Math back
By the end of Kindergarten,
ASES students will be able to:
- Count by 1’s and 10’s to 100;
- Count by 5’s to 50;
- Count backwards from 10;
- Match sets and numbers (1 – 20);
- Identify, read, and write numbers to 20;
- Order one- and two-digit numbers;
- Identify equivalent sets;
- Compare sets of objects;
- Compare numbers through 20;
- Identify greatest and least;
- Identify more, same, and less;
- Identify numbers on a hundred number chart;
- Identify numbers before, after, and between;
- Estimate and count collections of objects to 100;
- Identify ordinal position;
- Find addition and subtraction answers using
pictures;
- Identify one more than a number;
- Identify one less than a number;
- Divide a set of objects into equal groups;
- Identify one half of pictured object;
- Divide a shape in half;
- Name and identify penny and its value;
- Name and identify dime and its value;
- Name and identify nickel and its value;
- Identify quarters and one-dollar bills;
- Identify, sort, and compare geometric shapes;
- Identify, sort, and compare common geometric
solids;
- Make and copy designs on a geoboard;
- Make and cover designs using tangrams;
- Create congruent shapes and designs;
- Identify similar shapes;
- Use positional words and phrases;
- Identify right and left;
- Identify today’s date;
- Identify yesterday, today, and tomorrow;
- Identify days of the week and months of the year;
- Identify seasons;
- Identify morning, afternoon, evening, and night;
- Tell and show time to the hour;
- Identify hot and cold objects;
- Compare and order objects by length;
- Estimate and measure length using nonstandard
units;
- Estimate and measure distance using nonstandard
units;
- Order objects by height;
- Compare and order objects by weight;
- Compare the capacity of containers;
- Compare and order objects by size;
- Sort objects and identify a sorting rule;
- Graph a picture on a pictograph;
- Make a real graph;
- Identify most, fewest, and same on a graph;
- Identify, read, and extend color patterns;
- Identify, read, and extend shape patterns;
- Identify the missing shape in a matrix;
- Identify, extend, and create sound and movement
patterns;
- Identify the missing number in a sequence.
By the end of First Grade, ASES students will be
able to:
- Count by 1’s and 5’s to 100
- Count by 2’s and 10’s to 100
- Draw pictures and write number sentences to solve
addition problems
- Master addition facts: doubles to 18
- Master addition facts: one to a number
- Master addition facts: adding 0 to a number
- Master addition facts: adding 2 to an even and
odd number
- Master addition facts: adding doubles plus one
- Master addition facts: sums of 10
- Add 2-digit numbers with regrouping
- Master addition facts: adding 9 to a number
- Master addition facts: adding four of the last
eight facts
- Master addition facts: the last four facts
- Add three single-digit numbers
- Draw pictures and write number sentences to solve
subtraction problems
- Master subtraction facts: subtracting 1 from a
number
- Master subtraction facts: subtracting 0 and
subtracting a number from itself
- Master subtraction facts: subtracting 2 from a
number
- Master subtraction facts: subtracting a number
from ten
- Master subtraction facts: differences of 1
- Master subtraction facts: differences of 2
- Master subtraction facts: subtracting half a
double
- Identify ten less than a number
- Master subtraction facts: 9-4, 9-5, 9-3, 9-6,
7-3, 7-4, 8-3, 8-5
- Check subtraction answers using addition
- Identify and know the value of a penny, a nickel,
a dime and a quarter
- Identify, know value and count all coins
- Write money amounts using cents symbol
- Identify one dollar
- Count dimes, nickels and pennies
- Select coins for a given amount up to $1.00
- Weigh objects using nonstandard units
- Measure and draw line segments to nearest inch
Identify 10 more than a number
- Measure length using nonstandard units
- Measure capacity using standard units
- Measure length using customary units
- Draw line segments using customary units and
centimeters
- Compare and order container by capacity (quart,
gallon and liter)
- Tell and show time to the hour and half hour
- Order events by time
- Match and set numbers
- Read and write numbers to 50
- Identify first, last, between and middle
- Identify ordinal positions to sixth
- Write numbers to ten using words
- Solve problems using a calendar
- Identify the missing number in a sequence to 50
- Graph data on a bar graph
- Draw and read a bar graph
- Identify even and odd numbers
- Identify pairs
- Identify ½ and ¼ of a fractional whole
- Identify addends and sums
- Identify dozen and half dozen
- Divide a set of objects into equal groups
- Identify the fractional parts of a whole
- Identify the fractional parts of a set
- Write observations about a graph
- Use comparison symbols (<, >, and =)
- Identify 1/3rd and 1/6th
- Read a Fahrenheit thermometer to the nearest 10
degrees
- Identify cold, cool, warm and hot temperatures
- Count by 100’s
- Subtract 2-digit numbers without regrouping
- Identify geometric shape: rectangular prism,
cones, spheres, cubes and cylinders
- Identify angles and sides of a polygon
- Identify and describe 3-dimensional geometric
objects
- Identify and create congruent shapes and designs
- Compare and order objects by length
- Identify the missing shape or design in a
repeating pattern
- Sort and classify objects
By the end of Second Grade, the
ASES student will be able to:
- Count by 3’s, 4’s, 25’s, and 100’s;
- Read and write numbers to 1,000;
- Compare numbers to 1,000;
- Order 2- and 3-digit numbers;
- Round number to the nearest ten;
- Write numbers in expanded form;
- Identify addends and sums;
- Write addition and subtraction fact families;
- Identify and use the commutative and associative
properties;
- Act out, draw pictures of, and writes number
sentences to show multiplication;
- Make, label, and write number sentences for an
array;
- Identify the properties of 0 and 1 in
multiplication;
- Add using mental computation;
- Add three or more single-digit numbers;
- Add 3-digit numbers and money amounts (decimals);
- Subtract using mental computation;
- Subtract 3-digit numbers and money amounts
(decimals);
- Master multiplication facts (0, 1, 2, 3, 4, 5);
- Multiplies by 10
and 100;
- Doubles a number;
- Solve problems involving multiplication;
- Divide by 2;
- Solve problems involving division;
- Write a fraction to show a part of a whole;
- Name and compare unit fractions;
- Write a fraction to show a part of a set;
- Identify equivalent fractions using concrete
objects;
- Represent and write mixed numbers;
- Select coins for a given amount;
- Make change from a $1.00;
- Identify, describe, and classify polygons;
- Identify and draw a line of symmetry;
- Tell and show time to the quarter hour, 5 minutes
and minute;
- Find elapsed time;
- Identify a.m. and p.m.;
- Write the date using digits;
- Identify equivalent units of time;
- Identify weekdays and days of the weekend;
- Read a Fahrenheit thermometer;
- Draw line segments using customary units (nearest
inch and half inch);
- Measure length using metric units (nearest
centimeter);
- Identify units of mass: customary or metric;
- Weigh object using customary or metric units;
- Order containers by capacity;
- Compare and order objects by size (area);
- Find area using nonstandard units;
- Estimate area;
- Find area of rectangle;
- Find perimeter of a polygon;
- Draw and read a pictograph;
- Tallies;
- Create and read a Venn diagram;
- Describe the likelihood of an event;
- Locate points of a number line;
- Locate and graph points on a coordinate graph.
By the end of the Third Grade, ASES
students will be able to:
·
Count
by 2's, 3's, 4's, 5's, 6's, 7's, 8's, 9's, and10's
·
Begin
to count by 12's, 25's, 100's, halves, and fourths
·
Reads
and write numbers to 100,000
·
Begin
to read and write money amounts to $99,999.99
·
Compare
numbers to 10,000
·
Order
2-, 3-, and 4-digit numbers
·
Begin
to round numbers to the nearest ten, hundred, and thousand
·
Begin
to identify place value in numbers to 100,000,000
·
Represent
3- and 4-digit numbers using concrete materials and pictures
·
Estimate
and count large collections
·
Begin
to write numbers in expanded form
·
Rename
numbers using grouping
·
Identify
ordinal position
·
Begin
to identify even and odd numbers
·
Identify
dozen and half dozen
·
Begin
to write numbers using words
·
Begin
to identify factors of a number
·
Begin
to identify multiples of a number
·
Begin
to identify prime numbers
·
Begin
to square numbers
·
Begin
to find square roots of perfect squares
·
Begins
to read and write Roman numerals
·
Begins
to act out, draw pictures of, and write number sentences to show addition and
subtraction
·
Identify
addends and sums
·
Write
addition and subtraction fact families
·
Begin
to act out, draw pictures of , and write number sentences to show
multiplication
·
Begin
to make, label, and write number sentences for an array
·
Identify
factors and products
·
Begin
to identify and use commutative and associative property
·
Identify
the properties of 0 and 1 in multiplication and division
·
Write
multiplication and division fact families
·
Act
out, draw pictures of, and write number sentences to show division
·
Identify
quotients
·
Begin
to write division problems in three ways
·
Identify
ten more than a number
·
Master
addition facts to 18
·
Identify
missing addends
·
Identify
a missing digit in an addition problem
·
Begin
to estimate a sum
·
Add
using mental computation
·
Add
three or more single-digit numbers
·
Add
2- and 3-digit numbers
·
Begin
to use estimation to check the reasonableness of calculated results
·
Add
whole numbers and money amounts (decimals) to $9,999.99
·
Begin
to solve problems using addition
·
Begin
to write story problems for addition number sentences
·
Master
subtraction facts to 18
·
Identify
ten less than a number
·
Estimate
a difference
·
Subtract
using 2- and 3-digit numbers
·
Begin
to subtract money amounts (decimals)
·
Begin
to check subtraction answers using addition
·
Begin
to solve problems involving subtraction
·
Begin
to write story problems for subtraction number sentences
·
Multiply
by 10, 100, and 1000
·
Master
Multiplication facts 0- 12's
·
Begin
to multiply using mental computation
·
Begin
using the multiply using the multiplication algorithm
·
Begin
to solve problems involving multiplication
·
Master
division facts 0-12's
·
Divide
by 10
·
Begin
to divide using mental computation
·
Divide
2- and 3-digit multiples of 10 by a 1-digit number
·
Begin
to check division answers using multiplication
·
Begin
to solve problems involving division
·
Begin
to identify fractional parts of a whole
·
Begin
to write a fraction to show a part of a whole
·
Begin
to identify a fractional part of a set
·
Begin
to compare fractions
·
Begin
to order fractions
·
Begin
to identify fractions equivalent to one-half
·
Find
half of a set of objects
·
Begin
to represent and write mixed numbers
·
Begin
to write tenths using common and decimal fractions
·
Begin
to write hundredths using common and decimal fractions
·
Write
fraction number sentences that equal one
·
Begin
to add and subtract fractions
·
Add
whole numbers and money amounts (decimals)
·
Subtract
money amounts (decimals)
·
Count
money to the hundreds of dollars
·
Begin
to compare the value of sets of coins
·
Begin
to write money amounts using the cent and dollar signs
·
Begin
to select coins for a given amount
·
Make
change from $1.00, $5.00, and $10.00
·
Begin
to write a check
·
Identify
and describe polygons
·
Begin
to identify and draw congruent line segments and shapes
·
Begin
to solve spatial problems
·
Begin
to sort common geometric shapes by attribute
·
Begins
to name line segments
·
Begin
to identify horizontal, vertical, and oblique line segments
·
Begin
to identify and draw a line of symmetry
·
Begin
to identify parallel lines and line segments
·
Begin
identify intersecting lines
·
Begin
to identify perpendicular lines and line segments
·
Begin
to identify right, acute, and obtuse angles
·
Begin
to name triangles by angle size
·
Begin
to identify and show transformations: translations, rotations, and reflections
·
Identify
and classify 3-demensional geometric objects
·
Identify
faces, vertices, and edges of a geometric solid
·
Begin
to construct a geometric solid
·
Tell
and show time to the hour, half hour, quarter hour
·
Begin
to show time to 5 minutes and minute
·
Begin
to find elapsed time
·
Begin
to identify a.m. and p.m.;
·
Begin
to write the date using digits
·
Begin
to identify equivalent units of time
·
Begin
to solve problems using a calendar
·
Begin
to estimate temperature
·
Begin
to read a Fahrenheit or Celsius thermometer
·
Begin
to identify common temperatures
·
Begin
to estimate length and distance
·
Begin
to measure length using nonstandard units
·
Begin
to measure length using customary units (nearest inch, half inch, quarter inch,
foot, and yard)
·
Begin
to draw line segments using customary units (nearest inch, half inch, and
quarter inch)
·
Begin
to measures length using metric units (nearest centimeter, millimeter, and
meter)
·
Begin
to draw line segments using metric units (nearest centimeter and millimeter)
·
Begin
to identify equivalent units of linear measure
·
Begins
to use scale to find distance on a map
·
Begins
to identify units of mass: customary and metric
·
Begins
to estimate mass
·
Begins
to weigh objects using customary or metric units
·
Begins
to estimate capacity
·
Begins
to order containers by capacity
·
Begin
to measure capacity using standard units
·
Begin
to identify equivalent units of capacity
·
Begin
to follow a recipe and measure
·
Compare
and order objects by size (area)
·
Begin
to find area using nonstandard units
·
Begin
to estimate area
·
Find
area of a rectangle
·
Find
perimeter of a polygon
·
Find
volume of a rectangular prism
·
Begin
to draw and read a bar graph with a scale of 10
·
Begin
to draw and read a line graph
·
Begin
to draw and read a pictograph
·
Begin
to Tally on a graph
·
Begin
to write observations about a graph
·
Begin
to conduct surveys
·
Begin
to describe the likelihood of an event
·
Begin
to predict the outcome of a probability experiment
·
Begin
to determine the fairness of a game
·
Begin
to conduct a probability experiment
·
Use
comparison symbols (>,<, and =)
·
Begins
to construct a number line and locates points on the number line
·
Begin
to show addition, subtraction, and multiplication on a number line
·
Begin
to add positive and negative numbers
·
Identify
the missing number in a sequence
·
Identify
the missing shape or design in a repeating pattern
·
Begin
to identify the missing shape or number in a matrix
·
Begin
to identify the function rule
·
Begin
to make an organized list to solve a problem
·
Begin
to simplify expressions containing parenthesis
·
Begin
to simplify expressions containing addition, subtraction, multiplication, and
division
·
Begin
to locate and graph points on a coordinate graph
By the end of the Fourth Grade, ASES
students will be able to:
·
Count
by 1's, 2's,3's,4's,5's,6's,7's,8's,9's,10's,12's,25's,100's,100's, halves, and
fourths
·
Read
and write numbers to 1,000,000,000
·
Read
and write money amounts to $99,999.99
·
Compare
and order numbers with 2, 3, and 4 or more digits
·
Round
numbers to the nearest ten, hundred, and thousand
·
Identifies
place value in numbers to 100,000,000
·
Write
a number in expanded form
·
Identify
even and odd numbers
·
Write
numbers using words
·
Identify
multiples of a number
·
Identify
prime numbers and composite numbers
·
Identify
perfect squares
·
Identify
and approximate square roots
·
Identify
cube roots and perfect cubes
·
Identify
rational numbers from pictures and draws pictures to show rational numbers
·
Locate
rational numbers on a number line
·
Identify
the approximate value of r
·
Identify
addends, sums, factors, products, differences, quotients, dividends, and
divisors
·
Acts
out, draws pictures of, and writes number sentences to show addition and
subtraction
·
Identify
and use the commutative and associative properties
·
Act
out, draw pictures of, and write number sentences to show multiplication and division
·
Make,
label, and write number sentences for an array
·
Use
the order of operations to simplify expressions
·
Write
division problems in three ways
·
Master
basic addition facts
·
Identify
missing addends
·
Estimate
a sum
·
Add
four or more single digit numbers
·
Add
4- and 5- digit numbers
·
Use
estimation to check the reasonableness of sums
·
Add
whole numbers and money amounts (decimals) to $99,999.99
·
Solve
problems involving addition
·
Write
story problems for addition number sentences
·
Master
basic subtraction facts
·
Subtract
using mental computation
·
Subtract
numbers with 2 to 5 digits
·
Subtract
money amounts (decimals)
·
Check
subtraction answers using addition
·
Solve
problems involving subtraction
·
Write
story problems for subtraction number sentences
·
Master
multiplication facts
·
Divide
2-, 3-, and 4- digit numbers by a single-digit numbers
·
Check
division answers using multiplication
·
Solve
problems involving division
·
Identify
fractional parts of a whole
·
Write
a fraction to show part of a set
·
Compare
fractions
·
Order
fractions
·
Identify
equivalent fractions
·
Identify
a fractional part of a set
·
Represent
and writes mixed numbers
·
Write
tenths using common and decimal fractions
·
Write
hundredths using common and decimal fractions
·
Pictures
decimal fractions
·
Add
and subtract fractions
·
Count
money
·
Compare
the value of sets of coins
·
Write
money amounts using the cent and dollar signs
·
Select
coins for a given amount
·
Make
change from $1.00 to $10.00
·
Estimate
and find amount of sales tax
·
Identify,
describe, and classify polygons
·
Identify
and draw congruent line segments and shapes
·
Solves
spatial problems
·
Identify
and sort common geometric shapes by attributes
·
Name
line segments
·
Identify
horizontal, vertical, and oblique line segments
·
Identify
and draw a line of symmetry
·
Identify
parallel lines and line segments
·
Identify
intersecting lines
·
Identify
perpendicular lines and line segments
·
Identify
right, acute, and obtuse angles
·
Identify
straight angles
·
Identify
and show transformations: translations, rotations, and reflections
·
Identify,
describe, and classify 3-dimensional geometric objects
·
Identify
faces, vertices, and edges of a geometric solid
·
Constructs
a geometric solid
·
Tell
and show time to the hour, half hour, quarter, 5 minutes, minute, and second
·
Find
elapsed time
·
Identify
a.m. and p.m.;
·
Write
date using digits
·
Identify
equivalent units of time
·
Estimate
temperature
·
Read
a Fahrenheit or Celsius thermometer
·
Identify
common temperatures
·
Estimate
length and distance
·
Measure
length using customary units (nearest inch, half inch, quarter inch, one-eighth
inch, and one-sixteenth inch)
·
Draw
line segments using customary units (nearest inch, half inch, quarter inch,
one-eighth inch, and one-sixteenth inch)
·
Measure
length using metric units (nearest centimeter, millimeter, and meter)
·
Draw
line segments using metric units (nearest centimeter and millimeter)
·
Identify
equivalent units of linear measure
·
Use
scale to find distance on a map
·
Identify
units of mass: customary or metric
·
Estimate
mass
·
Weighs
objects using customary or metric units
·
Estimate
capacity
·
Order
containers by capacity
·
Measure
capacity using standard units
·
Identify
equivalent units of capacity
·
Compare
and order objects by size
·
Measure
area using nonstandard units
·
Estimate
area
·
Measure
area of a rectangle
·
Measure
perimeter of a polygon
·
Measure
volume of a rectangular prism
·
Measure
volume of a cube
·
Graph
data on a bar graph
·
Draw
and read a bar graph
·
Draw
and read a bar graph with a scale of 2 or 10
·
Draw
and read a line graph
·
Draw
and read a line graph
·
Uses
a tally
·
Write
observations from a graph
·
Conduct
a survey
·
Find
the mean (average) and median of a set of data
·
Describe
the likelihood of an event
·
Predict
the outcome of a probability experiment
·
Conduct
a probability experiment
·
Use
comparison symbols (<, >, and =)
·
Construct
a number line and locate points on a number line
·
Graph
large numbers on a number line
·
Identify
the missing number in a sequence
·
Identify
the missing shape or design in a repeating pattern
·
Make,
label, and write number sentences for an array
·
Identify
the missing number in an array
·
Identify
and write a function rule
·
Make
an organized list to solve a problem
·
Make
a table to solve a problem
·
Draw
a picture to solve a problem
·
Simplify
expressions containing addition, subtraction, multiplication, and division
By the end of the Fifth Grade, ASES
students will be able to:
·
Use
sequencing with digits
·
Identify
even and odd numbers
·
Use
money to illustrate place value
·
Compare
whole numbers
·
Name
whole numbers through hundreds
·
Use
the addition algorithm
·
Write
and compare numbers through hundred thousands
·
Use
ordinal numbers
·
Use
fact families
·
Use
the subtraction algorithm
·
Identify
missing addends
·
Write
story problems
·
Write
story problems about combining
·
Draw
lines, number lines, and tally marks
·
Identify
multiplication as repeated addition
·
Add
and subtract dollars and cents
·
Identify
missing numbers in subtraction
·
Make
a multiplication table
·
Write
story problems about separating
·
Multiply
with three factors
·
Identify
missing numbers in multiplication
·
Write
division three ways
·
Identify
and use fractions using halves, fourths, and tenths
·
Solve
problems about equal groups
·
Solve
division problems with remainder
·
Identify
divisibility by 2, 5, and 10
·
Recognize
halves
·
Use
parenthesis and associative property
·
Begin
to list the factors of whole numbers
·
Begin
to use division algorithms
·
Read
scales
·
Measure
time
·
Multiply
by multiples of 10 and 100
·
Begin
to interpret pictures of fractions and percents
·
Identify
fractions of thirds, fifths, and eighths
·
Use
pairs of lines
·
Identify
angles and polygons
·
Round
numbers using a number line
·
Solve
division problems with zeros in the quotient
·
Solve
problems about comparing and elapsed time
·
Classify
triangles
·
Draw
pictures of fractions
·
Identify
fractions and mixed numbers on a number line
·
Compare
fractions by drawing pictures
·
Draw
pictures of mixed numbers
·
Begin
to write quotients as mixed numbers
·
Begin
to add and subtract fractions and mixed numbers
·
Measure
length with a ruler
·
Begin
to classify quadrilaterals
·
Begin
to write stories about fractions of a group
·
Begin
to simplify mixed measures
·
Read
and write whole numbers in expanded notation
·
Solve
two-step word problems
·
Begin
to find an average
·
Begin
to organize and analyze data
·
Multiply
by two-digit numbers
·
Name
numbers through hundred billions
·
Find
perimeter and measurements of a circle
·
Divide
by multiples of ten
·
Multiply
by three digit numbers that include zero
·
Begin
to identify simple probability
·
Begin
to write quotients as mixed numbers
·
Subtract
a fraction from 1
·
Use
money to model decimal numbers
·
Identify
decimal parts of a meter
·
Read
a centimeter scale
·
Write
tenths and hundredths as decimal numbers
·
Name
decimal numbers
·
Identify
fractions of a second
·
Compare
and order decimal numbers
·
Write
equivalent decimal numbers
·
Recognize
patterns
·
Finds
area
·
Add
and subtract decimal numbers
·
Convert
units of length
·
Change
improper fractions to whole of mixed numbers
·
Convert
units of length
·
Begin
to multiply fractions
·
Begin
to convert units of weight and mass
·
Identify
exponents and powers
·
Find
equivalent fractions by multiplying by 1
·
Identify
prime and composite numbers
·
Display
data
·
Reduce
fractions
·
Find
greatest common factor
·
Identify
properties of geometric solids
·
Find
mean, median, mode, and range
·
Begin
to convert units of capacity
·
Multiply
fraction and whole numbers
·
Use
manipulatives and sketches to divide fractions
·
Find
a square root
·
Create
line graphs
·
Simplify
improper fractions
·
Divide
by two-digit numbers
·
Compare
bar graphs
·
Use
estimation when dividing by two-digit numbers
·
Identify
reciprocals
·
Use
reciprocals to divide fractions
·
Find
ratios
·
Use
negative numbers
·
Simplify
decimal numbers
·
Graph
points on a coordinate plane
·
Round
mixed numbers to the nearest whole number
·
Subtract
decimal numbers using 0
·
Round
decimal numbers to the nearest whole number
·
Identify
symmetry
·
Read
and order decimal numbers through ten-thousandths
·
Use
percent to name part of a group
·
Begin
to create schedules
·
Multiply
decimal numbers using 0 as placeholder
·
Begin
to create scale drawings
·
Multiply
decimal numbers by 10,100,and 1000
·
Begin
to find the least common multiple of two numbers
·
Write
mixed numbers as improper fractions
·
Solve
problems with many solutions
·
Identify
problems with no solution
·
Find
common denominators to add, subtract, and compare fractions
·
Divide
a decimal number by a whole number
·
Use
0 as a placeholder
·
Divide
decimal numbers by 10, 100,and 1000
·
Divide
by a decimal number
·
Multiply
mixed numbers
·
Use
tessellations
By the end of the Sixth Grade, ASES
students will be able to:
·
Add
to four digits without regrouping
·
Subtract
to four digits without regrouping
·
Multiply
three digits by three digits with regrouping
·
Divide
four digits by two digits
·
Add
mixed numbers with numbers with different denominators
·
Subtract
mixed numbers with different denominators
·
Multiply
mixed numbers
·
Divide
mixed numbers
·
Add
whole numbers with decimals to the hundredth place by aligning place value
·
Subtracting
whole numbers with decimals to the hundredth place by aligning place value
·
Multiplying
by decimals
·
Dividing
by decimals
·
Use
sequencing
·
Identify
divisibility rules
·
Estimate
whole numbers and decimals by rounding
·
Begin
to use prime factorization
·
Compare
whole numbers, fractions and decimals
·
Add,
subtract, multiply and divide money
·
Begin
to calculate sales tax
·
Round
money to the nearest cent
·
Find
compound interest
·
Begin
to create tables
·
Crate
bar and line graphs
·
Create
circle graphs
·
Plot
rectangular coordinates
·
Measure
angles using a protractor
·
Calculate
perimeter and area of rectangles
·
Begin
to calculate surface area of prisms
·
Begin
to calculate circumference and area of circles
·
Begin
to calculate perimeter and area of complex shapes
·
Find
elapsed time
·
Identify
U.S. Customary System of length, liquid, and weight
·
Identify
Metric system of length, liquid, and weight
·
Begin
to add, subtract, and convert mixed measures
·
Begin
to order and compare integers
·
Begin
to find the unknown in equations
·
Begin
to add and subtract signed numbers
·
Begin
to multiply signed numbers
·
Use
square roots and perfect squares
·
Begin
to estimate square roots
·
Use
order of operations with exponents and expanded notation with exponents
·
Begin
to multiply the powers of 10
·
Begin
to use simple ratio
·
Begin
to use simple proportion
·
Begin
to write rates as ratios
·
Begin
to use proportion to solve percent problems
·
Identify
average of two or more groups
·
Find
mean, median, mode and range
·
Find
simple probability and chance
·
Begin
to find compound probability
By the end of the Seventh Grade,
ASES students will be able to:
·
Reduce
and convert by using prime factorization
·
Multiply
and divide mixed numbers
·
Add
and subtract mixed numbers with different denominators
·
Find
the whole when a fraction is known
·
Add,
subtract and multiply decimals
·
Divide
by decimals
·
Begin
to identify fraction, decimal, and percent equivalents
·
Find
the percent of a whole
·
Find
the whole when a percent is known
·
Find
the percent of change
·
Identify
sequences and divisibility rules
·
Use
prime factorization
·
Estimate
whole numbers and decimals by rounding
·
Compare
whole numbers, fractions, and decimals
·
Begin
to graph inequalities
·
Round
money to the nearest dollar
·
Calculate
sales tax
·
Calculate
commission and profit
·
Begin
to calculate markup and markdown
·
Begin
to calculate simple and compound interest
·
Plot
rectangular coordinates
·
Create
bar, line, and pie graphs
·
Begin
to use graphing functions
·
Begin
to graph nonlinear equations
·
Measure
angles using a protractor
·
Begin
to classify quadrilaterals and triangles
·
Begin
to use transformations
·
Begin
to angle bisectors
·
Calculate
circumference and area of complex shapes
·
Begin
to use Pythagorean theorem
·
Calculate
perimeter and area of complex shapes
·
Calculate
surface area of prisms
·
Calculate
volume of pyramids, cones, and spheres
·
Use
U.S. Customary System of length, liquid, and weigh
·
Add,
subtract and convert mixed measures
·
Begin
to use unit multipliers and unit conversion
·
Identify
volume, capacity, and mass
·
Begin
to order and compare integers
·
Begin
to find negative exponents
·
Add
and subtract signed numbers
·
Multiply
and divide signed numbers
·
Identify
algebraic terms
·
Begin
to identify negative coefficients
·
Begin
to evaluate expressions with variables and signed numbers
·
Begin
to factor algebraic expressions
·
Begin
to evaluate exponential expressions
·
Use
square roots and perfect squares
·
Multiply
by powers of 10
·
Use
order of operations with exponents
·
Identify
large and small numbers in scientific notation
·
Multiply
numbers in scientific notation
·
Estimate
square roots
·
Solve
equations with exponents
·
Begin
to use simple proportion
·
Write
rates as ratios
·
Use
simple ratios
·
Begin
to identify implied ratios
·
Use
proportion to solve percent problems
·
Begin
to use scale and scale factor
·
Use
mean, median, mode and range
·
Use
average
·
Use
compound probability
·
Begin
to use probability, chance, and odds
By the end of the Eighth Grade, ASES
students in Pre-Algebra will be able
to:
·
Multiply,
divide, estimate, and order decimal numbers
·
Multiply
and divide by powers of 10
·
Manipulate
points, rays, line segments, angles, and perimeters
·
Use
divisibility
·
Solve
word problems about equal groups
·
Find
products of prime and composite numbers
·
Find
common factor and greatest common factor
·
Expand
and reduce fractions
·
Round
repeaters
·
Use
exponents correctly
·
Identify
areas of rectangles
·
Show
fractional parts of a number
·
Use
symbols for multiplication
·
Identify
multiples and least common multiples
·
Average
numbers in word problems
·
Begin
to use multiple fractional factors
·
Manipulate
U.S. Customary System and unit multipliers
·
Use
Metric System
·
Show
area as a difference
·
Identify
areas of triangles
·
Create
graphs
·
Begin
to use Order of Operations
·
Use
variables and evaluation
·
Multiply
Unit Multipliers
·
Show
conversion of Units of Area
·
Identify
rate and use rate in word problems
·
Find
answers and solutions to equations
·
Identify
rectangular coordinates
·
Identify
equivalent equations
·
Use
addition-subtraction rule for equations
·
Use
multiplication and division rule for reciprocals
·
Identify
overall average
·
Use
symbols of inclusion
·
Use
evaluation of exponential expressions and radicals
·
Solve
fractional equations
·
Identify
surface area
·
Show
scientific notation for numbers greater than 10 and numbers Between 0 and 1
·
Identify
fractions and symbols of inclusion
·
Use
ratio, percent, and proportion with fractions
·
Use
reference numbers
·
Solve
equations with mixed numbers
·
Solve
distance problems
·
Manipulate
circles and semicircles
·
Solve
equations in two steps
·
Identify
proportion with mixed numbers and similar triangles
·
Use
ratio in word problems
·
Use
ratio to compare
·
Visualize
percents less than 10
·
Identify
absolute value
·
Add
signed numbers
·
Use
powers and roots of fractions
·
Graph
inequalities
·
Begin
to identify right circular cylinders
·
Use
order of addition and insert parenthesis
·
Begin
to identify implied ratios
·
Use
multiplication with Scientific Notation
·
Show
percents greater than 100
·
Identify
opposites
·
Begin
to simplify more difficult notation
·
Show
increases in percents
·
Multiply
and divide signed numbers
·
Use
evaluation with signed numbers
·
Rate
problems as proportion problems
·
Use
formats for the addition rule
·
Identify
negative coefficients and properties of equality
·
Solve
equations of a line
·
Graph
a line
·
Use
algebraic phrases
·
Identify
properties of algebra
·
Find
surface area of a right solid
·
Begin
to use trichotomy and symbols of negation
·
Begin
to form algebraic sentences
·
Use
Order of Operations with signed numbers and symbols of inclusion
·
Estimate
roots
·
Begin
to use fraction bars as symbols of inclusion
·
Add
like terms
·
Use
variables on both sides
·
Use
multiple-term equations
·
Solve
two-step problems
·
Use
adjacent angles, complimentary and supplementary angles
·
Begin
to solve advanced ratio problems
·
Use
multiplication in exponential expressions and variable bases
·
Use
distributive property
·
Classify
triangles and use angles in triangles
·
Begin
to evaluate powers of negative bases
·
Identify
roots of negative numbers, negative exponents and zero exponents
·
Find
simple and compound interest
·
Show
markup and markdown, commission, and profit
·
Find
congruence and transformation of polygons
·
Identify
congruence and transformation of polygons
·
Identify
area of parallelograms and trapezoids
·
Solve
equations with X to the second power
·
Use
the Pythagorean Theorem
·
Use
English volume and Metric volume conversions
·
Find
the volume of pyramids, cones, spheres, and surface area of pyramids and cones
·
Form
solids
·
Use
permutations
·
Identify
subsets of a real number
·
Manipulate
geometric constructions
·
Represent
data
·
Use
arithmetic in Base 2
·
Begin
to understand theorems about angles and circular arcs
·
Approximate
roots
·
Begin
to identify polynomials
·
Begin
to use transformational geometry
·
Begin
to use advanced graphing
·
Begin
to use slope
·
Begin
to use basic trigonometry
By the end of the Eighth Grade, ASES students in Algebra One will be able to:
Recognize, represent, model, and apply real numbers
and operations verbally, physically, symbolically, and graphically
- Demonstrate an understanding
of the subsets, properties, and operations of the real number system
- Demonstrate an
understanding of the relative size of rational and irrational numbers
- Articulate, model, and
apply the concept of inverse (e.g., opposites, reciprocals, and powers
and roots)
- Describe, model, and
apply inverse operations
- Apply number theory
concepts (e.g., primes, factors, divisibility and multiples) in
mathematical problem solving
- Connect graphical and
symbolic representations of absolute value
- Use real numbers to
represent real-world applications (e.g., slope, rate of change,
probability, and proportionality)
- Use a variety of notations
appropriately (e.g. exponential, functional, square root)
- Select and apply an
appropriate method (i.e., mental mathematics, paper and pencil, or
technology) for computing with real numbers, and evaluate the
reasonableness of results
- Perform operations on
algebraic expressions and informally justify the procedures chosen
- Perform operations on
matrices in real-world problem solving (i.e., addition, subtraction, and
scalar multiplication
Describe, extend, analyze, and create a wide variety of
patterns and functions using appropriate materials and representations in real
world problem solving
- Recognize, analyze, extend, and create a variety
of patterns
- Use algebraic thinking to generalize a pattern by
expressing the pattern in functional notation
- Solve linear systems using a variety of
techniques
- Communicate the meaning of variables in algebraic
expressions, equations, and inequalities
- Identify and represent a variety of functions
- Apply and interpret rates of change from
graphical and numerical data
- Analyze graphs to describe the behavior of
functions
- Interpret results of algebraic procedures
- Apply the concept of variable in simplifying
algebraic expressions, solving equations, and solving inequalities
- Interpret graphs that depict real-world phenomena
- Model real-world phenomena using functions and
graphs
- Articulate and apply algebraic properties in
symbolic manipulation
- Analyze relationships which can and which cannot
be represented by a function
- Graph inequalities and interpret graphs of inequalities
- Describe the domain and range of functions and
articulate restrictions imposed either by the operations or by the
real-life situations which the functions represent
- Describe the transformation of the graph that
occurs when coefficients and/or constants of the corresponding linear
equations are changed
Apply appropriate tools and units of measurement to
produce reasonable results.
- Use concepts of length, area,
and volume to estimate and solve real-world problems
- Apply and communicate
measurement concepts and relationships in algebraic and geometric
problem-solving situations
- Demonstrate an
understanding of rates and other derived and indirect measurements (e.g.,
velocity, miles per hour, revolutions per minute, cost per unit)
- Make decisions about
units, scales, and measurement tools that are appropriate for problem
situations involving measurement
Collect, organize, represent, and
interpret data and model situations to determine theoretical and experimental
probabilities.
- Collect, represent, and describe linear and
nonlinear data sets developed from the real world
- Make predictions from a linear data set using a
line of best fit
- Interpret a set of data using the appropriate
measure of central tendency
- Choose, construct, and analyze appropriate
graphical representations for a data set
- Understand the concept of random sampling