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 / Suggested Time Frame
BENCHMARK A
(same skills as June Benchmark in previous grade) / Sept 7 - Sept 17 testing window
UNIT 1: Whole Number Concepts / (7-12 days)
*Common Core / Ø 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 / Ø 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 / Ø Compare and Order Whole Numbers
· Compare numbers through the millions
· Order numbers through the millions / 2 – 3 days
UNIT 2: Whole Number Computation 1 / (7-11 days)
*Common Core / Ø Add Whole Numbers
· Add up to 4-digit whole numbers with regrouping / 1 – 2 days
*Common Core / Ø 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 / 3 – 4 days
*Common Core / Ø Estimate Sums and Differences
· Rounding whole numbers
· Estimating sums and differences / 2 – 3 days
Ø Compare Values of Mixed Currency
· Identify value of mixed currency
· Compare money sets / 1 – 2 days
Unit 3: Number Theory and Computation 2 / (10-20 days)
Ø Multiples
· Identify multiples / 1 – 2 days
Ø Factors
· Identify factors
· Create and interpret factor arrays / 1 – 3 days
*Common Core / Ø 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 / 2 – 4 days
*Common Core / Ø Divide Whole Numbers
· Divide 2-digits by 1-digit
· Divide 3-digits by 1 digit
· Divide 4-digits by 1 digit / 3 – 5 days
Ø Estimate Products and Quotients
· Estimate products
· Estimate quotients / 2 – 3 days
Ø 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 / 1 – 3 days
UNIT 4: Algebra 1 / (7–14 days)
Ø Numeric Patterns
· Identify the rule for and extend a number pattern / 1 – 2 days
Ø Repeating Patterns
· Identify the rule for and extend a repeating pattern / 1 - 2 days
Ø Growing Patterns
· Identify a rule for and extend a growing pattern / 1 - 3 days
Ø Solve for Unknown Quantities
· Find the unknown using addition and subtraction
· Find the unknown using multiplication / 2 – 3 days
Ø Function Tables
· Complete function tables using addition and subtraction
· Complete function tables using multiplication
· Complete function tables using division / 2 - 4 days
QUARTER 2 (Nov 8 – Jan 21)
46 days / Suggested Time Frame
BENCHMARK B
(all Quarter 1 skills assessed) / Nov 1 – Nov 12 testing window
Unit 5: Fraction Concepts / (7-12 days)
Ø 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 / 2 - 3 days
Ø Compare and Order Fractions and Mixed Numbers
· Compare proper fractions and mixed numbers
· Order proper fractions and mixed numbers / 1 – 2 days
Ø 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 / 2 – 4 days
*Common Core / Ø Add and Subtract Proper Fractions and Mixed Numbers
· Add proper fractions
· Subtract proper fractions
· Add mixed numbers
· Subtract mixed numbers / 2 – 3 days
Unit 6: Statistics and Probability / (11-18 days)
Ø Probability
· Express object probability as a fraction
· Express spinner probability as a fraction
· Express conditional probability as a fraction / 3 - 5 days
Ø 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 / 2 – 3 days
Ø Line Plots
· Create line plots
· Interpret line plots / 3 – 5 days
Ø Coordinate Grids
· Identify locations on a coordinate grid given object
· Identify objects on a coordinate grid given location / 1 – 2 days
Ø Line Graphs
· Interpret line graphs / 2 – 3 days
UNIT 7: Algebra 2 / (5-9 days)
Ø Write Expressions
· Write expressions using addition or subtraction
· Write expressions using multiplication or division / 2 – 3 days
Ø Equivalent Expressions
· Write equivalent expressions / 1 – 2 days
Ø Write Relationships
· Evaluate relationships with missing relational symbols
· Represent relationships in word problems / 2 – 4 days
Unit 8: Geometry 1 / (4-8 days)
Ø Angles
· Identify right angles
· Identify acute and obtuse angles
· Identify angles in shapes and objects / 2 – 4 days
Ø Transformations
· Identify and create translations
· Identify and create reflections
· Identify and create rotations / 2 – 4 days
QUARTER 3 (Jan 25 – Apr 7)
45 days / Suggested Time Frame
BENCHMARK C – Mock MSA
(all VSC assessed skills) / Jan 31 – Feb 11 testing window
Unit 9: Geometry 2 / (6-9 days)
Ø 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 / 4 – 6 days
Ø 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 – 3 days
Unit 10: Decimals / (8-16 days)
Ø Read, Write, Represent Decimals
· Read, write, represent decimals in the tenths
· Read, write, represent decimals in the hundredths / 2 – 4 days
Ø Place Value and Expanded Form of Decimals
· Represent decimals in expanded form through the hundredths / 1 – 3 days
Ø Compare and Order Decimals
· Compare decimals through the hundredths
· Order decimals through the hundredths / 1 – 2 days
Ø Add Decimals
· Add decimals through the tenths
· Add decimals through the hundredths / 1 – 2 days
Ø Subtract Decimals
· Subtract decimals through the tenths
· Subtract decimals through the hundredths / 1 – 2 days
Ø 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 / 2 – 3 days
Unit 11: Measurement 1 / (5-9 days)
Ø Measure Length
· Draw length to nearest ¼ inch
· Measure length to nearest ¼ inch
· Measure length to nearest mm / 2 – 4 days
Ø Determine Equivalent Units of Length
· Convert yards to inches
· Convert inches to yards, feet / 3 – 5 days
Unit 12: Measurement 2 / (7-11 days)
Ø Perimeter
· Find perimeter given all sides
· Find perimeter with missing sides / 2 – 3 days
Ø Area
· Find area on grid
· Find area using formula / 2 – 3 days
Ø Start time, Elapsed Time, and End Time
· Find end time
· Find start time
· Find elapsed time / 3 – 5 days
Maryland State Assessment / March 7 to March 16
POST-MSA CURRICULUM / Suggested Time Frame
Unit 13: Fraction Concepts 2 / (10 - 15 days)
Ø Least Common Multiple
· Identify the least common multiple of 2 numbers
· Identify the least common multiple of 3 numbers / 2 - 3 days
*Common Core / Ø 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 / 3 - 5 days
*Common Core / Ø Add and Subtract Proper Fractions with Unlike Denominators
· Add proper fractions with unlike denominators
· Subtract proper fractions with unlike denominators / 5 - 7 days
Unit 14: Simplify & Compare Fractions / (10 - 14 days)
Ø Identify GCF and Simplify Fractions
· Identify the Greatest Common Factor
· Use the Greatest Common Factor to simplify fractions / 5 - 7 days
*Common Core / Ø 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
· / 5 - 7 days
Unit 15: Decimal Notation for Fractions / 7-13 days
*Common Core / Ø Express a fraction with denominator 10 as an equivalent fraction with denominator 100 / 2-4 days
*Common Core / Ø Use decimal notation for fractions with denominators 10 or 100 / 3-5 days
*Common Core / Ø Compare two decimals to hundredths by reasoning about their size / 2-4 days
Unit 16: Whole Number Computation 2 / (9 – 15 days)
*Common Core / Ø Multiply Whole Numbers
· Multiply 2-digit by 2-digit as multiple of ten
· Multiply 2-digit by 2-digit / 3 – 5 days
*Common Core / · Divide Whole Numbers
· Divide with 2-digit divisor as multiple of ten with reminders
· Divide with 2-digit divisor with remainders
· Division word problems / 3 – 5 days
BENCHMARK D – End of Year Benchmark
(all skills from Quarters 1-4 assessed) / May 16 – May 27 testing window
*Common Core - This skill will infuse the Maryland State Standards and the
Common Core.
Unit 5: Concept 1
Proper Fractions and Mixed Numbers
Knowledge and Skills / TIME FRAME: 2-3 days / PREREQUISITE SKILLSProper Fractions and Mixed Numbers
· Fractions as part of a set
· Fractions as part of a whole
· Mixed numbers / · Fractions of a region (halves, thirds, fourths)
· Identify fractional sets (halves, thirds, fourths)
· Represent fractional sets (halves, thirds, fourths)
· Writing fractions
VSC OBJECTIVE (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.
ESSENTIAL QUESTIONS
· 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?
CONCEPT KNOWLEDGE AND PROCESS
§ 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.
ERROR INTERVENTION
IF students confuse the numerator and denominator / THEN consider using the mnemonic that the denominator 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.
IF students misread what the question is asking for in the numerator / 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?”).
IF students do not recall that fractions must have equal pieces / THEN consider showing numerous examples of equal and non-equal pieces.
Baltimore City Schools – Office of Mathematics Grade 4 Math Curriculum DRAFT Page 62