Download Knowledge and Skills - Baltimore City Public Schools

Updated 10/1/10
Baltimore City Schools
Dr. Andrés Alonso
Chief Executive Officer
Dr. Sonja Santelises
Chief Academic Officer
Linda Eberhart
Executive Director
Teaching and Learning
Curriculum Writers
Thanks to all City Schools teachers who wrote, revised, and provided feedback for this curriculum. A special thanks to
the following curriculum writers:
Kim Alexander
Margo Berish
Julia Bonkowski
Megan Bovill
Thomas Coleman
Megan Cooper
Matthew Damseaux
Kimberly David
Melanie Davison
Chritian Fisher
Geneve Garcia
Beth Goldscher
Andrew Hlavka
Gil Laqui
Maggie Lasaga-Flister
Benjamin Lawrence
Luis Lima
Genevieve Mason
Scott Messinger
Kevin Older
Elizabeth Renwick
Estelito Reyes
Katherine Schlee
Weston Schreiber
Levi Straight
Odessa Tamayo
Siriporn Vinijkul
Smitha Viswanathan
Shanekwa Winfield
Math Works Homework
Homework can be an effective part of your math
program - giving students the practice they need to
master skills. Below are some Math Works methods for
utilizing homework.
Suggested Homework Procedures:
o Check homework every night
o Give students an opportunity to revise homework
o Start the homework assignment together at the
beginning or end of class.
o Dedicate 10 minutes to going over 2-5 problems that
students are having trouble with (they pick some, you
pick some). Model how you work through the
problems on the board.
o Reward students for doing homework and revising it.
Homework Tips:
o Homework should consist primarily of skills that
students have already been exposed to. Skills should
cycle in and out depending on what your students
have been taught AND what they have mastered.
o Require students to show their work on homework
problems, not just write the answer. Give credit only
when there is work.
o Circulate throughout the classroom while talking
about homework problems to be sure students are
writing down what you are talking about and are
showing work.
o At the beginning of the year, homework should
consist of skills taught in the previous grade level.
Grade 4 Homework
Other Useful Links

MSA Daily Reviews

Mathematics Study Guide

Vocabulary Activities

Math Templates

Structuring Your Math Block Weekly Planning Grid

Sample Lesson Plan Template
Grade 4 Math Curriculum Sequence
School Year 2010-2011
QUARTER 1 (Aug 30 – Nov 5)
45 days
BENCHMARK A
(same skills as June Benchmark in previous grade)
Sept 7 - Sept 17
testing window
*COMMON
CORE
 Read, Write, Represent Whole Numbers
 Represent numbers with models through the millions
 Represent numbers in numeric and word form through the
millions
 Create equivalent representations through the millions
 Represent numbers in expanded form through the millions
2 – 4 days
*COMMON
CORE
(7-12 days)
 Place Value and Expanded Form of Whole Numbers
 Identify the value of a digit through the millions using the
base ten model
3 – 5 days
*COMMON
CORE
UNIT 1: Whole Number Concepts
Suggested Time
Frame
 Compare and Order Whole Numbers
 Compare numbers through the millions
 Order numbers through the millions
2 – 3 days
*COMMON
CORE
*COMMON
CORE
*COMMON
CORE
UNIT 2: Whole Number Computation 1
 Add Whole Numbers
 Add up to 4-digit whole numbers with regrouping
 Subtract Whole Numbers
 Subtract up to 4-digit minus 4-digit regrouping once
 Subtract up to 4-digit minus 4-digit regrouping twice
 Subtract up to 4-digit minus 4-digit regrouping three times
 Estimate Sums and Differences
 Rounding whole numbers
 Estimating sums and differences
 Compare Values of Mixed Currency
 Identify value of mixed currency
 Compare money sets
Unit 3: Number Theory and Computation 2
 Multiples
 Identify multiples
(7-11 days)
1 – 2 days
3 – 4 days
2 – 3 days
1 – 2 days
(10-20 days)
1 – 2 days
*COMMON
CORE
*COMMON
CORE
 Factors
 Identify factors
 Create and interpret factor arrays
 Multiply Whole Numbers
 Multiply up to 3-digits by 1 digit no regrouping
 Multiply up to 3-digits by 1 digit with regrouping
 Multiply up to 4-digits by 1 digit with regrouping
 Divide Whole Numbers
 Divide 2-digits by 1-digit
 Divide 3-digits by 1 digit
 Divide 4-digits by 1 digit
 Estimate Products and Quotients
 Estimate products
 Estimate quotients
 Divisibility Rules
 Identify numbers divisible by 2
 Identify numbers divisible by 5
 Identify numbers divisible by 10
 Identify numbers divisible by a combination of 2, 5, or 10
UNIT 4: Algebra 1
 Numeric Patterns
 Identify the rule for and extend a number pattern
 Repeating Patterns
 Identify the rule for and extend a repeating pattern
 Growing Patterns
 Identify a rule for and extend a growing pattern
 Solve for Unknown Quantities
 Find the unknown using addition and subtraction
 Find the unknown using multiplication
 Function Tables
 Complete function tables using addition and subtraction
 Complete function tables using multiplication
 Complete function tables using division
QUARTER 2 (Nov 8 – Jan 21)
46 days
BENCHMARK B
(all Quarter 1 skills assessed)
Unit 5: Fraction Concepts
 Proper Fractions and Mixed Numbers
 Read, write, represent fractions as part of a whole
 Read, write, represent fractions as part of a set
 Read, write, represent mixed numbers
1 – 3 days
2 – 4 days
3 – 5 days
2 – 3 days
1 – 3 days
(7–14 days)
1 – 2 days
1 - 2 days
1 - 3 days
2 – 3 days
2 - 4 days
Suggested Time
Frame
Nov 1 – Nov 12
testing window
(7-12 days)
2 - 3 days
*COMMON
CORE
 Compare and Order Fractions and Mixed Numbers
 Compare proper fractions and mixed numbers
 Order proper fractions and mixed numbers
 Fractional Number Lines
 Create fractional number lines
 Write fractions on number lines
 Identify locations on number lines
 Write and identify mixed numbers on number lines
 Add and Subtract Proper Fractions and Mixed Numbers
 Add proper fractions
 Subtract proper fractions
 Add mixed numbers
 Subtract mixed numbers
Unit 6: Statistics and Probability
 Probability
 Express object probability as a fraction
 Express spinner probability as a fraction
 Express conditional probability as a fraction
 Median, Mode and Range
 Determine the range of a set of data
 Determine the mode of a set of data
 Determine the median of a set of data
 Line Plots
 Create line plots
 Interpret line plots
 Coordinate Grids
 Identify locations on a coordinate grid given object
 Identify objects on a coordinate grid given location
 Line Graphs
 Interpret line graphs
UNIT 7: Algebra 2
 Write Expressions
 Write expressions using addition or subtraction
 Write expressions using multiplication or division
 Equivalent Expressions
 Write equivalent expressions
 Write Relationships
 Evaluate relationships with missing relational symbols
 Represent relationships in word problems
1 – 2 days
2 – 4 days
2 – 3 days
(11-18 days)
3 - 5 days
2 – 3 days
3 – 5 days
1 – 2 days
2 – 3 days
(5-9 days)
2 – 3 days
1 – 2 days
2 – 4 days
Unit 8: Geometry 1
(4-8 days)
 Angles
 Identify right angles
 Identify acute and obtuse angles
 Identify angles in shapes and objects
2 – 4 days
 Transformations
 Identify and create translations
 Identify and create reflections
 Identify and create rotations
QUARTER 3 (Jan 25 – Apr 7)
45 days
BENCHMARK C – Mock MSA
(all VSC assessed skills)
Unit 9: Geometry 2
 Geometric Solids
 Identify cones and cylinders
 Identify and describe pyramids by the number of edges, faces, or
vertices
 Identify and describe prisms by the number of edges, faces, or
vertices
 Nets for Cubes and Pyramids
 Identify the number and arrangement of squares needed to
create cubes
 Identify the number and arrangement of rectangles/triangles
needed to create pyramids
2 – 4 days
Suggested Time
Frame
Jan 31 – Feb 11
testing window
(6-9 days)
4 – 6 days
2 – 3 days
Unit 10: Decimals
(8-16 days)
 Read, Write, Represent Decimals
 Read, write, represent decimals in the tenths
 Read, write, represent decimals in the hundredths
2 – 4 days
 Place Value and Expanded Form of Decimals
 Represent decimals in expanded form through the hundredths
 Compare and Order Decimals
 Compare decimals through the hundredths
 Order decimals through the hundredths
 Add Decimals
 Add decimals through the tenths
 Add decimals through the hundredths
 Subtract Decimals
 Subtract decimals through the tenths
 Subtract decimals through the hundredths
 Estimate Decimal Sums and Differences
 Round decimals
 Estimate sums to the tenths
 Estimate sums to the ones place
 Estimate differences to the tenths
 Estimate differences to the ones place
Unit 11: Measurement 1
1 – 3 days
1 – 2 days
1 – 2 days
1 – 2 days
2 – 3 days
(5-9 days)
 Measure Length
 Draw length to nearest ¼ inch
 Measure length to nearest ¼ inch
 Measure length to nearest mm
 Determine Equivalent Units of Length
 Convert yards to inches
 Convert inches to yards, feet
2 – 4 days
3 – 5 days
Unit 12: Measurement 2
(7-11 days)
 Perimeter
 Find perimeter given all sides
 Find perimeter with missing sides
2 – 3 days
 Area
 Find area on grid
 Find area using formula
2 – 3 days
 Start time, Elapsed Time, and End Time
 Find end time
 Find start time
 Find elapsed time
3 – 5 days
Maryland State Assessment
POST-MSA CURRICULUM
Unit 13: Fraction Concepts 2
Suggested Time
Frame
(10 - 15 days)
*COMMON
CORE
2 - 3 days
3 - 5 days
*COMMON
CORE
 Least Common Multiple
 Identify the least common multiple of 2 numbers
 Identify the least common multiple of 3 numbers
 Equivalent Forms of Fractions
 Concrete representations of equivalent fractions using
visual models with attention to how the number and size of
the parts differ even though the two fractions themselves
are the same size
 Process of finding equivalent fractions
 Add and Subtract Proper Fractions with Unlike Denominators
 Add proper fractions with unlike denominators
 Subtract proper fractions with unlike denominators
March 7 to
March 16
5 - 7 days
Unit 14: Simplify & Compare Fractions
 Identify GCF and Simplify Fractions
 Identify the Greatest Common Factor
 Use the Greatest Common Factor to simplify fractions
(10 - 14 days)
5 - 7 days
*COMMON
CORE
 Compare and Order Fractions with Unlike Denominators
 Compare fractions with unlike denominators
 Order fractions with unlike denominators Compare mixed
numbers with unlike denominators
 Order mixed numbers with unlike denominators

*COMMON
CORE
 Express a fraction with denominator 10 as an equivalent
fraction with denominator 100
2-4 days
*COMMON
CORE
7-13 days
 Use decimal notation for fractions with denominators 10 or
100
3-5 days
*COMMON
CORE
Unit 15: Decimal Notation for Fractions
5 - 7 days
 Compare two decimals to hundredths by reasoning about their
size
2-4 days
*COMMON
CORE
*COMMON
CORE
Unit 16: Whole Number Computation 2
 Multiply Whole Numbers
 Multiply 2-digit by 2-digit as multiple of ten
 Multiply 2-digit by 2-digit




Divide Whole Numbers
Divide with 2-digit divisor as multiple of ten with reminders
Divide with 2-digit divisor with remainders
Division word problems
(9 – 15 days)
3 – 5 days
3 – 5 days
BENCHMARK D – End of Year Benchmark
May 16 – May 27
(all skills from Quarters 1-4 assessed)
testing window
*Common Core - This skill will infuse the Maryland State Standards and the
Common Core.
Nov 8-Jan 21
SY 2010-2011
QUARTER 2 PLANNING CALENDAR* (46 DAYS)
MONDAY
DECEMBER
NOVEMBER
8
9
WEDNESDAY
10
THURSDAY
FRIDAY
11
12
BENCHMARK B
(Nov 1-12)
19
15
16
17
18
22
23
24
25
29
30
1
2
3
Thanksgiving Holiday
26
Thanksgiving Holiday
6
7
8
9
10
13
14
15
16
17 Early Release Day
20
21
22
23
24
Winter Break
31
Winter Break
27
JANUARY
Quarter 2 Begins
TUESDAY
Winter Break
28
Winter Break
29
Winter Break
30
Winter Break
3
4
5
6
7
10
11
12
13
14
18
19
20
21
17
MLK Holiday
Quarter 2 Ends
Grade 4: Unit 5
Fraction Concepts
Unit Resources
Unit Vocabulary
Unit Assessment
Unit 5: Concept 1
Proper Fractions and Mixed Numbers
TIME FRAME: 2-3 days
PREREQUISITE SKILLS
Proper Fractions and Mixed Numbers




Knowledge and Skills



Fractions as part of a set
Fractions as part of a whole
Mixed numbers
VSC OBJECTIVE
Fractions of a region (halves, thirds, fourths)
Identify fractional sets (halves, thirds, fourths)
Represent fractional sets (halves, thirds, fourths)
Writing fractions
(calculators allowed)
4.6.A.2.b Read, write, or represent proper fractions of a set which has the same number of items as the denominator using
symbols, words, and models
ASSESSMENT LIMIT: Use denominators of 6, 8, and 10 with sets of 6, 8, and 10, respectively
4.6.A.2.a Read, write, and represent proper fractions of a single region using symbols, words, and models
ASSESSMENT LIMIT: Use denominators 6, 8, and 10
VOCABULARY
fraction
Numerator
Denominator
fraction bar
set
region
mixed number
ENDURING UNDERSTANDINGS



Fractions represent parts of a whole or group.
Fractions can be compared using a variety of models.
Fractions express a relationship between two numbers.




How are the numerator and denominator related?
How can the fractional parts of a set be modeled?
How can fractions be modeled using numerals, regions, sets, and number lines?
When is it appropriate to use fractions?


A fraction is an EQUAL part of a whole or EQUAL part of a group.
The numerator is the number of equal parts you have or want; the denominator is the
TOTAL number of equal parts in the whole.
A mixed number is a whole number and a fraction.
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS

ERROR INTERVENTION
IF students confuse the
THEN consider using the mnemonic that the denominator
numerator and
denominator
Baltimore City Schools – Office of Mathematics
[email protected]
means down. Have students label and count the total
number of equal pieces and write that in the denominator
first before they write the numerator.
Grade 4 Math Curriculum DRAFT
Page 14
Unit 5: Concept 1
Proper Fractions and Mixed Numbers
IF students misread what
the question is asking
for in the numerator
IF students do not recall
that fractions must
have equal pieces
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider requiring that students circle key words that
identify what the question is asking for (e.g. highlight the
difference between “How many pieces are shaded?” and
“How many pieces are not shaded?”).
THEN consider showing numerous examples of equal and nonequal pieces.
Grade 4 Math Curriculum DRAFT
Page 15
Unit 5: Concept 1
Proper Fractions and Mixed Numbers
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Visual
Spatial
Flagging Conversation
SF Grade 4 TE Lesson
9-1 (p. 500b)
Literature
Connection
Visual
Spelling Fractions
Visual
Social
What’s Your Favorite?
The students survey their classmates to find out
their favorite pizza and create a pie chart to
determine different fractional parts.
Visual
Spatial
Fractions in Paintings
SF Grade 4 TE Lesson
9-2 (p.502b)
How Many in the Group
SF Grade 4 TE Lesson
9-2 (p.502b)
Food and Fractions
The students identify fractional parts in a group
in pictures and in artwork.
Social
Cooperative
Visual
Kinesthetic
Visual
Kinesthetic
Kinesthetic
Mixed Number Bamboo
Painting
Different Names, Same
Number
SF Grade 4 TE Lesson
9-10 (p. 530a)
The students learn about fractions as a part of a
region by looking at boating signal flags.
*You can extend this activity by giving the
students a fraction to represent and having them
create their own signal flag with a meaning.
The students shade parts of a region and
determine the fraction of consonants or vowels in
their spelling words.
The students write the fractions for different
characteristics of the students in their tables or
groups.
The students use food to replicate fractions as a
part of a set.
The students use the integration of art to gain an
understanding of mixed numbers. The students
create a bamboo painting to represent a mixed
number.
The students investigate the concept of mixed
numbers using grid paper and by cutting wholes
into parts.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
 Picture of signal flags with
an explanation of their
meanings.
 Spelling Fractions worksheet
 List of spelling words from
Reading, Science or Social
Studies
 Crayons or colored pencils
 Crayons
 What’s Your Favorite?
worksheet #1
 What’s Your Favorite?
worksheet #2
 Books or magazines with
paintings or pictures
 M&M’s, Skittles or Trail Mix







Water Color Paints
White Paper
Bamboo Paint Brushes
Bamboo Plant
10 x 10 grid paper
Teaching Tool 5
Scissors
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 16
Unit 5: Concept 1
Assessments
Suggested Learning Plan
Proper Fractions and Mixed Numbers
RESOURCES
Sub-Skills
Fractions as part
of a whole
Teacher Created Materials
 MW Exploring Fractions
 MW Exploring Fractions
with tiles
 MW Fractional Regions
Fractions as part
of a set
 MW Fractional Sets
Mixed numbers


Adopted Textbooks



SF Grade 4 TE Lesson 9-1 (pp.
500A-501)
SF Grade 4 TE Lesson 9-2 (pp.
502A-503)
SF Grade 4 TE Lesson 9-10
(pp. 530-533)
Technology

WEB: NLVM - Fraction Naming
MW Exploring Mixed
Numbers
MW Mixed Numbers
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 17
Unit 5: Concept 2
Compare and Order Fractions and Mixed Numbers
TIME FRAME: 1 – 2 days
PREREQUISITE SKILLS
Compare and Order Fractions and Mixed Numbers





Compare proper fractions and mixed numbers
Order proper fractions and mixed numbers
Comparing numbers
Ordering numbers
Fractional number lines
VSC OBJECTIVE (calculators allowed)
Knowledge and Skills
4.6.A.2.g Compare and order fractions and mixed numbers with or without using the symbols (<, >, or =)
Assessment Limit: Use like denominators and no more than 3 numbers (0 to 20)
VOCABULARY
fraction
numerator
denominator
fraction bar
mixed number
whole number
compare
order
greater than
less than
equal to
ENDURING UNDERSTANDINGS



Fractions represent parts of a whole or group.
Fractions can be compared using a variety of models.
Fractions express a relationship between two numbers.





How is the ordering of fractions the same as ordering whole numbers and how is it different?
How are the numerator and denominator related?
How can the fractional parts of a set be modeled?
How can fractions be modeled using numerals, regions, sets, and number lines?
When is it appropriate to use fractions?


A fraction is an EQUAL part of a whole or EQUAL part of a group.
The numerator is the number of equal parts you have or want; the denominator is the TOTAL
number of equal parts in the whole.
A mixed number is a whole number and a fraction.
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS

ERROR INTERVENTION
IF students are having trouble
visualizing the size of
fractions
IF students overlook the value
of the whole number when
comparing/ordering fractions
and mixed numbers
IF students read the relational
symbol incorrectly
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider using fraction tiles and have students compare
and order fractions by laying out the tiles on their desks.
THEN consider requiring that students circle the whole
numbers first and then compare/order the fractions.
They should learn to compare the whole numbers first
and then the numerators when the denominators are the
same.
THEN consider having them draw teeth inside the > or <
symbol because the sign wants to “eat” the greater
fraction or mixed number.
Grade 4 Math Curriculum DRAFT
Page 18
Unit 5: Concept 2
Compare and Order Fractions and Mixed Numbers
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Kinesthetic
Visual
Spatial
Comparing Fraction Tiles
The students use fraction tiles to compare
fractions and are able to visualize which
fraction is greater or smaller.



Fraction tiles *
Blank paper
Pencil
Cooperative
Visual
Kinesthetic
Place Your Order
The students work with their groups to
represent and order fractions with like
denominators.

Index cards with fractions
written on them
Pencil or crayons
Visual
I Spy
The students spy on their classmates to
determine fractions as a part of a group.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]



I Spy! worksheet
Pencil
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 19
Unit 5: Concept 2
Compare and Order Fractions and Mixed Numbers
Assessments
Suggested Learning Plan
RESOURCES
Sub-Skills
Compare proper
fractions and
mixed numbers
Teacher Created Materials




Order proper
fractions and
mixed numbers


MW Exploring Compare &
Order Fractions
MW Compare Fractions
MW Exploring Compare
Mixed Numbers
MW Compare Mixed
Numbers
Adopted Textbooks

SF Grade 4 TE Lesson 9-9 (pp.
524A-527)
Technology

WEB: Greater Than, Less Than,
or the Same
MW Order Fractions
MW Order Mixed
Numbers
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 20
Unit 5: Concept 3
Knowledge and Skills
Proper Fractions and Mixed Numbers on a Number Line
TIME FRAME: 2-4 days
PREREQUISITE SKILLS
Proper Fractions and Mixed Numbers on a
Number Line





Create fractional number lines
Write numbers on number line
Identify locations on number line
Write and Identify mixed numbers on number line
VSC OBJECTIVE

Finding a fraction on a number line (up to
fourths)
Finding a location on a number line (up to
fourths)
(calculators allowed)
4.1.C.1.a Represent mixed numbers and proper fractions on a number line
Assessment Line: Use proper fractions with a denominators of 6, 8, or 10
VOCABULARY
fraction
numerator
denominator
fraction bar
mixed number
whole number
ENDURING UNDERSTANDINGS


Fractions represent parts of a whole or group.
Fractions can be compared using a variety of models.



How are the numerator and denominator related?
How can the fractional parts of a set be modeled?
How can fractions be modeled using numerals, regions, set, and number lines?


A fraction is an equal part of a whole or part of a group (set).
The numerator is the number of equal parts you have or want; the denominator is the
TOTAL number of equal parts in the whole.
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS
ERROR INTERVENTION
IF students count the number of lines
THEN consider having students highlight each
IF students forget to label the whole
THEN consider having students trace each whole
instead of the number of spaces
number past 1 on a number line
(mixed numbers on a number line)
Baltimore City Schools – Office of Mathematics
[email protected]
space with a different color to find the
denominator of the fraction.
Grade 4 Math Curriculum DRAFT
number on a number line in a different color
and write in the whole number before they
actually write the mixed number/fraction.
Page 21
Unit 5: Concept 3
Proper Fractions and Mixed Numbers on a Number Line
IF students find the denominator by
counting all of the equal spaces on
a number line and not just the
number of spaces between whole
numbers
IF students have trouble identifying a
fraction/mixed number located
between two other fractions
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider modeling this common mistake and
emphasizing that the denominator is only the
number of equal spaces between two whole
numbers.
THEN consider requiring that students fill in all
Grade 4 Math Curriculum DRAFT
missing fractions on the number line before
choosing the correct answer.
Page 22
Unit 5: Concept 3
Proper Fractions and Mixed Numbers on a Number Line
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Visual
Spatial
Concrete
Make a Number Line
The students use fraction tiles to create a
number line.

Fraction tiles *
Kinesthetic
In the Fold
SF Grade 4 TE Lesson 9-3
(p. 504b)
The students create fractional number
lines by folding strips of paper into equal
sections and by labeling the fractions.

Strips of paper that are at
least 11 inches long
Pencils
Kinesthetic
Visual
Pin the Fraction on the
Number Line
The students place Post-it notes on
number lines to begin to the connection
between the denominator and the equal
number of spaces on a number line.

Kinesthetic
Visual
Number Line on a Floor
The students use the floor and create a
class-size number line to plot specific
points



DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]


Post-it notes with various
fractions written on them
Blank number lines to
accommodate fractions with
different denominators
Fraction cards
Students
Sentence strip
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 23
Unit 5: Concept 3
Suggested Learning
Plan
Proper Fractions and Mixed Numbers on a Number Line
RESOURCES
Sub-Skills
Create fractional
number lines
Teacher Created Materials

MW Create Fractional
Number Line
Adopted Textbooks


Write numbers
on number line

MW Write Fractions on a
Number Line
Find locations on
number line

MW Identify Locations on
a Number Line
Mixed numbers
on number line

MW Mixed Numbers on a
Number Line
SF Grade 4 TE Lesson 9-3 (pp.
504A-507)
SF Grade 4 TE Lesson 9-11
(pp. 534-535)
Assessments
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Technology




WEB: Identify Fractions
WEB: Fractions on a Number Line
– Drag and Drop
WEB: Find Grammy
WEB: Identify Mixed Fractions
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 24
Unit 5: Concept 4
Knowledge and Skills
Add and Subtract Proper Fractions and Mixed Numbers
TIME FRAME: 2-3 days
PREREQUISITE SKILLS
Add and Subtract Proper Fractions and
Mixed Numbers





Basic addition and subtraction facts
Add proper fractions
Subtract proper fractions
Add mixed numbers
Subtract mixed numbers
VSC OBJECTIVE
(calculators not allowed)
4.6.C.1.e Add and subtract proper fractions and mixed
numbers
Assessment Limits: Use 2 proper fractions with a single digit
like denominators, 2 mixed numbers with a single digit,
like denominators a whole number and a proper fraction
with a single digit denominator and numbers (0 to 20)
VOCABULARY
fraction
numerator
denominator
fraction bar
mixed number
whole number
proper fraction
ENDURING UNDERSTANDINGS



Operation strategies with fractions are similar to those used with whole numbers.
Fractions represent parts of a whole or group.
Fractions can be compared using a variety of models.



What strategies can be developed to show computation with fractions?
How are models used to show how fractional parts are combined or separated?
How can fractions be modeled using numerals, regions, sets, and number lines?


A fraction is an equal part of a whole or part of a group (set).
The numerator is the number of equal parts you have or want; the denominator is the TOTAL
number of equal parts in the whole.
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS
ERROR INTERVENTION
IF students add both the
numerator and denominator
IF students add both the
numerator and denominator
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider emphasizing repeatedly that the
denominator stays the same when you are adding and
subtracting like denominators.
THEN consider having the students show the work with
fraction tiles.
Grade 4 Math Curriculum DRAFT
Page 25
Unit 5: Concept 4
Add and Subtract Proper Fractions and Mixed Numbers
IF students have trouble adding
and subtracting a whole
number with a fraction (e.g. 3
– ½)
IF students have trouble knowing
what parts of a mixed number
and fraction to add together or
subtract
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider requiring that students draw a picture before
adding or subtracting. If subtracting, they should
cross out the part that needs to be taken away.
THEN consider having students line up the problem
vertically with one column for the fraction and one
column for the whole number. This should help them
stay organized.
Grade 4 Math Curriculum DRAFT
Page 26
Unit 5: Concept 4
Add and Subtract Proper Fractions and Mixed Numbers
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Visual
Concrete
Adding Fraction Tiles
The students use fraction tiles to visualize
the concept of adding fractions with like
denominators.
 Fraction tiles *
Linguistic
Quilt Story
SF Grade 4 TE Lesson 10-2
(p. 564b)
The students create stories and illustrate
them to demonstrate adding fractions.
 Centimeter grid paper
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 27
Unit 5: Concept 4
Add and Subtract Proper Fractions and Mixed Numbers
Suggested Learning
Plan
RESOURCES
Sub-Skills
Teacher Created Materials
Add proper
fractions

Subtract proper
fractions

MW Subtraction Proper
Fractions
Add mixed
numbers

MW Exploring Mixed
Number Computation
MW Add Mixed Numbers
Subtract mixed
numbers



MW Exploring Fraction
Computation
MW Add Proper Fractions
Adopted Textbooks


SF Grade 4 TE Lesson 10-2
(pp. 564-567)
SF Grade 4 TE Lesson 10-4
(pp. 574A-577)
MW Subtract Mixed
Numbers
Writing in Math
Assessments
Technology
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 28
Grade 4: Unit 6
Statistics
Unit Resources
Unit Vocabulary
Baltimore City Schools – Office of Mathematics
[email protected]
Unit Assessment
Grade 4 Math Curriculum DRAFT
Page 29
Unit 6: Concept 1
Probability
TIME FRAME: 3-5 days
PREREQUISITE SKILLS
Probability






Express object probability as a fraction
Express spinner probability as a fraction
Express conditional probability as a fraction
Knowledge and Skills
VSC OBJECTIVE
Object probability (describing using words)
Spinner probability (describing using words)
Fractions
(calculators allowed)
4.5.B.1.a Express the probability as a fraction
Assessment Limit: Use a sample space of no more than 6 outcomes
VOCABULARY
probability
favorable outcomes
total outcomes
possible outcomes
numerator
denominator
fraction bar
event
likely
unlikely
equally likely
impossible
certain
fair
unfair
ENDURING UNDERSTANDINGS


The likelihood of an event depends on the possible outcomes.
Probability can be represented numerically and graphically.



How can the possible outcomes for an event be determined?
How is probability represented numerically?
How is the likelihood of an event determined and communicated?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS


Probability is the chance or likelihood of something happening.
Probability can be written in terms of certain [WILL ALWAYS HAPPEN], impossible [WILL
NEVER HAPPEN], less likely, more likely, or equally likely.
ERROR INTERVENTION
IF students forget to write probability
as a fraction (e.g., they simply
write the number of favorable
outcomes)
IF students forget that adding or
taking away objects changes the
denominator and may change the
numerator
IF students write the fraction as the
number of favorable outcomes over
the number of remaining objects
instead of the number of total
outcomes
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider modeling this error for them and
create a process chart for finding the
probability with probability itself written as a
fraction.
Example: proba
Bility
THEN consider requiring that students draw
pictures to show items that are added or
taken away.
THEN consider requiring that students label and
Grade 4 Math Curriculum DRAFT
count the total number of objects and write
that in the denominator first. Students
should then circle the objects that make up
the favorable outcomes.
Page 30
Unit 6: Concept 1
Probability
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Kinesthetic
Visual
Concrete
Food and Probability
The students use food to explore the
probability of a certain outcome. The
students also discover how conditions can
change the probability of an event.
 Skittles, M&Ms, Trail Mix or
Fruit Loops
 Pencil and paper
Visual
Concrete
Raffle Jar
The students win raffle tickets in class and
participate in a weekly drawing in order to
learn the concept of events and outcomes.
 Raffle jar *
 Raffle tickets or strips of paper
Linguistic
Literature
Connection
Hundred Penny Box
The students find the probability of picking
SF Grade 4 TE Lesson 12-7 a penny with certain years printed on
(p. 706b)
them after reading the story Hundred
Penny Box.
 Book Hundred Penny Box by
Sharon Bell Mathis
Kinesthetic
Coin Toss
The students flip coins to determine the
SF Grade 4 TE Lesson 12-7 possible outcomes and the probability of
(p. 706b)
flipping heads or tails.
 Play money or
 Teaching Tool 7
 Coins
Social
Cooperative
Probability Design
The students develop a set of index cards
SF Grade 4 TE Lesson 12-7 and determine the probability of picking
(p. 706b)
certain favorable outcomes.
 Index Cards
Visual
Concrete
Fractions = Probability
The students create a spinner and express
SF Grade 4 TE Lesson 12-7 the probability of landing on different
(p. 706b)
colors as a fraction.
 Spinner *
 Teaching Tool 20 with six
sections
 Crayons
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 31
Unit 6: Concept 1
Assessments S u g g e s t e d L e a r n i n g P l a n
Probability
RESOURCES
Sub-Skills
Object
probability
Teacher Created Materials


MW Exploring Probability
MW Object Probability
Spinner
probability

MW Spinner Probability
Conditional
probability

MW Conditional
Probability
Adopted Textbooks



SF Grade 4 TE Lesson 12-5
(pp. 700A-703)
SF Grade 4 TE Lesson 12-6
(pp. 704A-705)
SF Grade 4 TE Lesson 12-7
(pp. 706-709)
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Technology





US: “Setting Up a Probability
Experiment”
US: “Probability”
US: “Understanding: Probability
and Odds”
WEB: NLVM - Spinners
US: “Discovering Math:
Probability”
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 32
Unit 6: Concept 2
Median, Mode, and Range
TIME FRAME: 2 -3 days
PREREQUISITE SKILLS
Median, Mode, and Range





Determine the range of a set of data
Determine mode of a set of data
Determine median of a set of data
Interpreting tables
Ordering numbers
Knowledge and Skills
VSC OBJECTIVE (calculators allowed)
4.4.B.2.a Determine median, mode, and range
ASSESSMENT LIMIT: Use no more than 8 pieces of data and whole numbers (0 to 100)
VOCABULARY
statistics
data
median
mode
range
ENDURING UNDERSTANDINGS


The type of data determines how data sets can be organized, displayed, and analyzed.
Statistical measures provide a numeric picture of the shape of the data.



In what ways can sets of data be represented by statistical measures?
How can the mean, median, mode, and range be used to describe the shape of the data?
How can range, median, and mode be computed and compared?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS



Median is the middle number in a set of ordered data.
Mode is the number that occurs the most often in a set of data.
Range is the difference between the greatest number and the least number in a set of data.
ERROR INTERVENTION
IF students attempt to find the
median, mode, and range
without ordering the numbers
from least to greatest
IF students do not remember the
definitions of median, mode,
and range
IF students have trouble finding
the median when there is an
event amount of data
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider requiring that they order the numbers from
least to greatest before they solve the problem.
THEN consider thinking of creative ways to teach the
meanings of the words:
Median: the median is the middle barrier on a street; draw
three shirts (small, medium, and large) and label the
middle one with an M for median and middle.
Mode: most often in data; relate the mode to what’s in
style. Median, mode, and range rap
THEN consider having them “spread out” the missing
numbers between the two middle numbers and then
find the median.
Grade 4 Math Curriculum DRAFT
Page 33
Unit 6: Concept 2
Median, Mode, and Range
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Social
Kinesthetic
Pet Summary
SF Grade 4 TE Lesson 4-12
(p. 226A)
The students are introduced to mode,
median, and range by taking a survey of
how many pets that they have.
 Index cards
Kinesthetic
Visual
Comparing Cubits
SF Grade 4 TE Lesson 4-12
(p. 226B)
The students work in groups to visualize
what mode, median, and range look like.
 Adding machine tape or other
strips of paper
 Scissors
Kinesthetic
Visual
Concrete
Hands-on Activity
The students use data that is relevant to
them and complete a hands-on activity in
order to find the mode, median, and
range of the data.
Auditory
Mode, Median, Range Rap
The students learn the meaning of mode,
median, and range by learning a rap.








DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
Scissors
Construction paper
Crayons
1-inch graph paper
Data on a transparency
Song on overhead
Teacher copy of the rap
Student copy of the rap
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 34
Unit 6: Concept 2
Assessments
Suggested Learning Plan
Median, Mode, and Range
RESOURCES
Sub-Skills
Teacher Created Materials
Determine the
range of a group
of data


MW Exploring Median,
Mode, and Range
MW Range
Determine mode
of a group of
data

MW Mode
Adopted Textbooks

SF Grade 4 TE Lesson 4-12
(pp. 226A-229)
Technology






Determine
median of a
group of data

MW Median
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
US: “Estimating a Range"
WEB: "Rags to Riches"
US: "Mean, Median, Mode,
Range, and Overall Distribution"
WEB: Maths: Handling Data Mode, median, and mean
US: Math Mastery: Graphs and
Statistics
WEB: BrainPOP: Spelling Test
Scores
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 35
Unit 6: Concept 3
Line Plots
TIME FRAME: 3-5 days
PREREQUISITE SKILLS
Line Plots





Create line plots
Interpret line plots
Interpreting tables
Ordering numbers
Range, median, and mode
Knowledge and Skills
VSC OBJECTIVE (calculators allowed)
4.4.B.1.a Interpret line plots
ASSESSMENT LIMIT: Use no more than 20 pieces of data with a range no more than 10 and whole numbers (0 to 100)
4.4.A.1.b Organize and display data in line plots and frequency tables using a variety of categories and sets of data
ASSESSMENT LIMIT: Use line plots with no more than 20 pieces of unorganized data and a range of no more than 10 and
whole numbers (0 – 100)
VOCABULARY
statistics
graph
data
title
key
horizontal axis
median
mode
range
outlier
gap
cluster
line plot
ENDURING UNDERSTANDINGS


Representation of data depends on the characteristics of that data.
The type of data determines how data sets can be organized, displayed, and analyzed.
ESSENTIAL QUESTIONS



What data display is appropriate for a given set of data?
How does the type of data influence the choice of graph?
What kinds of questions can be answered using different data displays?

Line plots show the frequency and spread of data.
CONCEPT KNOWLEDGE AND PROCESS
ERROR INTERVENTION
IF students randomly guess an
THEN consider requiring that students draw the
IF students confuse the meaning of
THEN consider having students design a large
answer in a multiple choice
problem or miss a data point
IF students confuse line plots and line
graphs
the Xs
Baltimore City Schools – Office of Mathematics
[email protected]
data in a line plot before matching it with the
best answer.
THEN consider making the connection between a
line plot and planting seeds in which they plot
one or more seeds on a direct line.
Grade 4 Math Curriculum DRAFT
class line plot and then place individual cutout X’s on the plot. They will then see that
one X represents one person.
Page 36
Unit 6: Concept 3
Line Plots
IF students have trouble finding the
median, mode, and range by
simply looking at a line plot
IF students have trouble
understanding the difference
between “3 or more” and “more
than 3”
IF students do not understand the
meaning of the question
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider requiring that they translate the Xs
into a list of numerical data from least to
greatest.
THEN consider having them circle the data on the
graph. This helps visual learners understand
the meaning of the question.
THEN consider having them underline key words
Grade 4 Math Curriculum DRAFT
and ask themselves: “Is this question asking
me to look at the Xs or to look at the
horizontal axis?”
Page 37
Unit 6: Concept 3
Line Plots
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Social
Cooperative
Line Up the Kids
SF Grade 4 TE Lesson 4-7
(p. 206B)
The students interpret a line plot that is
based on class survey results.
 Chalkboard or white board
 Chalk or dry erase markers
Kinesthetic
How Many Breaths per
Minute?
SF Grade 4 TE Lesson 4-7
(p. 206B)
The class collects data and displays it on a
line plot. The students interpret the data
on the line plot by looking at the number
of “Xs” over each number.
 Clock with a second hand or
stop watch
Verbal
Journal Idea
SF Grade 4 TE Lesson 4-7
(p. 207)
 Pencil
 Paper or journal notebook
Kinesthetic
Visual
Social
Human Line Plot *
The students demonstrate that they are
able to create a line plot based on data by
completing a journal assignment where
they have to describe the steps to create
a line plot.
The students create a line plot using
information based on themselves and
place their data on the horizontal axis.
Kinesthetic
A Handful of Counters
SF Grade 4 TE Lesson 4-7
(p. 206A)
The students create a line plot based on
the number of counters that they grab in
their hands.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
 Chart paper or large poster
board
 1 paper X per student
 Tape or glue
 Markers
 Crayons
 Counters or
 Teaching Tool 14
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 38
Unit 6: Concept 3
Assessments S u g g e s t e d L e a r n i n g P l a n
Line Plots
RESOURCES
Sub-Skills
Teacher Created Materials
Create line plots
 MW Create Line Plots
Interpret line
plots
 MW Exploring Interpret
Line Plots
 MW Interpret Line Plots
Adopted Textbooks

SF Grade 4 TE Lesson 4-7 (pp.
206A-207)
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Technology

WEB: Plop It!
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 39
Unit 6: Concept 4
Coordinate Grids
TIME FRAME: 1-2 days
PREREQUISITE SKILLS
Coordinate Plane


Knowledge and Skills


Identify locations on a coordinate grid given object
Identify objects on a coordinate grid given location
VSC OBJECTIVE
Number lines
Identifying the X and Y axis
(calculators allowed)
4.1.C.1.b Identify positions in a coordinate plane
ASSESSMENT LIMIT: Use the first quadrant and ordered pairs of whole numbers (0 to 20)
VOCABULARY
coordinate grid
coordinate plane
ordered pair
horizontal
vertical
plot
origin
ENDURING UNDERSTANDINGS


Ordered pairs show an exact location on a coordinate plane.
Functional relationships can be represented graphically and symbolically.


How is the location of a point on a grid described?
How are graphs, tables, and symbols used to represent relationships?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS

A coordinate grid describes the location of an object by its distance from a horizontal and
vertical axis.
ERROR INTERVENTION
IF students mistakenly label
points by writing the vertical
point first and then the
horizontal point
IF students forget to start at
zero
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider teaching students a creative mnemonic
to remember “over, then up.”
Examples: 1.) Superman runs before he flies.
2.) In basketball, you dribble the
ball before you shoot.
THEN consider requiring that they put a star at zero
Grade 4 Math Curriculum DRAFT
before plotting any points.
Page 40
Unit 6: Concept 4
Coordinate Grids
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Kinesthetic
Classroom Coordinate Grid
Games
Treasure Map Bingo
Visual
Spatial
What’s the Location?
SF Grade 4 TE Lesson 4-9
(p. 212A)
Create a coordinate grid on the classroom
floor and allow the students to slide
horizontally and vertically to the ordered
pair that they drew from the deck of
cards.
The students choose five locations on a
coordinate grid treasure map and win
BINGO if all of their ordered pairs are
called on their Treasure Map.
 Blue painter’s tape *
 Deck of cards
The students compare a coordinate grid to
a map and describe the ordered pairs as
streets and avenues.
 Chalkboard or whiteboard
 Chalk or dry erase markers
 Ruler
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
Materials
 1-inch graph paper
 Deck of cards
 Markers
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 41
Unit 6: Concept 4
Assessments
Suggested Learning Plan
Coordinate Grids
RESOURCES
Sub-Skills
Teacher Created Materials
Identify locations
on a coordinate
grid given object

Identify objects
on a coordinate
grid given
location


MW Exploring Coordinate
Grid
MW Identify Locations
Coordinate Grid
Adopted Textbooks

SF Grade 4 TE Lesson 4-9 (pp.
212A-215)
Technology


US: "Coordinate Mapping"
WEB: Plot Points on a Coordinate
Grid
MW Identify Objects
Coordinate Grid
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 42
Unit 6: Concept 5
Interpret Line Graphs
TIME FRAME: 2 - 3 days
PREREQUISITE SKILLS
Interpret Line Graphs




Interpret line graphs
Addition
Subtraction
Range, median, mode
Knowledge and Skills
VSC OBJECTIVE (calculators allowed)
4.4.B.1.b Interpret line graphs
ASSESSMENT LIMIT: Use the x-axis representing no more than 6 time intervals, the y-axis consisting of no more than 10
intervals with scales as factors of 100 using whole numbers (0 to 100)
VOCABULARY
statistics
graph
data
title
scale
Interval
horizontal axis
vertical axis
Increase
decrease
no change
line graph
ENDURING UNDERSTANDINGS


Representation of data depends on the characteristics of that data.
The type of data determines how data sets can be organized, displayed, and analyzed.



What data display is appropriate for a given set of data?
How does the type of data influence the choice of graph?
What kinds of questions can be answered using different data displays?


Line graphs show how data changes over time.
Horizontal axis will always be time.
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS
ERROR INTERVENTION
IF students do not see where the
THEN consider having them subtract between each
IF students do not recognize where a
THEN consider using arm signals for up, down, and
IF students don’t understand the
THEN make a list of typical questions and
greatest increase or decrease is
line graph increases, decreases, or
stays the same
question
Baltimore City Schools – Office of Mathematics
[email protected]
data point to show the change.
no change and having students draw arrows
on each segment of the line graph.
Grade 4 Math Curriculum DRAFT
operations that could be used to answer a
question.
Page 43
Unit 6: Concept 5
Interpret Line Graphs
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Linguistic
What Story Does the Graph
Tell?
SF Grade 4 TE Lesson 4-10
(p. 216B)
The students look at a line graph and
create a story to describe how the data in
the graph changed over time.
 Paper or journal notebook
 Pencil
Concrete
Visual
How Am I Doing?
Students look at their own class work or
tests to create a line graph and determine
how their grades have changed over the
school year.




Kinesthetic
Visual
Arm Signals
The students use movements of their
arms to indicate whether the data
increases, decreases or remains the same
as time progresses.
 Example of a line graph on the
overhead
 Overhead projector
Linguistic
What Story Does the Graph
Tell?
SF Grade 4 TE Lesson 4-10
(p. 216B)
The students look at a line graph and
create a story to describe how the data in
the graph changed over time.
 Paper or journal notebook
 Pencil
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
Student work samples
Graph paper
Rulers
Pencils
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 44
Unit 6: Concept 5
Assessments
Suggested Learning Plan
Interpret Line Graphs
RESOURCES
Sub-Skills
Interpret line
graphs
Teacher Created Materials
 MW Interpret Line Graphs
Adopted Textbooks

SF Grade 4 TE Lesson 4-10
(pp. 216A-221)
Writing in Math
TRACKING SHEET
Technology


WEB: Create A Graph
WEB: Print Your Own Graph
Paper
Other Resources
CONCEPT
ASSESSMENT
Baltimore City Schools – Office of Mathematics
[email protected]
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 45
Grade 4: Unit 7
Algebra 2
Unit Resources
Unit Vocabulary
Baltimore City Schools – Office of Mathematics
[email protected]
Unit Assessment
Grade 4 Math Curriculum DRAFT
Page 46
Unit 7: Concept 1
Write Expressions
TIME FRAME: 2 - 3 days
PREREQUISITE SKILLS
Write Expression




Write expressions using addition and subtraction
Write expressions using multiplication and division
Knowledge and Skills
VSC OBJECTIVE
Writing expressions using addition
Writing expressions using subtraction
(calculators allowed)
4.1.B.1.a Represent numeric quantities using operational symbols (+, -, ×, ÷ with no remainders)
ASSESSMENT LIMIT: Use whole numbers (0 to 100)
VOCABULARY
operation
operational symbols
ENDURING UNDERSTANDINGS


Mathematical expressions and equations represent relationships among quantities.
Symbolic notation is used to represent mathematical relationships.



How does a mathematical expression differ from a number sentence?
How is a number sentence like a balance scale?
How are symbols used to represent mathematical relationships including operations,
equality, and inequality?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS
 An expression names an amount.
ERROR INTERVENTION
IF students do not understand
which operation to use to
write or solve the problem
IF students do not understand
which operation to use to
write or solve the problem
IF students do not understand
which operation to use to
write or solve the problem
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider making a list of addition, subtraction,
multiplication, and division clue words. Students
should then circle important numbers and
underline clue words before determining the
operation needed.
THEN consider having them draw a picture to represent
the problem. They can then usually identify the
correct operation.
THEN consider having them visualize the problem,
determine if the answer is increasing (+ or x) or
decreasing (- or ÷) in equal groups or non-equal
groups, and then identify the correct operation.
Grade 4 Math Curriculum DRAFT
Page 47
Unit 7: Concept 1
Write Expressions
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Verbal
Develop Clue Words *
The students create an ongoing list of clue
words that will aid them in choosing the
appropriate operational symbol to
complete the expression.




Chart paper
Markers
Teacher clue word sheet
Student clue words sheets
Auditory
Kinesthetic
Visual
Name That Expression




White board
White board markers
Overhead
Pre-prepared word problems
Linguistic
Auditory
Read to Understand
SF Grade 4 TE Lesson 2-10
(p. 94B)
The students use clue words to determine
if the solution to an expression will be
bigger or smaller and to determine the
appropriate operational symbol to use in
the expression.
Students identify clue words and record
them on a chart as they read different
phrases.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
 Chart paper
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 48
Unit 7: Concept 1
Write Expressions
Assessments
Suggested Learning Plan
RESOURCES
Sub-Skills
Teacher Created Materials
Write
expressions
using addition
and subtraction

Write
expressions
using
multiplication
and division


MW Exploring Write
Expression
MW Write Expressions
Addition and Subtraction
Adopted Textbooks


SF Grade 4 TE Lesson 2-10
(pp. 94A-95)
SF Grade 4 TE lesson 3-12
(pp. 160A-163)
Technology


WEB: Math Playground: Various
Word Problems
WEB: Four Square for Story
Problems
MW Write Expressions
Multiplication and
Division
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 49
Unit 7: Concept 2
Equivalent Expressions
TIME FRAME: 1 - 2 days
PREREQUISITE SKILLS
Equivalent Expressions


Knowledge and Skills

Write equivalent expressions
VSC OBJECTIVE
Writing expressions for addition
Writing expressions for subtraction
(calculators allowed)
4.1.B.1.b Determine equivalent expressions
ASSESSMENT LIMIT: Use whole numbers (0 to 100)
VOCABULARY
equivalent
expression
equal
fact family
ENDURING UNDERSTANDINGS


Mathematical expressions and equations represent relationships among quantities.
Symbolic notation is used to represent mathematical relationships.
ESSENTIAL QUESTIONS



How does a mathematical expression differ from a number sentence?
How is a number sentence like a balance scale?
How are symbols used to represent mathematical relationships including operations,
equality, and inequality?
CONCEPT KNOWLEDGE AND PROCESS

An expression names an amount.
ERROR INTERVENTION
IF students assume that because
two problems have the same
numbers, they are equivalent
(Example: students think that 5
+ 3 = 5 x 3)
IF students do not understand
what equivalent means
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider requiring students to solve each
expression before determining the correct
answer. They will then see that 5 + 3 ≠ 5 x 3.
THEN consider underlining the “equ” in equivalent,
Grade 4 Math Curriculum DRAFT
equal, and equation.
Page 50
Unit 7: Concept 2
Equivalent Expressions
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Visual
Kinesthetic
Cooperative
Balancing Act
The students use a number balance to
determine whether their expressions are
equivalent to their partner’s expression.
 Number balance *
 Calculator *
Kinesthetic
Visual
Equal Expressions
The students use white boards to compose
an expression equivalent to an expression
that is given.
 Whiteboards
 Dry erase markers
Concrete
How Many Ways to 12
The students learn about writing
equivalent expressions by finding how
many different ways they can make 12
using addition, subtraction, multiplication
and division.
 Pencil
 Paper
 Calculator *
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 51
Unit 7: Concept 2
Equivalent Expressions
Assessments
Suggested Learning Plan
RESOURCES
Sub-Skills
Write equivalent
expressions
Teacher Created Materials


MW Exploring Write
Equivalent Expressions
MW Write Equivalent
Expressions
Adopted Textbooks


SF Grade 4 TE Lesson 2-11
(pp. 96A-97)
SF Grade 4 TE Lesson 2-12
(pp. 98A-99)
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Technology



WEB: Can You Balance?
WEB: Match Equivalent
Expressions
WEB: Cyberchase – Poodle Weigh
In
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 52
Unit 7: Concept 3
Write Relationships
TIME FRAME: 2 – 4 days
PREREQUISITE SKILLS
Write Relationships




Evaluate relationships with missing relational symbols
Represent relationships in word problems
Knowledge and Skills
VSC OBJECTIVE

Comparing expressions
Evaluate relationships with addition and
subtraction
Represent relationships in addition and
subtraction word problems
(calculators allowed)
4.1.B.2.a Represent relationships using relational symbols (>, <, =) and operational symbols (+, -, ×, ÷) on either side
Assessment Limit: Use operational symbols (+, -, ×) and whole numbers (0 to 200)
VOCABULARY
expression
relational symbols
operational symbols
equal
balance
not equal
Inequality
equivalent
ENDURING UNDERSTANDINGS


Mathematical expressions and equations represent relationships among quantities.
Symbolic notation is used to represent mathematical relationships.



How does a mathematical expression differ from a number sentence?
How is a number sentence like a balance scale?
How are symbols used to represent mathematical relationships including operations,
equality, and inequality?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS


A relationship where two expressions have the same value has an = sign.
A relationship where two expressions do not have the same value has a > or < sign.
ERROR INTERVENTION
IF students become overwhelmed by
the wordiness of the problem
IF students rush to input operational
symbols
IF students choose a relationship as
correct just by looking at the
numbers
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider having them highlight the first
expression in one color and the second
expression in another color; write the first
expression, then write the second
expression; finally, compare the expressions.
THEN consider requiring that they plug in all
possible operational symbols before
determining the correct answer.
THEN consider requiring that they solve each
Grade 4 Math Curriculum DRAFT
expression before determining the correct
answer.
Page 53
Unit 7: Concept 3
Write Relationships
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Verbal
Develop Clue Words
Auditory
Kinesthetic
Visual
Name That Expression
Linguistic
Auditory
Kinesthetic
Visual
The students create an ongoing list of clue
words that will aid them in choosing the
appropriate operational symbol to
complete the expression.
The students use clue words to determine
if the solution to an expression will be
bigger or smaller and to determine the
appropriate operational symbol to use in
the expression.
Read to Understand
Students identify clue words and record
SF Grade 4 TE Lesson 2-10 them on a chart as they read different
(p. 94B)
phrases.
Pinch Cards
The students use an index card with
relational symbols on it to indicate the
appropriate relationship between two
expressions.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
Materials
 Chart paper
 Markers
 Student clue words sheets




White board
White board markers
Overhead
Pre-prepared word problems

Chart paper

Index Cards with
them
Markers

> < = on
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 54
Unit 7: Concept 3
Assessments
Suggested Learning
Plan
Write Relationships
RESOURCES
Sub-Skills
Teacher Created Materials
Evaluate
relationships with
missing relational
symbols


MW Exploring Relationships
MW Evaluate Relationships
Missing Relationships
Represent
relationships in word
problems

MW Represent Relationships
in word problems
Adopted Textbooks

SF Grade 4 TE Lesson
2-11 (pp. 96A-97)
Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
Technology

WEB: BrainPOP: Inequalities
Movie
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 55
Grade 4: Unit 8
Geometry 1
Unit Resources
Unit Vocabulary
Baltimore City Schools – Office of Mathematics
[email protected]
Unit Assessment
Grade 4 Math Curriculum DRAFT
Page 56
Unit 8: Concept 1
Angles
TIME FRAME: 2-4 days
PREREQUISITE SKILLS
Angles




Identify right angles
Identify acute and obtuse angles
Identify angles in shapes and objects
VSC OBJECTIVE
Knowledge and Skills
Rays, lines, and line segments
(calculators allowed)
4.2.A.1.b Identify, compare, classify, and describe angles in relationship to another angle
ASSESSMENT LIMIT: Use acute, right, or obtuse angles
VOCABULARY
geometry
point
Line
ray
line segment
vertex
angle
endpoint
right angle
acute angle
obtuse angle
ENDURING UNDERSTANDINGS


Objects can be described and compared using geometric attributes.
A three dimensional figure can be analyzed in terms of its two-dimensional parts.


How are angles classified?
What makes one angle different from another?
ESSENTIAL QUESTIONS
CONCEPT KNOWLEDGE AND PROCESS




An angle is created from two rays that share an endpoint.
A right angle forms the corner of a square.
An acute angle is smaller than a right angle.
An obtuse angle is bigger than a right angle.
ERROR INTERVENTION
IF students confuse acute angles,
right angles, and obtuse angles
IF students have trouble identifying
angles within shapes
IF students have trouble identifying
angles within shapes
IF students have trouble identifying
angles that are turned
Baltimore City Schools – Office of Mathematics
[email protected]
THEN consider using a mnemonic to distinguish between
the types of angles:
An acute angle is “a cute” little baby angle.
An obtuse angle looks like an open book.
A right angle is “just right.” It makes a perfect L.
THEN consider having students highlight the rays to
better see the angle.
THEN consider having them put a square in the angle.
THEN consider encouraging students to turn their paper
so that the angle looks “right side up.”
Grade 4 Math Curriculum DRAFT
Page 57
Unit 8: Concept 1
Angles
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Materials
Visual
Spatial
Geometry on the
Geoboard
SF Grade 4 TE Lesson 8-3
(p. 440a)
The students use Geoboards to represent
different types of angles by intersecting
lines.
 Geoboard or
 Geoboard paper
 Rubber bands
Visual
Kinesthetic
Cooperative
Angles on the Floor
The students work in pairs to identify
types of angles using a index card to see
if the angle is bigger, smaller, or equal to
a right angle.
 Blue painter’s tape
 Index cards *
Visual
Kinesthetic
I Spy Right Angles
The students identify right angles that
they see within the classroom and mark
them by creating a square inside the
angle with blue painter’s tape.
 Blue painters tape
Visual
Kinesthetic
Game
Geometry Simon Says
The students play a game of Simon Says
where they have to create angles and
lines using arm signals.
DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 58
Unit 8: Concept 1
Assessments
Suggested Learning Plan
Angles
RESOURCES
Sub-Skills
Identify right
angles
Teacher Created Materials


MW Exploring Angles
MW Identify Right Angles
Identify acute
and obtuse
angles

MW Identify Acute
Obtuse Angles
Identify angles in
shapes and
objects

MW Identify Angles in
Objects
Adopted Textbooks

SF Grade 4 TE Lesson 8-3 (pp.
440A-443)
Technology



Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
WEB: Alphabet Geometry: Right
Angles
WEB: Alphabet Geometry: Acute
Angles
WEB: Alphabet Geometry: Obtuse
Angles
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 59
Unit 8: Concept 2
Transformations
TIME FRAME: 2-4 days
PREREQUISITE SKILLS
Transformations








Identify translations
Identify reflections
Identify rotations
Knowledge and Skills
VSC OBJECTIVE
Flips
Turns
Slides
Congruence
Symmetry
(calculators allowed)
4.2.E. 1.a Identify and describe the results of translations, reflections, and rotations
ASSESSMENT LIMIT: Use a horizontal line translation, reflection over a vertical line, or rotation of 90° clockwise around a
given point of a geometric figure or picture
4.2.D.1.a Identify and describe geometric figures as congruent
ASSESSMENT LIMIT: Identify the result in a transformation as being congruent to the original figure
VOCABULARY
geometry
congruent
transformation
translation
reflection
rotation
ENDURING UNDERSTANDINGS


A transformation is a specific movement of an object.
Changing the position of an object does not affect its attributes.
ESSENTIAL QUESTIONS


In what ways can the position of geometric figures be changed?
What are translations, rotations, and reflections?





A transformation moves a shape to a new spot without changing its size or shape
You can transform (move) a shape three ways: by flipping it, sliding it, or turning it.
A flip, or reflection, is a mirror image of a figure on the opposite side of a line.
A slide, or translation, is a figure moved a certain distance in a given direction.
A turn, or rotation, moves a figure around a point.
CONCEPT KNOWLEDGE AND PROCESS
ERROR INTERVENTION
IF students confuse translations,
IF students confuse translations,
THEN consider emphasizing the similar letters
SLide is a tranSLation.
TuRn is a RoTation.
FLip is a reFLection.
THEN consider doing hand movements to help them identify
IF students forget that transformations
THEN consider requiring that they trace the initial figure and
reflections, and rotations
reflections, and rotations
IF students have trouble identifying a
rotation
must be congruent
Baltimore City Schools – Office of Mathematics
[email protected]
the transformations.
THEN consider having them actually turn their paper and
observe how the figure looks as it turns.
then translate, rotate, or reflect it to check their work
Grade 4 Math Curriculum DRAFT
Page 60
Unit 8: Concept 2
Transformations
LEARNING ACTIVITIES AND STRATEGIES
Suggested Learning Plan
Activity
Description
Visual
Kinesthetic
Finger Painting *
Visual
Kinesthetic
Spatial
Letter Cut Outs *
Kinesthetic
Auditory
“Transformation Shuffle”
Materials
The students learn about translations by
using finger paints and their hands as
the object being transformed.

The students use letter cut-outs to
translate, reflect, and rotate over a
dotted line.

The students translate, reflect and rotate
to the tune of a popular hip-hop song.




DIFFERENTIATION
Accommodations*
Baltimore City Schools – Office of Mathematics
[email protected]
Three large pieces of paper
folded in half (per student)
Finger paints
Large pieces of construction
paper
Letter cut outs of the first
letter of the first name of
each student in the class.
Words to transformation
shuffle
Song “Cupid Shuffle” by
Cupid
CROSS-CURRICULAR CONNECTIONS
G.A.T.E./Enrichment
Artful Teaching
Grade 4 Math Curriculum DRAFT
Literacy Integration
Page 61
Unit 8: Concept 2
Assessments
Suggested Learning Plan
Transformations
RESOURCES
Sub-Skills
Identify
translations
Teacher Created Materials
 MW Identify Translations
Adopted Textbooks

SF Grade 4 TE Lesson 8-6 (pp.
452A-455)
Technology


Identify
reflections
 MW Identify Reflections
Identify rotations
 MW Identify Rotations


Writing in Math
TRACKING SHEET
Baltimore City Schools – Office of Mathematics
[email protected]
WEB: NLVM - Playing with
Translations
WEB: NLVM - Playing with
Reflections
WEB: NLVM - Playing with
Rotations
WEB: Alphabet Geometry:
Transformations
Other Resources
CONCEPT
ASSESSMENT
MULTIPLE CHOICE
QUESTION BANK
Grade 4 Math Curriculum DRAFT
OTHER WAYS TO
ASSESS
Page 62