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Mathematics
Curriculum
K - 2
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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1. Number and
Operations
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Explore
and identify the number of objects in a set
Explore
and identify equal and unequal sets of objects
Count
pictorial representations of objects up to 20
Count
concrete objects up to 20
Explore
the order relation of whole numbers on a number line
Identify
numerals 0 – 20
Explore
the use of numbers and numerals in daily life
Develop
the skills of recognizing half an object and half a set of objects
Tell
which objects in a line are first, second, or last
Match
two sets of objects with 1 to 1 correspondence
Identify
number words 0 – 10
Given
sets of 0 – 20, write the correct numeral
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Count
by ones to 100
Count
objects to 100 grouping by 10’s and 1’s
Read
and write numerals to 100
Know
place value of tens and ones
Identify
whole objects, one-half, one-fourth, and one-third of an object
Recognize
and use symbols of ½, ¼, and 1/3.
Match
numerals and number words 0 – 20
Count
by 2’s to 20
Count
by 5’s and 10’s to 100
Use
+, -, and = symbols
Add
to 18 using manipulatives
Know
addition facts to 10
Add
three single digit numbers
Subtract
from numbers to 10 with manipulatives
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Count,
read and write 0 – 1000
Identify
a numeral 0 – 1000 out of sequence
Know
place value to hundreds
Indicate
ordinal number to 20
Recognize
and use less than, greater than and equal to
Rewrite
numerals into words and words into numerals 0 – 99
Recognize
and use symbols ½, 1/3, ¼, 2/3, ¾
Identify
dozen and half dozen
Count
by 2’s, 5’, and 10’s to 100
Recognize
even and odd numbers
Know
additions facts to 18
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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1. Number and
Operations
(continued)
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Given
a numeral 0 – 20, match a set with that number of elements
Write
the numerals 0 – 20 in numerical order
Using
concrete objects, explore the process of joining and separating sets
Explore
joining a set of zero to a set of objects
Using
sets of concrete objects, explore addition and subtraction
Solve
one step word problems involving addition and subtraction
Count
by 10’s to 100
Divide
a group of objects into 2 equal sets
Identify
penny, nickel, dime, and quarter
Count
up to 10 pennies and designate value
Count
dimes to one dollar
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Add
two-digit numbers without regrouping
Solve
word problems with oral explanation given
Divide
a group of objects into 2 or more equal sets
Name
and assign value to penny, nickel, dime, and quarter
Choose
coins equal to a given value up to 50¢
Solve
one step word problems using money with oral explanation given
Apply
the commutative property to addition
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Add
three digits vertically and horizontally (column and math sentences)
Add
2 and 3 digit numbers with regrouping
Solve
number sentences with missing addends
Know
subtractions facts to 10
Subtract
from numbers to 18
Subtract
2 and 3 digit numbers, no regrouping
Subtract
two digit numbers with regrouping
Solve
written word problems with work shown and explanation given
Understand
situations that require multiplication and division
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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1. Number and
Operations
(continued)
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Use
a variety of methods and tools to compute, including objects, mental
computation, estimation, paper and pencil, and calculators
Name
and assign value to all coins and one dollar
Use
¢, $, and decimal point correctly
Know
equivalent value of all coins 10¢ = 2 nickels, 2 quarters = half dollar,
etc.
Count
values of any combination of coins to 99¢
Addition/subtraction
of decimals with dollar signs
Solve
word problems involving money with work shown and explanation given
Apply
the commutative property of addition
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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2. Algebra
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Given
a simple pattern be able to reproduce the same
Classify
by size, color, and shape
Sort,
classify and order by one attribute, such as size, color or shape
Use
concrete, pictoral, and verbal representations to develop an understanding,
using objects, pictures and symbols
Demonstrate
the addition and subtraction of whole numbers, using objects, pictures and
symbols
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Classify
by size, color, and shape
Identify
and copy simple patterns
Recognize
and extend patterns
Use
concrete, pictoral, and verbal representations to develop an understanding,
using objects, pictures, and symbols
Demonstrate
the addition and subtraction of whole numbers, using objects, pictures, and
symbols
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Identify
and continue complex numeric and geometric patterns
Analyze
and identify different types of patterns including repeating and growing
patterns
Use
concrete, pictoral, and verbal representations to develop and
understanding, using objects, pictures, and symbols
Demonstrate
the addition and subtraction of whole numbers, using objects, pictures, and
symbols
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3. Geometry
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Recognize
plane shapes – circle, triangle, square, and rectangle
Recognize
similar shapes in the environment
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Identify
number of sides in a basic plane shape
Recognize
similar shapes in the environment
Expand
use of positional words to include left and right
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Recognize
basic solid figures – cubes, cylinders, pyramids, spheres, rectangular
solids, and cone
Recognize
symmetric figures
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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3. Geometry
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Draw
shapes – circle, triangle, square, and rectangle
Classify
by size, color, and shape
Use
positional words to describe the relationship of two or more objects (over,
under, beside, etc.)
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Identify
number of angles/sides in basic plane shapes in the environment
Recognize
similar shapes in the environment
Recognize
rotated shapes
Explore
symmetry through paper folding & cutting
Investigate
and predict the results of combining, dividing, and changing 2 dimensional
shapes
Further
expand use of positional words to include: to the left of, to the right of,
vertical, horizontal, etc.
Explore
concept of area, perimeter, and volume using non-standard measures
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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4. Measurement
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Explore
the reasons for measuring objects
Measure
with non-standard unit of measure (length, weight)
Use
the terms morning, afternoon and night correctly
Read
clocks to the hour – analog & digital
Read
calendars to identify current month, day, date, and year
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Read
a ruler to nearest whole inch
Measure
length and height with non-standard and customary units (inches)
Weigh
with non-customary units
Choose
appropriate measuring tools
Read
clocks to hour and half hour – analog & digital
Expand
use of calendars to include yesterday, today and tomorrow
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Measure
in inches, feet and centimeters
Estimate
length to the nearest whole inch or foot
Read
balance scales
Read
thermometers (F)
Understand
second, minute, hour, day, week, month, season, and year as unit of time
Tell
time to five-minute intervals – analog and digital
Expand
the use of calendars to identify dates in the recent future and past
Weigh
using pounds and grams
Measure
using cups, pints, quarts, and liters
Choose
appropriate units of measure
Understand
60 minutes in an hour and 30 minutes in half hour
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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5. Data Analysis and Probability
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Read charts
Interpret
simple charts
Read
simple pictograph using key
Draw
conclusions from graphs
Read
and interpret bar graphs
Use
concepts of chance to predict and record outcomes of simple events
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Read charts
Interpret
simple charts
Read
simple pictograph using key
Draw
conclusions from graphs
Read
and interpret bar graphs
Use
concepts of chance to predict and record outcomes of simple events
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Read charts
Interpret
simple charts
Read
simple pictograph using key
Draw
conclusions from graphs
Read
and interpret bar graphs
Collect and organize
data to make a graph include tallies, check marks and pictoral
representations
Use
concepts of chance to predict and record outcomes of simple events
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6. Problem Solving
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Tell the number sentence
that could be used to solve the word problem
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Write the number
sentence that could be used to solve a word problem
Use
the best operation for solving a problem
Explain
orally how you solved the problem
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Design
a picture that represents a problem
Choose the best strategy
to solve a problem
Choose
the best strategy to solve a problem; solve the problem with work shown and
explanation given; and label the solution appropriately
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Skill Area:
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The student will be able
to:
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Kindergarten
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Grade 1
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Grade 2
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7. Reasoning and Proof
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Understand estimation is
a reasonable guess
Visually
estimate number of objects (guessing jar, comparing objects)
Check
work to see if the solution is reasonable
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Use estimation skills to
compare number, length, and weight
Check
work to see if the solution is reasonable
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Use
estimation skills to include estimate of number, height, weight, and length
of time
Check
work to see if the solution is reasonable
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8. Communication
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Communicate his/her
mathematical thinking coherently and clearly to others, in a grade
appropriate manner
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Communicate his/her
mathematical thinking coherently and clearly to others, in a grade
appropriate manner
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Communicate
his/her mathematical thinking coherently and clearly to others, in a grade
appropriate manner
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9. Connections
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Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize
and apply mathematics in contexts outside of mathematics
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Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize and apply
mathematics in contexts outside of mathematics
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Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize
and apply mathematics in contexts outside of mathematics
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Return
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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1. Number and
Operations
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Know
place value to thousands
Write
in expanded notation
Read
and write numbers through thousands
Round
off numbers to tens and hundreds
Rewrite
numerals into words and words into numerals to 999
Recognize
any even and odd number
Recognize
and use ( )
Add/subtract
up to 3 digit numbers with or without regrouping
Solve
written word problems with work shown and explanation given
Know
multiplication facts 0 – 5
Multiply
two or three digit numbers by a one digit number
Divide
a 2 digit number by a 1 digit number with or without remainders
Know
subtract facts through 18
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Know place value to 1 million
Write number in expanded notation
through hundred thousand
Round off numbers to thousands
Add/subtract multi-digit numbers
with and without regrouping
Know multiplication facts up to
the tens
Multiply two-digit numbers by two
digit numbers
Divide any number by one digit
with or without a remainder
Solve word problems with work
shown and explanation given
Create equivalent fractions
Add/subtract fractions with like
denominators
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Round off numbers to ten thousand
Read number line including decimal
numbers
Determine greatest common factor
Determine least common multiple
Name and use the divisibility
rules for 2, 3, 5, and 10
Explore exponents
Add and subtract any whole numbers
fluently
Multiply three digit number by two
digit numbers
Divide by one digit and two digit
divisors
Demonstrate order of operations
using parentheses and explain order of operations (M, D, A, S)
Add or subtract fractions with
like and unlike denominators
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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1. Number and
Operations
(continued)
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Recognize
and use equivalent fractions
Add
and subtract fractions with like denominators
Recognize
shaded areas as fractional parts
Make
change up to $1.00 using fewest possible coins
Add/subtract
decimals with dollar signs
Solve
one and two step word problems involving money with work shown and
explanation given
Add
decimal numbers
Estimate
total cost of several items with prices given
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Understand
the concept of mixed numbers
Add,
subtract and multiply decimals with dollar signs
Solve
one and two step word problems involving money with work shown and
explanation given
Estimate
total cost of several items with prices given
Make
change up to $5.00 using the fewest possible coins and bill
Add/subtract
decimal numbers
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Add
and subtract mixed numbers
Calculate
the fractional part of a whole number
Discuss
and solve routine one and two step word problems requiring addition and
subtraction of fractions with work shown and explanation given
Order
fractions
Add
or subtract numbers with varying numbers of decimal places
Solve
routine word problems involving decimals
Compare
decimals to the thousandths place
Recognize
and generate equivalent forms of commonly used fractions, decimals, and
percents
Describe
classes of #’s according to characteristics
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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1. Number and
Operations
(continued)
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Explore
ratios and proportions of whole numbers
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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2. Algebra
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Find
replacements for variables that make single operation number sentences true
Investigate
how a change in one variable relates to a change in another variable
Represent
the idea of a variable as an unknown quantity using letters or symbols
Identify
and continue complex numeric and geometric patterns
Identify
and use commutative property to compute with whole numbers
Express
mathematical relationship using equations
Represent
and analyze patterns and functions using words
Use
representations such as graphs, tables, and equations to draw conclusions
Identify
and describe situations with constant or varying rates of change and
compare them
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Find
replacements for variables that make dual operation number sentences true
Investigate
how a change in one variable relates to a change in a second variable
Represent
the idea of a variable as an unknown quantity using a letter or symbol
Identify
and use the commutative and associative properties to compute with whole
numbers
Express
mathematical relationships using equations
Identify
and continue complex numeric and geometric patterns
Represent
and analyze patterns and functions using words and tables
Use
representations such as graphs, tables, and equations to draw conclusions
Identify
and describe situations with constant or varying rates of change and
compare them (students should have opportunities to study situations that
display different patterns of change – constant such as someone walking at
a constant speed; rate change (increase or decrease) such as plants
growing)
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Find
replacements for variables that make multiple operation number sentences
true
Investigate
how to change in one variable relates to a change in a second variable
Represent
variables as a letter or symbol
Identify
and use the commutative, associative and distributive properties
Express
mathematical relationships using equations
Identify
and continue complex numeric and geometric patterns
Represent
and analyze patterns and functions using words, tables, and graphs
Use
representations such as words, tables, and graphs
Identify
and describe situations with constant or varying rates of change and
compare them
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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3. Geometry
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Recognize
number of angles/sides in basic plane figure
Identify
basic plane figures/polygons
Identify,
compare, and analyze attributes of two dimensional shapes
Put
together needed blocks to complete larger blocks
Recognize
result of cutting solid shapes (solid/cross sections)
Recognize
rotating two dimensional figures
Identify
congruent and symmetrical figures
Experiment
with paper folding cutting/symmetry
Build
and/or draw geometric objects
Use
the properties of shapes and figures to describe the physical world
Use
geometric models to solve problems in other areas of mathematics, such as
number and measurement
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Identify number of angles/sides in
basic plane figure
Identify basic plane
figures/polygons
Identify and build a three dimensional
representation of a two dimensional object
Predict and describe the results
of rotating two dimension figures
Recognize and describe line of
symmetry in two dimensional figures
Use geometric models to solve
problems in other areas of mathematics, such as number and measurement
Use the properties of shapes and
figures to describe the physical world
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Identify basic plane
figures/polygons
Identify types of quadrilaterals
Identify basic solid shapes
Know there are 360 degrees in a circle
Estimate the size of an angle
Use properties of circles
Find the coordinates of a point
Identify and describe congruent,
similar, and symmetric figures
Identify and build two dimensional
representation of a three dimension object
Discuss and define the properties
of triangles
Identify
the different types of triangles
Predict
and describe the results of sliding, flipping, and turning two dimensional
shapes and designs
Identify
and describe line and rotational symmetry in two dimensional and three
dimensional shapes and designs
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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3. Geometry (continued)
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Recognize
geometric ideas and relationships and apply them to other disciplines and
to problems that arise in the classroom or in everyday life
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Use
geometric models to solve problems in other areas of mathematics, such as
number and measurement
Recognize
geometric ideas and relationships and apply them to other disciplines and
to problems that arise in the classroom or in everyday life
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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4. Measurement
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Compute
perimeter of a rectangle
Compute
the area of a rectangle using blocks
Tell
time to the minute-analog and digital
Know
concept of a.m. and p.m.
Read
thermometers
Read
scales
Read
and use calendars
Estimate
and measure to nearest inch, centimeter, foot, yard, and meter
Convert
cups, pints, quarts and gallons using a visual aid
Estimate
and weigh using 16 oz.
Read
map scales
Convert
minutes after hour to minutes before hour
Estimate
distance on a map using key
Choose
appropriate units and tools of measurement
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Compute
perimeter of any polygon
Compute
area of a rectangle using formula: length times width
Determine
the surface areas and volumes of rectangular solids
Read
map scales
Estimate
distance on a map using a scale
Measure
to the ¼ inch
Read
thermometers
Read
clock
Convert
minutes after hour to minutes before next hour
Convert
inches to feet and feet to inches
Estimate
and measure to nearest meter
Convert
feet to yards and yards to feet
Convert
ounces to pounds and pounds to ounces
Choose
appropriate units and tools of measurement
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Compute
the area of a rectangle, triangle, and parallelogram
Read
protractors
Read
rulers to the nearest quarter inch
Read
thermometers
Develop
strategies for estimating the perimeters, areas, and volumes of irregular
shapes
Convert
unit equivalents within the metric system
Convert
unit equivalents with the English system
Experiment
with the selection of the appropriate metric unit of measuring a particular
linear distance
Choose
appropriate units and tools of measurement
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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4. Measurement
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Understand
such attributes as length, area, weight, volume, and size of angle and
select the appropriate type of units for measuring each attribute
Understand
that measurements are approximations and understand how differences in
units affect precision
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Understand
such attributes as length, area, weight, volume, and size of angle and
select the appropriate type of unit for measuring each attribute
Understand
that measurements are approximations and understand how differences in
units affect precision
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Understand
that measurement are approximations and understand how differences in units
affect precision
Explore
what happens to measurements of a two dimensional shape such as its
perimeter and area when the shape is changed in some way
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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5. Data Analysis and Probability
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Collect
and organize data using observations, surveys, and experiments
Represent
data using various types of graphs, charts, and tables
Represent
data using bar graphs, line graphs, pictographs, and tables
Use
concepts of chance to predict the probability of outcomes and test the
predictions
Compare
different representations of the same data and evaluate how well each
representation shows important aspects of the data
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Collect and organize data using
observations, surveys, and experiments
Read and interpret various types
of graphs, charts, and tables
Draw conclusions from graphs
Represent data using bar graphs,
pictographs, and tables
Use concepts of chance to predict
the probability of outcomes and test the predictions
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Collect data using observations,
surveys, and experiments
Represent data using bar graphs,
pictographs, circle graphs, and tables
Use concepts of chance to predict
the probability of outcomes and test the predictions
Compare different representations
of the same data and evaluate how well each representation shows important
aspects of the data
Organize and analyze data using
mean, median, mode, and range
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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6. Problem Solving
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Restate a problem
Choose
the best strategy to solve a single or multi-step problem: i.e., picture,
graph, table, number sentence, etc.
Solve
the problem with work shown and explanation given
Determine
essential information to solve a problem
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Restate
a problem
Choose
the best strategy to solve a single or multi-step problem: i.e., picture,
graph, table, number sentence, etc.
Solve
the problem with work shown and explanation given
Determine
essential information to solve a problem
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Restate
a problem
Choose
the best strategy to solve a single or multi-step problem: i.e., picture,
graph, table, number sentence, etc.
Solve
the problem with work shown and explanation given
Determine
essential information to solve a problem
Interpret
and solve non routine word problems
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Skill Area:
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The student will be able
to:
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Grade 3
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Grade 4
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Grade 5
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7. Reasoning and Proof
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Using
estimation skills to make and investigate mathematical conjectures
Check
work to see if the answer is reasonable
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Using
estimation skills to make and investigate mathematical conjectures
Check
work to see if the answer is reasonable
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Using
estimation skills to make and investigate mathematical conjectures
Check
work to see if the answer is reasonable
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8. Communication
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Communicate their
mathematical thinking coherently and clearly to others, in a grade
appropriate manner
|
Communicate their
mathematical thinking coherently and clearly to others, in a grade
appropriate manner
|
Communicate
their mathematical thinking coherently and clearly to others, in a grade
appropriate manner
|
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9. Connections
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Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize
and apply mathematics in contexts outside of mathematics (use simple tables
and graphs to communicate ideas and information in a concise and clear
manner)
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Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize and apply
mathematics in contexts outside of mathematics
|
Recognize and use
connections among mathematical ideas
Understand
how mathematical ideas interconnect and build on one another to produce a
coherent whole
Recognize
and apply mathematics in contexts outside of mathematics
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Return
Grades 6 - 8
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Data Analysis and Probability
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STANDARD
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EXPECTATION
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Instructional Programs from
grade 6-8 should enable students to-
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In grade 6 all students
should-
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In grade 7 all students should-
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In grade 8 all students should-
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Formulate questions that can
be addressed with data and collect, organize, and display relevant data to
answer them
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collect data about a
characteristic
shared by two populations or different characteristics within one
population
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collect data about a
characteristic
shared by two populations or different characteristics within one
population
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formulate questions, design
studies, and collect data about a characteristic
shared by two populations or different characteristics within one
population
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select, create, and use
appropriate
graphical representations of data, including line, bar, pie pictograph,
line plots, stem and leaf and circle graphs
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create, and use appropriate
graphical representations of data, including, but not limited to, histograms, box plots, and scatterplots
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select, create, and use
appropriate
graphical representations of data, including, but not limited to,
histograms, box plots, and scatterplots
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Select and use appropriate
statistical methods to analyze data
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find measures of center and
spread (to
include median and mode) including mean, median, mode and range
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use and interpret measures of
center and spread (to include median and mode) including mean and
interquartile range
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discuss and understand the
correspondence between data sets and their graphical
representations,especially histograms, stem-and-leaf plots, box plots, and
scatterplots
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Develop and evaluate inferences
and predictions that are based on data
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use observations about
differences between two or more samples to make conjectures about the
populations from which the samples were taken
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