Knowledge and Skills
A special thanks to all the teachers, ISTs, and administrators
who wrote, revised, and provided feedback for our curriculum.
http://www.bcpss.org/bbcswebdav/institution/MATH_CURRICULUM/Grade%201/ASSESSMENTS/Adding%20and%20Subtract%20Basic%20Facts%20Skill%20Assessment/Skill%20Assessment%20Unit%201%20Concept%201%20Addition%20and%20Subtraction%20Basic%20Facts.doc
Baltimore City Schools
Dr. Andrs Alonso
Chief Executive Officer
Dr. Mary Minter
Chief Academic Officer
Dr. Kathy Volk
Academic Achievement Officer
Linda Eberhart
Office of Mathematics
Curriculum Writers
A special thanks to all the teachers, ISTs, and administrators
who wrote, revised, and provided feedback for our curriculum.
Kim Alexander
Tara Barnes
Lisa Beckman
Melissa Boston-Jackson
Raymond Braxton
David Brelsford
Sheila Burke
Elizabeth Clark
Tiffany Cole
Shannen Coleman
Megan Cooper
Ben Crandall
Megan Delong
Keith Dysarz
Jason Eckles
Erinn Eifler
Kim Felton
Cathy Ferguson
Charlene Footman
Leila Frain
Helen Garcia
Lindsay Giel
Beth Goldscher
Nicole Hauser
Monique Hibbert
Antwonette Hooper
Felipe Jackson
Matt Kalthoff
Sarah Kenders
Ronald Krach
Tracy Larkins
Elisabeth Lim
Dr. Luis Lima
Danielle Long
Genevieve Mason
Karen Matthews
Campbell McLean
Stanley Munro
Regina Paige
Michelle Perzinski
Sarah Pessagno
Shane Prada
Michael Pugh
Brian Rainville
Ryan Reid
Beth Renwick
Courtney Robinson
Brian Schanbacher
Frances Schwartz
Clarence Scott
Patricia Storke
Heather Torretta
Siriporn Vinijkul
Smitha Viswanathan
Lembric Walker
Brent Watkins
Mary Welliver
Anne Whelan
ShaNekwa Winfield
Kim Worthington
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:
Check homework every night
Give students an opportunity to revise homework
Start the homework assignment together at the beginning or end
of class.
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.
Reward students for doing homework and revising it.
Homework Tips:
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.
Require students to show their work on homework problems, not
just write the answer. Give credit only when there is work.
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.
At the beginning of the year, homework should consist of skills
taught in the previous grade level.
8th Grade Homework
Grade 8 Math Curriculum Sequence
School Year 2008-2009
QUARTER 1 (Aug 25 Oct 31)
Suggested Time Frame
BENCHMARK 1
(same skills as June Benchmark in previous grade)
Aug 26 - Sept 5 testing window
UNIT 1: Computation & Representing Numbers
3 weeks
(12 17 days)
Determine equivalent forms of rational numbers
Converting fraction ( decimal ( percent ( ratio
Ratio to fraction
3 4 days
Compare, order, describe rational numbers Compare rational
numbers
Order rational numbers
Use scientific calculator to convert fractions to decimals
3 4 days
Operation with decimals
Add and subtract decimals
Multiply decimals
Divide decimals by whole number divisors
2 3 days
Operation with fractions
Add and subtract fractions and mixed numbers
Multiply fractions and mixed numbers
Divide fractions and mixed numbers
4 6 days
UNIT 2: Integers
2 weeks
(7 11 days)
Compare, order, describe rational numbers
Absolute value
Compare rational numbers
Order rational numbers
2 3 days
Add and subtract integers
Add integers
Subtract integers
3 4 days
Multiply and divide integers
Multiply integers
Divide integers
1 2 days
UNIT 3: Order of Operations
2 weeks
(8 12 days)
Powers of integers
Positive bases
Negative bases
1 2 days
Laws of exponents
Product rule
Quotient rule
Combining products and quotient rule
1 2 days
Square Roots
Square roots
Estimating square roots
Square roots with a calculator
1 2 days
Scientific notation
With positive exponents
With negative exponents
2 3 days
Order of Operations
With exponents
With brackets
With absolute value
With division bar
Mixed review
4 5 days
Unit 4: Expressions
2 weeks
(9 13 days)
Write algebraic expression
Write one-step story problem
Write one-, two-, or three-step verbal phrase
Write two-, or three-step story problem
2 3 days
Evaluate an algebraic expression [substituting]
With integers
With fractions
With decimals
4 5 days
Properties
Identity property
Additive inverse property
Commutative property
Associative property
Distributive property
1 2 days
Combining like terms
Combining like terms
Distributive property
2 3 days
QUARTER 2 (Nov 3 Jan 23)
Suggested Time Frame
BENCHMARK 2
(all Quarter 1 skills assessed)
Nov 4 Nov 13 testing window
UNIT 5a: Equations & Relationships
2 weeks
(8 13 days)
Arithmetic Sequences
Using words or numbers
Using table and graph
1 - 2 days
Geometric sequence (use calculator to assist)
Using words and numbers
Using table and graph
1 2 days
Write equations
One-step
Two-, or three-step; variable on one side
Two-, or three-step; variable on both sides
2 3 days
Solve equations
Two-step equations
Combining like terms
Distributive property
3 4 days
Identify equivalent equations
identify equivalent equations
1 2 days
UNIT 5b: Equations & Relationships
2 weeks
(5 8 days)
Write inequalities to represent relationships
One step
Two-, or three-step; variable on one side
Two-, or three-step; variable on both sides
2 3 days
Solve inequalities
Two-step inequalities
Distributive property
2 3 days
Graph solutions of inequalities
Graph solutions on a number line
Minimum/maximum value
1 2 days
Unit 6: Proportional Thinking
1.5 weeks
( 7 11 days)
Proportional reasoning
Solve proportion using cross multiplication
Solve word problems using proportions
2 3 days
Unit rates
Calculate unit rate
Apply unit rate to word problems
1 2 days
Measurement problems with proportions
Measurement problems using proportions
Scale drawings
2 3 days
Similar polygons
Identify similar polygons
Determine missing side/angle
2 3 days
Unit 7: Graphing
2 weeks
( 8 11 days)
Graph linear equations- Part 1
Solutions
Intercepts
2 days
Slope
Slope from a graph
2 3 days
Graph linear equations Part 2
Slope-intercept form
Point-slope form
Coefficients of y
2-3 days
Linearity
Linear and nonlinear functions
1 2 days
Unit 8: Formulas
1.5 weeks
(6 10 days)
Circles
Circumference
Area
1 2 days
Area of a composite figure
Area of composite figures
2 3 days
Volume
Volume of rectangular prisms
Volume of cylinders
1 2 days
Apply formulas
Temperature formula
Distance formula
Simple interest formula
2 3 days
QUARTER 3 (Jan 26 March 31)
Suggested Time Frame
Unit 9: Percents & Graphs
1 weeks
(4 6 days)
Percent problems
Percent of a number
Part given percent and total
Total given percent and part
Discount
Sales tax/commission
Simple interest
Percent increase/decrease
3 4 days
Circle graphs
Make circle graphs
Interpret circle graphs
1 2 days
Unit 10: Data Analysis
2 weeks
(7 11 days)
Measures of central tendency
Mean
Median
Mode
1 2 days
Interpret tables
Interpret data table
1 2 days
Box & Whisker plots
Make a box & whiskers plot
Interpret a box and whiskers plot
3 4 days
Scatter plots
Make a scatter plot
Interpret a scatter plot
2 3 days
BENCHMARK 3 MOCK MSA
(all VSC assessed skills)
Feb 17 Feb 20 testing window
Unit 11: Probability
1.5 weeks
(7 11 days)
Outcomes
Combinations
The counting principle
Permutations and arrangements
3 4 days
Independent probability
One event
Two events
1 2 days
Dependent Probability
Second event
First and second event
2 3 days
Make predictions
Make predictions from experimental probability
1 2 days
Unit 12: Geometry
2.5 weeks
(9 15 days)
Angle pairs in a transversal
Identify angle pairs
Find missing angle
1 2 days
Construct perpendicular line segments
Construct perpendicular segments
1 2 days
Construct congruent triangles
Construct congruent triangles
1 2 days
Construct quadrilaterals
Given 4 angles
Given 4 sides
Given 3 sides and 1 angle
Rhombus given 1 side and 1 angle
2 3 days
Pythagorean Theorem
Parts of a right triangle
Solving for hypotenuse
Solving for leg
Word problems
2 3 days
Multiple transformations
Translation
Reflection
Rotation
Multiple transformations
2 3 days
Maryland State Assessment
March 16 to March 25
QUARTER 4 (April 1 June 9)
Suggested Time Frame
Unit 13: Integers
2.5 weeks
(10 18 days)
Integer Concepts
Compare and order integers
Absolute value
1 - 2 days
Add Integers
Add 2 positive or 2 negative numbers
Add 1 negative and 1 positive number
Apply the addition of integers to word problems
Add with more than 2 addends
1 - 3 days
Subtract Integers
Subtract a positive number from a positive or negative
number
Subtract a negative number from a positive or negative
number
Apply the subtraction of integers to word problems
2 - 4 days
Multiply & Divide Integers
Multiply and divide 2 integers
Multiply and divide more than 2 integers
2 - 3 days
Order of Operations
Concept of order of operations (whole numbers and integers to
start)
Exponents of integer bases
Expressions with parenthesis and brackets
Absolute value
4 - 6 days
Unit 14: Representing the Unknown
2 weeks
(8 - 13 days)
Numeric & Geometric Patterns
Making tables
Write rules for sequences
Identify arithmetic and geometric sequences
3 - 4 days
Write Expressions
Write two-step expressions from verbal phrases
Write two-step expressions from word problems
Write three-step expressions from verbal phrases or word
problems
3 - 5 days
Simplify Expressions
Identify like terms and constants
Simplify by combining like terms and constants
Simplify using the distributive property
2 - 4 days
Unit 15: Solving & Using Equations
3.5 weeks
(15 - 23 days)
Write Equations
Write one-step equations from verbal translations (all
operations)
Write two- or three-step equations from verbal translations (all
operations)
3 - 5 days
Solve Linear Equations
One-step equations (all operations)
Two- to three-step equations without parenthesis; only integers
and whole numbers
Two- to three-step equations with parenthesis and all rational
numbers
Two- to three-step equations (simplifying first)
Equations whose solution is null set or infinite solution
5 - 8 days
Use Formulas
Distance and average
Area and perimeter of a triangle, square, or rectangle
Volume
2 - 4 days
Percent of a Number
Understand percents greater than 100, less than 1 or that
include a decimal
Find the part
Find the total
Find the percent
Discount, commission, and sales tax
5 - 6 days
BENCHMARK 4 End of Year Benchmark
(all skills from Quarters 1-4 assessed)
May 26 June 5 testing window
Knowledge and Skills
TIME FRAME: 3-4 days
PREREQUISITE SKILLS
Equivalent Forms of Rational Numbers
Converting fractions, decimals, and percents
Ratio to fraction
Long division
Greatest common factor
Ratios
VSC OBJECTIVE (no calculators allowed)
7.6.A.1.c. Determine equivalent forms of rational numbers
expressed as fractions, decimals, percents, and ratios
ASSESSMENT LIMIT: Use positive rational numbers (0 to 100)
VOCABULARY
numerator
denominator
fraction bar
fraction
decimal
percent
ratio
proper fraction
mixed number
equivalent forms
rational numbers
convert
divide
dividend
divisor
terminating
repeating
Vocabulary Activities
Teacher Definitions
Student Vocabulary
Word Wall Vocabulary
Total Vocabulary Matrix
ENDURING UNDERSTANDINGS
Fractions, decimals, percents and ratios are a part of total or
whole.
Numbers can have the same value, but be written in different
forms.
ESSENTIAL QUESTIONS
What determines the appropriate representation of a number?
How are number converted among different forms without changing
the value?
CONCEPT KNOWLEDGE AND PROCESS
A fraction can be changed to a decimal by dividing the numerator
by the denominator. This works because a fraction represents the
division of a whole into parts.
Percents and fractions both describe a ratio out of 100.
Percents are simply hundredths and represent another way to write
both fractions and decimals.
Ratios can be part-part or part-whole relationships that can be
written as a fraction. Only part-whole ratios can then be
represented as a decimal or percent.
ERROR INTERVENTION
IF students have difficulty remembering to divide the numerator
by the denominator
THEN consider telling students to turn the fraction on its
side
8
7
8
7
.
IF students write decimals to the tenths place value as percents
less than 10% 0.5 = 5%
THEN consider having students draw two place value lines after
the decimal, which encourages students to annex a zero 0.5 _.
Suggested Learning Plan
Learning Activities and Strategies
Activity
Description
Materials
Game
BINGO
Teacher calls out a fraction. Students convert fraction to
decimal and locate decimal on BINGO chart.
Blank BINGO chart
Colored chips
Cooperative Learning
Fall In Line
Each student is given a fraction, decimal, or percent. Students
order themselves from least to greatest.
Note cards or construction paper
Game
War
Students use a deck of fraction, decimal, and percent cards to
play a game similar to war.
War activity cards
Social
Scavenger Hunt
Students use converting skills to answer clues and spell out a
message.
Scavenger hunt clues
Prizes
Visual
Using Benchmarks
Students use a number line to create fractional benchmarks and
find decimal and percent equivalents.
Fraction bars
Colored pencils
Logical
Repeater or Terminator*
Students use a list of the first 20 unit fractions and complete
a table of the prime factorization of the denominators and the
decimal equivalent for the fraction. The goal is for students to
generate a rule to determine if a fraction will repeat or terminate
in decimal form.
Calculators*
DIFFERENTIATION
Accommodations* G.A.T.E./Enrichment
Suggested Learning Plan
Resources
Sub-Skills
Math Works Teaching Skill
Textbook
Other Resources
Converting fractions, decimals, and percents
MW Equivalent Forms.fraction decimal percent
CMP Bits and Pieces I TE Inv 5.1-5.3 (pp. 53-66) Fraction (
Decimal
CMP Bits and Pieces II TE Inv 3.1-3.2 (pp. 31-41) Fraction (
Decimal( Percent
MSA Coach 7 (pp. 174-179)
MSA Finish Line 7 (pp. 120-123)
MSA Grand Slam 7 (pp. 12-13)
SF Grade 7 TE Lesson 8-2 (pp. 390-393)
Brainpop.com- Converting Fractions to Decimals
Ratio to fraction
MW Equivalent Forms.ratio to fraction
CMP Bits and Pieces I TE Inv 5.1 (pp. 53-54)
CMP Comparing and Scaling TE Inv 1.1-1.3 (pp. 5-14)
MSA Grand Slam 7 (pp. 12-13)
Brainpop.com- Introduction to Ratios
Writing in Math
Math Works BCRs
Assessments
TRACKING SHEET
CONCEPT
ASSESSMENT
MULTIPLE CHOICE QUESTION BANK
OTHER WAYS TO ASSESS
Knowledge and Skills
TIME FRAME: 3-4 days
PREREQUISITE SKILLS
Compare and Order Rational Numbers
Compare rational numbers
Order rational numbers
Relational symbols
Order integers
Equivalent forms
VSC OBJECTIVE (calculators allowed)
7.6.A.1.d. Compare, order, and describe rational numbers with or
without relational symbols (>, , , ,, ,
