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

