.abcya.com/latitude_and_longitude_practice.htm)
o Students go geocaching, using a GPS and their knowledge of angle measures as a
means of locating specific points, in order to find hidden caches.
o Arrange students in groups of 3 or 4. Then, as a read aloud, share The Doorbell Rang
by Pat Hutchins. Students must figure out how to share the plate of cookies in the
story as more visitors arrive at the house. Ultimately, have students act out the
story and use their knowledge of “fraction-of” problems, in order to figure out how
to equally share the cookies.
o Provide students with a recipe. Ask them to double, triple, or quadruple the recipe
and have them use their knowledge of adding and subtracting fractions to generate
a revised recipe.
4.NF.4
sum of fractions with the same
denominator in more than one
way, recording each
decomposition by an equation.
Justify decompositions, e.g., by
using a visual fraction model.
c. 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.
d. 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.
Apply and extend previous
understandings of multiplication
to multiply a fraction by a whole
number.
a. Understand a fraction a/b as a
multiple of 1/b.
b. Understand a multiple of a/b
as a multiple of 1/b, and use this
understanding to multiply a
Technology Integration
• SMART Exchange – word problems http://exchange.smarttech.com/search.html?q=word+problems
• Fraction Word Problem Mystery http://school.nettrekker.com/goExternal?np=/external.ftl&pp=/error.ftl&evlCode=1994
83&productName=school&HOMEPAGE=E
• Create a word problem and the answer in iMovie and post on classroom blog for other
students.
• Everyday Math games
• Apple Baskets Division
http://www.kidsnumbers.com/apple-baskets-division.php
• Snork’s Long Division
http://www.kidsnumbers.com/long-division.php
• AAA Math – Equivalent Fractions Match
http://www.sheppardsoftware.com/mathgames/fractions/memory_equivalent1.htm
• Flowering Fractions
http://www.learningbox.com/fractions/index.html
• Pizza Fractions
http://www.softschools.com/math/fractions/games/
Media Literacy Integration
• PBS Kids – Don’t Buy It, Buying Smart
http://pbskids.org/dontbuyit/buyingsmart/hotorsnot.html
• Partnership for 21st Century Skills (p. 22-23)
http://www.p21.org/storage/documents/P21_Math_Map.pdf
Global Perspectives
• Research why the metric system is a base 10 system.
• Make a timeline of the major achievements in the history of mathematics (dating back to
fraction by a whole number.
c. Solve word problems
involving multiplication of a
fraction by a whole number,
e.g., by using visual fraction
models and equations to
represent the problem.
Understand decimal notation for fractions, and
compare decimal fractions.
4.NF.6
4.NF.7
Use decimal notation for
fractions with denominators 10
or 100.
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
symbols >, =, or <, and justify
the conclusions, e.g., by using a
visual model.
Measurement and Data
4.MD
Solve problems involving measurement and
conversion of measurements from a larger unit to a
smaller unit.
4.MD.2
Use the four operations to solve
word problems involving
distances, intervals of time,
B.C.) Identify where the invention of the decimal system falls along the timeline.
21st Century Skills:
Creativity and Innovation
• Write a song that only consists of ½ notes or 1/8 notes.
• Interview the librarian about how s/he uses the Dewey Decimal System to sort books in
the library. Then, try to come up with a different system for sorting the books in the
library and propose it to the librarian.
Critical Thinking and Problem Solving
• Write a paragraph about whether fractions or decimals are more accurate and be sure to
include your reasoning.
Communication and Collaboration
• Division Arrays
• High-Number Toss
• Buzz and Bizz-Buzz
• Robot
• Angle Tangle
• Beat the Calculator
• Fraction Of
• Fraction Match
• Fraction Top-It
• Chances Are
Information Literacy
Life and Career Skills
• What jobs use these skills?
• How do your parents use these skills?
liquid volumes, masses of
objects, and money, including
21st Century Themes (as applies to content area):
problems involving simple
Financial, Economic, Business, and
fractions or decimals, and
Entrepreneurial Literacy
problems that require expressing
measurements given in a larger
Civic Literacy
unit in terms of a smaller unit.
Represent measurement
Health Literacy
quantities using diagrams such
• Students track the food that they eat over the course of the day. They compute the
as number line diagrams that
fraction of the calories that they consume that are fat-based, protein-based, and
feature a measurement scale.
carbohydrate-based.
• Students calculate the fraction of bones that are in their:
Represent and interpret data.
o Skull
4.MD.4
Make a line plot to display a data
o Ear
set of measurements in fractions
o Hands
of a unit (1/2, 1/4, 1/8). Solve
o Feet
problems involving addition and
subtraction of fractions by using
information presented in line
plots.
Geometric measurement: understand concepts of
angle and measure angles.
4.MD.5
Recognize angles as geometric
shapes that are formed
whenever two rays share a
common endpoint, and
understand concepts of angle
measurement:
a. 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.
And angle that turns through
1/360 of a circle is called a
“one-degree angle,” and can be
used to measure angles.
b. 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 wholenumber degrees using a
protractor. Sketch angles of a
specified measure.
4.MD.7
Recognize angle measure as
additive. When an angle is
decomposed into nonoverlapping 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
problems, e.g., by using an
equation with a symbol for the
unknown angle measure.
Standard
Operations and Algebraic Thinking 4.OA
Number and Operations in Base Ten 4.NBT
Number and Operations – Fractions 4.NF
Measurement and Data 4.MD
Geometry 4.G
Big Ideas: Course Objectives / Content Statement(s)
Operations and Algebraic Thinking 4.OA
• Use the four operations with whole numbers to solve problems.
• Generate and analyze patterns.
Number and Operations in Base Ten 4.NBT
• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations – Fractions 4.NF
• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
4.MD
• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Geometric measurement: understand concepts of angle and measure angles.
Geometry
4.G
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Essential Questions
What provocative questions will foster inquiry,
understanding, and transfer of learning?
• How are geometric properties used
to solve problems in everyday life?
• How can patterns be used to
Enduring Understandings
What will students understand about the big ideas?
Students will understand that…
• Geometry and spatial sense offer ways to interpret and reflect on our physical environment.
• Objects have distinct attributes that can be measured.
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determine standard formulas for
area and perimeter?
How is computation with rational
numbers similar and different to
whole number computation?
Areas of Focus: Proficiencies
(CCSS)
Students will:
Operations and Algebraic Thinking
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Analyzing geometric relationships develops reasoning and justification skills.
Fractions and decimals represent a relationship between two numbers.
Examples, Outcomes, Assessments
Instructional Focus:
4.OA
Use the four operations with whole numbers to solve
problems.
4.OA.2
Multiply or divide to solve
word problems involving
multiplicative comparison,
e.g., by using drawings and
equations with a symbol for
the unknown number to
represent the problem,
distinguishing multiplicative
comparison from additive
comparison.
4.OA.3
Solve multistep word
problems posed with whole
numbers and having wholenumber answers using the
four operations, including
problems in which
remainders must be
interpreted. Represent these
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Measure distances in feet and inches.
Calculate the perimeter of a triangle.
Make a scale drawing of the classroom.
Use a scale drawing to estimate the area of the classroom.
Find the areas of polygons by counting squares and partial squares.
Use patterns in a table to develop a formula for the area of a rectangle.
Develop a formula for calculating the area of a parallelogram.
Find the areas of rectangles and parallelograms.
Develop a formula for calculating the area of a triangle.
Use “times as many” language to compare area measurements.
Rename fractions with denominators of 100 as decimals.
Explore terminating and repeating decimals.
Use a calculator to rename fractions as decimals.
Round decimals and estimate products.
Round decimals and estimate quotients.
Explore lines of reflection and reflected images.
Solve problems involving spatial visualization.
Describe, compare, and classify plane and solid figures.
Use multiplication to solve volume problems.
problems using equations
with a letter standing for the
unknown quantity. Assess
the reasonableness of
answers using mental
computation and estimation
strategies including
rounding.
Gain familiarity with factors and multiples.
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.
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Sample Assessments:
• Exit slips
o Write the formula for calculating the area of a rectangle.
o Write the formula for calculating the area of a triangle.
o Calculate the perimeter and area of a square with a side length of 4 inches.
o Calculate the area of a triangle with a base that is 2 inches and a height of 6 inches.
o Area is measured in ____________ units.
o Express the following as a fraction and a decimal:
“At Magic Fountain 3 out of every 10 customers order vanilla ice cream.”
o Express the following as a fraction and a decimal:
“In Miss Jensen’s class, 3 out of every 5 students are girls.”
o Express 0.24 as a fraction in simplest terms.
o Express 2/5 as a decimal.
o 1.2 x 6 = ______
o Calculate the area of a rectangle with a base of 1.5 cm. and a height of 3 cm.
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Generate and analyze patterns.
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.
Describe examples of rates.
Use patterns and rules to solve rate problems.
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Game record sheets
o Fraction Match
o Rugs and Fences
o Polygon Pair-Up
o Dart Game
o Pocket-Billiards Game
o Name That Number
Student self-assessment
Writing prompts
Number & Operations in Base Ten 4.NBT
Generalize place value understanding for multi-digit
whole numbers.
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 >, =, and <
symbols to record the results of
comparisons.
Number & Operations in Base Ten 4.NBT
Generalize place value understanding for multi-digit
whole numbers.
4.NBT.2
4.NBT.3
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 >, =, and <
symbols to record the results of
comparisons.
Use place value understanding
to round multi-digit whole
numbers to any place.
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o Why is it necessary to use a scale when drawing a blueprint of a house or room in a
house?
o Bobby and Jimmy were arguing over whose room was bigger. Bobby’s room is 12
feet by 5 feet, while Jimmy’s room is 6 feet by 10 feet. Whose room has a greater
area? Please explain your reasoning.
o Betsy learned the formula for finding the area of a rectangle. Her friend asked her
to find the area of a square; however, she said she didn’t learn that formula, yet.
Can Betsy use what she has learned about rectangles to help her calculate the area
of a square? Why or why not?
o Use your calculator to divide 1 by 3. What do you notice about the decimal
equivalent of 1/3? What do you call this type of decimal?
o What is the only difference between multiplication of whole numbers and
multiplication of decimals?
o Bernadette was trying to solve the following problem: 34.7 x 18.3. She got 6,350.1.
Please find her mistake and explain where she went wrong.
o At one food store, apples are 4 for $2.00. At another food store, apples are 5 for
$3.00. Which is the better deal? How do you know?
Math journals/Interactive Student Notebooks
Record sheets
Teacher observation
Beginning, Middle, End-of-Year assessments
Progress check written assessment
Class checklists
Interdisciplinary Connections
• Interactive Student Notebooks
• Reading/writing word problems
• Math literature list (see attached)
• Suggested Projects:
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
4.NBT.4
Fluently add and subtract multidigit whole numbers using the
standard algorithm.
4.NBT.5
Multiply a whole number of up
to four digits by a one-digit
whole number, and multiply two
two-digit numbers, using
strategies based on place value
and the properties of
operations. Illustrate and
explain the calculation by using
equations, rectangular arrays,
and/or area models.
4.NBT.6
Find whole-number quotients
and remainders with up to fourdigit 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.
Number and Operations – Fractions 4.NF
o Students draw a blueprint for a house. They calculate the perimeter and area of
each room. (Enrichment: Students calculate the cost of flooring and
wallpaper/paint, based on a unit price.)
o Given a table of batting averages of several baseball players, students convert the
decimals to fractions (in simplest form), using a calculator. They also explore
patterns of any repeating decimals.
o Students go to the store and collect several examples of unit prices and using
multiplication, figure out how much the same object would cost in groups of 2, 5,
and 10.
Technology Integration
• Everyday Math games
• Use Microsoft Excel to create a circle graph to represent the current demographic
information of the United States.
• Khan Academy Videos on perimeter
• BrainPop – Geometry
• Cyberchase: Can You Fill It?
http://pbskids.org/cyberchase/math-games/can-you-fillit/
• Cyberchase: Pour to Score
http://pbskids.org/cyberchase/math-games/pour-score/
• Fraction/Decimal Match-Up
http://www.hbschool.com/activity/con_math/con_math.html
• Cyberchase: Poddle Weigh-In
http://pbskids.org/mayaandmiguel/english/games/cooking/index.html
• Gamequarium – Death to Decimals
http://www.mrnussbaum.com/deathdecimals.htm
• BBC Education – Builder Ted
Extend understanding of fraction equivalence and
ordering.
4.NF.1
4.NF.2
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 number and size of
the parts differ even though the
two fractions themselves are the
same size. Use this principle to
recognize and generate
equivalent fractions.
Compare two fractions with
different numerators and
different denominators, e.g., by
creating common denominators
or numerators, or by comparing
to a benchmark fraction such as
1/2. Recognize that
comparisons are valid only
when the two fractions refer to
the same whole. Record the
results of comparisons with
symbols >, =, or <, and justify
the conclusions, e.g., by using a
visual fraction model.
Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.
4.NF.4
Apply and extend previous
http://www.bbc.co.uk/education/mathsfile/shockwave/games/laddergame.html
Media Literacy Integration
• PBS Kids – Don’t Buy It, Buying Smart
http://pbskids.org/dontbuyit/buyingsmart/hotorsnot.html
• Partnership for 21st Century Skills (p. 22-23)
http://www.p21.org/storage/documents/P21_Math_Map.pdf
Global Perspectives
• Numbers, Mayan Style Project (Project #7)
• Students select a country and compare its area to that of the United States. They focus on
using “times as many” language to compare area measurements.
• Students calculate what fraction/decimal of the population in the U.S. is:
o White
o Black
o Hispanic
o Asian
o Hawaiian/Pacific Islander
o Other
They then represent this information in the form of a circle graph, using Microsoft Excel.
21st Century Skills:
Creativity and Innovation
• Which Soft Drink Is the Best Buy? Project
• Come up with a mnemonic or silly sentence to remember the formulas for the area of a
rectangle, triangle, and parallelogram.
Critical Thinking and Problem Solving
• Research the unit price of a specific food product (e.g., milk, eggs, cookies, bread). They
compare several different brands of the same product and consider how the company
understandings of multiplication
to multiply a fraction by a whole
number.
a. Understand a fraction a/b as a
multiple of 1/b.
b. Understand a multiple of a/b
as a multiple of 1/b, and use this
understanding to multiply a
fraction by a whole number.
c. Solve word problems
involving multiplication of a
fraction by a whole number,
e.g., by using visual fraction
models and equations to
represent the problem.
Understand decimal notation for fractions, and
compare decimal fractions.
4.NF.5
4.NF.6
Express a fraction with
denominator 10 as an equivalent
fraction with denominator 100,
and use this technique to add
two fractions with respective 10
and 100.
Use decimal notation for
fractions with denominators 10
or 100.
Measurement and Data
4.MD
Solve problems involving measurement and
conversion of measurements from a larger unit to a
advertises so the consumer appears to be getting the most for their money.
Communication and Collaboration
• Fraction Match
• Rugs and Fences
• Polygon Pair-Up
• Dart Game
• Pocket-Billiards Game
• Name That Number
• Making a Quilt Project
• Which Soft Drink Is the Best Buy? Project
Information Literacy
Life and Career Skills
• What jobs use these skills?
• How do your parents use these skills?
21st Century Themes (as applies to content area):
Financial, Economic, Business, and
Entrepreneurial Literacy
Civic Literacy
Health Literacy
• Student investigates capacity of water they should consume over the course of a day. Then,
they use multiplication to figure out how much water they should consume in a week,
month, and finally, a year.
• Lesson 8.4 – What Is the Area of My Skin?
• Over the course of five days, students calculate the time (and distance) that it takes them to
smaller unit.
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.
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.3
Apply the area and perimeter
formulas for rectangles in real
world and mathematical
problems.
Geometric measurement: understand concepts of
walk to school. Using their knowledge of rates, they figure out how quickly they walk to
school each day. Then, they represent this information in the form of a bar graph.
angle and measure angles.
4.MD.6
Measure angles in wholenumber degrees using a
protractor. Sketch angles of a
specified measure.
4.MD.7
Recognize angle measure as
additive. When an angle is
decomposed into nonoverlapping 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
problems, e.g., by using an
equation with a symbol for the
unknown angle measure.
Geometry
4.G
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles.
4.G.1
Draw points, lines, line
segments, rays, angles (right,
acute, obtuse), and
perpendicular and parallel lines.
Identify these in twodimensional 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.
4.G.3
Recognize a line of symmetry
for a two-dimensional figure as
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.
Math Book Center Directions
1. Pick a book to read from the Math Book Center.
2. From the envelope, pick and read a question.
3. As you read the book, consider an answer to the question. Use PostIts to collect your thoughts.
4. When you are finished, write a complete answer to the question.
5. Use the guide below to write an answer to the question.
Question: How does reading about the math concept in this book help you deepen your
understanding of the concept?
Label the answer with the book, pages referencing and math unit. Title: How Much Is a Million
Page #: 8, 18
Unit/Concept: Place Value
Use math vocabulary. In the book, How Much is Million, it gives me a new idea of how much a million is. I’ve always
understood that 1 million is a 1 and 6 zeros and that’s a lot but it’s so much that I tried to count to 1
million it would take me 23 days straight. This shows me that a million is not a typical number I
would use to count something – not like 100 or 1,000. But we still need the numbers millions and
billions to describe how much money the United States spends each year. That does leave me
wondering how they count all of that money!
Support your answer with details. Math Book Center Questions
What is something new that you have
discovered in this story? Why is your discovery
important?
What are the repetitive patterns you notice in
this story? Be sure to compare math concepts.
How does this book relate to the math concepts How are the math concepts in this connected
covered in class? Give specific examples.
to the real world?
Write a book review of the story. Be sure to
Write a word problem using the story as a
include the math concepts covered in the story. guide. Be sure to solve the problem.
Many people like to say they aren’t “math
people.” Explain how this book might help
them understand the importance of math.
What were some of the math concepts/ideas
you wondered about during this book?
If you were teaching this math concept to
Does this book remind you of any other you’ve
someone, how would you use the story to help
read? How? Be sure to compare math
you teach?
concepts.
Create a picture illustrating a math concept
Write a new math problem that corresponds
from the story you read.
with the book. Be sure to solve your problem.
Write a new ending to the story based by
changing the math.
How does reading about the math concept in
this book help you deepen your understanding
of the concept?
Book List –
A Cloak for the Dreamer by Alileen Friedman
A Million Fish…More or Less by Patricia C. McKissak
Among the Odds and Evens by Priscilla Turner
A Remainder of One by Elinor J. Pinczes
Counting Crocodiles by Judy Sierra
How Much is a Million? By David M. Schwertz
If You Hopped Like a Frog by David M. Schwartz
Jim and the Beanstalk by Raymond Briggs
Math Appeal by Harry Briggs
Math for Smarty Pants by Marilyn Burns
One Grain of Rice by Demi
One Tiny Turtle by Nicola Davies
Spaghetti and Meatballs for All by Marilyn Burns
The $1.00 Wird Riddle Book
The Amazing Book of Mammal Records by Samuel G. Woods
The I Hate Mathematics! Book by Marilyn Burns
Tiger Math by Ann Whitehead Nagda and Cindey Bickel
Tikki Tikki Temo retold by Arlene Mosel