Concept
& Month taught 
Alpine
District/State Objective Starred (*) objectives, every 6th grader must know. Blue objectives were added by Northridge teachers. 
Learn

Practice

Quiz/Test

Review August September 
*Pass times tables test to the 12's 
The 12 Times Tables 
Multiplication
Facts 

*Demonstrate a working math vocabulary 
Math
6 Spy Guy Glossary 

*Show place value (counting, reading,
and writing to 1 billion) 
Place
Value 1 
Place Value 

Represent rational numbers August September 
Recognize a rational number as a
ratio of two integers, a to b, where b is not equal to zero. 

*Change whole numbers with
exponents to standard form (e.g., 2^4=16) and recognize that any nonzero whole number to the zero power equals 1 (e.g., 9^0 = 1). 
Exponents
 1st half of lesson 
Exponent

UTIPs
 Exponents 

*Write a whole number in
expanded form using exponents (e.g., 876,539=8x10^5 + 7x10^4 + 6x10^3 + 5x10^2 + 3x10^1+ 9x10^0). 

*Demonstrate an understanding of Square
numbers 
Number
Cop  Other Games  Perfect Squares 

*Express numbers in scientific
notation using positive powers of ten. 
Place Value
 Scientific Notation 

Relation ships and equivalen cies among rational numbers August September 
Place rational numbers on the
number line. 

*Compare and order rational
numbers, including positive and negative mixed fractions and decimals,
using a variety of methods and symbols, including the number line and finding common denominators. 
Spy
Guy  Understanding Integers Comparing Fractions  Fact Sheet 
Fractions
 Ordering  Fractions Fractions  Ordering  Decimals Fraction Inequality Ordering Six Digit Numbers Comparing Fractions Games Fraction Sorter Comparing Decimals 
Comparing
Fractions 

Find equivalent forms for common
fractions, decimals, percents, and ratios, including repeating or terminating decimals. 
Decifractator 
Simplify fractions, decimals, percent, and ratios. 

Relate percents less than 1% or
greater than 100% to equivalent fractions, decimals, whole numbers, and mixed numbers. 
Spy
Guy  Improper Fractions and Mixed Numbers 

Recognize that the sum of an
integer and its addtitive inverse is zero. 

Prime factoriza tions least common multiples greatest common factors August September 
*Determine whether whole numbers
to 100 are prime, composite, or neither. 
Eratosthenes' Sieve 
Prime and Composite
Numbers Number Cop  Other Games  Prime Numbers 

*Find the prime factorization of
composite numbers to 100. 
Spy
Guy  Factors, Multiples, and Prime Factorization 

*Find the greatest common factor
and least common multiple for two numbers using a variety of methods
(e.g., list of multiples, prime factorization.) 
Greatest Common Factor Least Common Multiple Least Common Multiple 
Greatest
Common Factor Rags to Riches 

Money August September 
*Use Money (counting, comparing and
making change) 
Money
Fun Brain  Making Change Math Playground  Making Change 

Operations October to May 
Relate fractions to
multiplication and division and use this relationship to explain procedures for multiplying and dividing fractions. 

Recognize the ratios derived
from pairs of rows in the multiplication table and connect with equivalent fractions. March 

Give mixed number and decimal
solutions to division problems with whole numbers. 

Solve problems with multiple steps October to May 
Select appropriate methods to
solve a multistep problem involving multiplication and division of fractions and decimals. 
Spy Guy  Lottery Tickets  
*Use estimation to determine
whether results obtained using a calculator are reasonable. 
Estimating
Percentages 

*Use estimation of calculation
to compute results, depending on the context and numbers involved in the problem. 
Spy
Guy  Rounding 
Comparison
Estimator Fermi Questions Library 

* Define, read, and write ratios.
March 
Spy
Guy  Ratio 
Ratios Determining Ratios 

*Solve problems involving ratios
and proportions (and find % of
numbers). March 
Ratios
and Proportions Ratio and Proportion Proportion Method Spy Guy  Percents 
Rags to Riches  Ratios and
Proportions Troy's Toys 

Proficiency of four operations Addition and Subtraction of integers October to May 
*Add, subtract, multiply, and divide
whole numbers. 
Arithmetic Addition and Subtraction Multiplication Disaster Math 

*Add, subtract, multiply, and divide
decimals. 
Decimals Spy Guy  Decimals 
Fractions and
Decimals Spy Guy  Solving Problems with Decimals Multiplying with Decimals 

*Multiply and divide a
multidigit number by a twodigit number, including decimals 
Fractions and
Decimals 

*Add, subtract, multiply, and
divide fractions and mixed numbers. 
Fractions Multiply Fractions with circles 
Fractions and
Decimals Adding Fractions  Same Denominator Adding Fractions  Mixed Denominator Subtracting Fractions  Same Denominator Multiplying Fractions Divide Fractions with circles 

*Add and subtract integers. 
How
to Add and Subtract Postive and Negative Numbers Adding and Subtracting Integers Gizmo 
Virtual
Dice  +/ Dice Adding and Subtracting Integers 

Patterns relations and algebraic expressions August to May 
*Analyze algebraic expressions,
tables, and graphs to determine patterns, relations, and rules. 
Spy
Guy  Summarizing/ Extending Patterns 
Algebra Puzzle 
Spy Guy  Handshakes 
*Describe simple relationships
by creating and analyzing tables, equations, and expressions. 

*Draw a graph and write an
equation from a table of values. 
Spy Guy  Understanding and Interpreting Graphs  
*Draw a graph and create a table
of values from an equation. 

Problem Solving August to May 
*Demonstrate knowledge of properties of
multiplication and addition. 

*Demonstrate
knowledge of Order of operations (PEMDAS) 
Exploring
Order of Opera tions Order of Operations Tutor ial 
Math
Frog  Order of Opera tions 
Order
of Operations Pretest APlus Math Worksheet 

Solve single variable linear
equations using a variety of strategies. 
Linear
Function 


Recognize that expressions in
different forms can be equivalent and rewrite an expression to
represent a quantity in a different way. 
Spy
Guy  Balancing Equations 

*Evaluate and simplify
expressions and formulas, substituting given values for the variables
(e.g., 2x + 4; x=2; therefore, 2 (2) + 4 = 8). 
Algebra  Solve (y) Solve (x)  
Geometric Shapes December to May 
*Identify, classify, and measure planes
and solid figures. 
Pete's
Polygons Polygons 
Shapes 

Identify the midpoint of a line
segment and the center and circumference of a circle. 

*Identify angles as vertical,
adjacent, complemetary, or supplementary and provide descriptions of these terms. 
Angles
and Types of Angles 
Classifying
Angles 

*Develop and use the properties
of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle in a triangle or quadrilateral. 
Angles  Triangle 

Transform ing geometric shapes December to May 
*Rotate a polygon about the
origin by a multiple of 90 degrees and identify the location of the new
vertices. (Turn) 
Transformations  scroll
down Transformations Tutorial Playing with Rotations 

*Translate a polygon either
horizontally or vertically on a coordinate grid and identify the location of the new vertices. (Slide) 
Transformations  scroll
down Spy Guy  Slides and Flips Playing with Translations 

Reflect a polygon across either
the x or yaxis and identify the location of the new vertices. (Flip) 
Transformations  scroll
down Spy Guy  Slides and Flips Playing with Reflections 

Measure: Circum ference and area of a circle February 
*Explore the relationship
between the radius and diameter of a circle to the circle's
circumference to develop the formula for circumference. 

*Find the circumference of a
circle using a formula. 

Describe pi as the ratio of the
circumference to the diameter of a circle. 

Decompose a circle into a number
of wedges and rearrange the wedges into a shape that approximates a
parallelogram to develop the formula for the area of a circle. 

*Find the area of a circle using
a formula. 
Spy
Guy  Area
and Perimeter 
Geometry
 Area  Circle 

Units of Measure ment February 
Recognize that measurements are
approximations and describe how the size of the unit used in measuring
affects the precision. 
Measure 

*Convert units of measurement
within the metric system and convert units of measurement within the
customary system. 
Teaching Measures
 metric Length, Weight, Capacticy  metric Factsheet 
Equivalent
Customary Measures Length, Weight, Capacity  metric 
Length,
Weight Capacity  metric 

Compare a meter to a yard, a
liter to a quart, and a kilometer to a mile. 

Determine when it is appropriate
to estimate or use precise measurement when solving problems. 

*Derive and use the formula to
determine the surface area and volume of a cylinder. 
Spy
Guy Volume  rectangular prism 
Geometry
 Surface  Cylinder Click on: See Formulas Geometry  Volume  Cylinder Click on: See Formulas 

Time  Accuraely measure and estimate 
Time


Data Analysis April 
Design investigations to answer
questions. 

*Extend data display and
comparisons to include scatter plots and circle graphs. 
Reading
Percentages in Charts Pie Chart Scatter Plot 

Compare two similar sets of data
on the same graph and compare two graphs representing the same set of data. 
Maths
 Interpreting Data 
Maths
 Interpreting Data 

Recognize that changing the
scale influences the appearance of a display of data. 
Bar
Chart 

*Propose and justify inferences
and predictions based on data. 

Probability April 
*Write the results of a
probability experiment as a fraction between zero and one, or an equivalent percent. 
Spy
Guy  Probability 
Probability 

*Compare experimental results
with theoretical results (e.g., experimental: 7 out of 10 tails; whereas, theoretical 5 out of 10 tails.) 

Compare individual, small group,
and large group results of a probability experiment in order to more
accurately estimate the actual probabilities. 
Chances Coin Tossing Stick or Switch Virtual Dice 