Number Sense
and Numeration
– includes solving problems with ratios, proportions, fraction-decimal
relationships, exponents, number theory, place value, and the relationship
between numbers.
Skills and
Concepts
RIT scores between
151 and 160
Whole Numbers
- Match sets of objects
to numerals 0-40 to demonstrate an understanding of one-to-one
correspondence
- Identify and count
numbers 0-20
- Identify and order
ordinal numbers (first to tenth)
Fractions
- Identify equal parts of
a region (halves, thirds, fourths)
- Represent fractions by
using models and drawings
Ordering, Equalities and Inequalities
- Compare and order
numbers and sets of objects 0-10
New
Vocabulary in this Range: how many
New
Signs and Symbols: — for answer
RIT scores between
161 and 170
Whole Numbers
·
Identify missing numbers in a series through 100
- Identify the number
that is “one more than”, “one less than”, “10 more than”, and “10 less
than” a given number
- Count objects that are
grouped into tens and ones
Fractions
- Identify one-half of an
object from a picture
Place Value
- Identify and understand
the place value and value of each digit in numbers through the hundreds
Ordering, Equalities and Inequalities
New
Vocabulary in this Range: ones, tens, hundreds, thousands, numeral, ordinal numbers through
eleventh, counting
New
Signs and Symbols: none
RIT scores between
171 and 180
Whole Numbers
- Compare two or more
sets of objects (up to ten objects in each group) and identify which set
is equal to, more than, or less than the other
- Count and write by 10’s
to 100
- Compare, group, and
order whole numbers to 100 by using the symbols for “less than”, equal
to”, and “greater than” (<, =, >)
- Distinguish between odd
and even numbers
- Count by 2’s to 20
Fractions
·
Identify one-half of an object or set
- Identify fractional
parts of a region or group
Place Value, Expanded and Standard Notation
- Write numerals in
expanded form through the thousands place
Ordering, Equalities and Inequalities
- Use > or <
symbols to compare two numbers
New
Vocabulary in this Range: even numbers, same as, fewest
New
Signs and Symbols: < and > signs, = sign
RIT Scores between 181 and 190
Whole Numbers
- Identify one more and
one fewer
- Count and write by 2’s
and 3’s
- Complete a number
pattern
- Round 2- and 3-digit
numbers to the nearest hundred and tens
- Identify the value of
Roman Numerals using I, V, and X
- Apply rules of
divisibility by 5
- Identify the greatest
common factor of two whole numbers each of which is less than 100
- List some common
multiples of two whole numbers
Fractions
- Separate regions into
sub regions that are equivalent (halves, thirds, fourths)
- Change a fractional
numeral to its simplest form (lowest terms)
Decimals
·
Identify the greater or lesser of two decimals
Place Value, Expanded and Standard Notation
- Match number words to
numerals to the ten thousands place
·
Identify and understand the place value and value of
each digit in numbers through the hundred thousands
- Add whole numbers using
place value
- Identify and understand
place value for decimals (tenths, hundredths, and thousandths)
Ordering, Equalities and Inequalities
- Order sets of objects
0-20
- Identify the greater or
lesser of two numerals
- Order numerals through
999
- Identify the numeral
that comes before, between, or after any given numeral through 999
- Compare and order
fractions*
- Compare and order
decimals to the hundredths place
New
Vocabulary in this Range: first, second, third, etc., odd, one-fourth, one-half, reduce,
fractions, order, divisible, round, smallest, largest, lowest terms, greatest
common factor, least common multiple, closest, units, set, digit, greater than,
greatest
New
Signs and Symbols: none
RIT Scores between 191 and 200
Whole Numbers
- Order numerals through
9999
- Count and convert to
dozens
- Round 4- and 5-digit
numbers to the nearest hundred thousand, thousand, hundred or ten
- Identify numbers as
prime or composite
- Apply rules of
divisibility by 2’s
- Complete a factor tree
for a number (prime factorization)*
- Understand and
demonstrate that many whole numbers break down in different ways (e.g., 12
= 4 x 3 = 2 x 6 = 2 x 2 x 3)
- Identify the least
common multiple of two whole numbers*
Fractions, Ratio and Proportion
- Write equivalent
fractions using pictorial representation
- Find equivalent
fractions using multiples and factors*
- Write mixed numbers as
improper fractions and improper fractions as mixed numbers*
- Identify the least
(lowest) common denominator of two fractions
- Express a fraction as a
decimal and vice versa
·
Solve proportions using the cross product method*
Decimals
- Write a decimal for a
shaded region (to tenths place)
- Identify and understand
place value for decimals (tenths, hundredths, and thousandths)
Percents
- Model percents using a
10 x 10 grid
- Write a decimal or
fraction as a percent and vice versa
Place Value, Expanded and Standard Notation
- Identify the number and
written word for ordinal numbers
- Write numerals in
expanded form through the hundred thousands
- Match word names to
numerals through billions
- Identify place value
using model to count
·
Add whole numbers using place value
Ordering, Equalities and Inequalities
·
Identify and understand the greater or lesser of two
numerals (use the symbols < and > through 999,999)
- Compare and order
fractions and mixed numbers
Exponents
- Exponential
representation of 3 multiplied numbers (2x2x2)
New
Vocabulary in this Range: thirds, fourths, rounded, thousands, exponential form, mixed number,
improper fraction, lowest common denominator, percent, expanded form, prime,
factor, proportion
New
Signs and Symbols: use of dot as a multiplication symbol
RIT scores between 201 and 210
Whole Numbers
- Round to the nearest
millions and billions
- Apply rules of
divisibility
- Identify the greatest
common factor of two whole numbers each of which is less than 100
- Write the Roman numeral
equivalent of Arabic numbers 1-2000 and vice versa
Fractions, Ratio and Proportion
- Change a fractional
numeral to its simplest form (lowest terms)
- Write the missing
number in two equivalent ratios
- Use a number line to
identify a fractional point
Decimals
- Write a decimal for a
shaded region (hundredths)
- Write a terminating
decimal as a fraction or mixed number
- Round decimals to
nearest whole number, tenth, hundredth, or thousandth
- Multiply a decimal by
multiples of 10, 100, or 1000
Percents
- Find a percent of a
number
- Write a decimal or
fraction as a percent or vice versa
Place Value, Expanded and Standard Notation
- Understand and identify
the place value and value of each digit in numerals through the billions
·
Write the word name for a decimal and vice versa
- Write numerals in
expanded form through the hundred billions
Ordering, Equalities and Inequalities
·
Order numbers from least to greatest and greatest to
least
- Compare and order
numbers through the billions
·
Order decimals and fractions to the hundred thousandths
- Identify the greater or
lesser of 2 integers
- Ordering integers that
include fractions and wholes
- Translate verbal
statements into equations (all four operations; several operations)
- Ordering exponential
values
Exponents and Scientific Notation
- Write whole number in
exponential form and compute the power of a number
New
Vocabulary in this Range: missing number, pentagon, simplest fraction, biggest, hundredths, one
less, decimal numeral, squared, divisible, inequality, expanded numeral,
equivalent, point, standard numeral, sequence
New
Signs and Symbols: + used as positive symbol, - used as negative symbol
RIT
scores between 211 and 220
Whole Numbers
- Understand and use
rules of divisibility
- Identify the greatest
common factor of two whole numbers: list the factors or prime factorization
- Identify the greatest
common factor and least common multiple of two whole numbers
Fractions, Ratio and Proportion
- Write improper
fractions from picture presentations
- Change a fractional
numeral to its simplest form (lowest terms)
Decimals
·
Round monetary amounts to the nearest single coin or
bill which could be used to pay for a purchase up to and including $20.00
- Write the decimal
equivalent of a fraction and label as repeating or terminating
Percents
- Express a fraction as a
decimal and as a percent
Ordering, Equalities and Inequalities
- Compare and order
fractions with the same denominator and with different denominators
- Order decimals to
thousandths; identify the greater or lesser of two decimals to thousandths
Exponents and Scientific Notation
- Order of “powers”
- Write a whole number or
a decimal in scientific notation
- Write a number
expressed in scientific notation in standard form
New
Vocabulary in this Range: counting number, portion, fractional part, lowest terms, reciprocal,
order, scientific notation, prime factorization, not prime, factor tree, common
multiples, greatest common denominator, equivalent, nearest dollar
New
Signs and Symbols: square root symbol
RIT scores between
221 and 230
Fractions, Ratio and Proportion
- Model and write numerical
fractions
- Understand the concept
of ratio using concrete and pictorial models
·
Identify the least common denominator for 3 or more
fractions: list the multiples or prime factorization
- Determine if a pair of
ratios is equal or not equal using the equivalent fractions method
- Write the missing
number in 2 equivalent ratios
- Solve proportions using
the cross product method
Decimals
- Identify and order
decimal and fractional coordinates on a number line
Percents
- Write a ratio
(fraction) as a percent and a percent as a ratio (fraction): denominators
of 100
Integers
- Understand the meaning
of integers
Place
Value, Expanded and Standard Notation
- Match word names to
numerals to the hundred thousands in decimals
Ordering, Equalities and Inequalities
- Order a set of integers
from least to greatest
Exponents and Scientific Notation
- Identify and use powers
of 10
Square Roots
- Evaluate expressions
using square roots
New
Vocabulary in this Range: always true, proportion, multiply, between, tens digit, standard
numeral, ratio
New
Signs and Symbols: none
RIT scores between
231 and 240
Fractions, Ratio and Proportion
- Define ratio
- Write ratios in a
variety of ways
Decimals
- Write a decimal or
mixed decimal for a fraction
- Write a whole number or
a decimal in scientific notation (negative exponents)
Place
Value, Expanded and Standard Notation
- Write numerals in
expanded form through the billions
- Understand and identify
place value and value of each digit in numerals through the hundred
billions
Exponents and Scientific Notation
·
Evaluate
expressions using the order of operations that include exponents
·
Find
products by applying rules for exponents
Square Roots
- Identify perfect
squares in a list of numbers and calculate the positive square root of a
perfect square
New
Vocabulary in this Range: none
New
Signs and Symbols: none
RIT scores between
241 and 250
Square Roots
- Evaluate expressions
using square roots
New
Vocabulary in this Range: Base ten, prime factors
New
Signs and Symbols: none
RIT scores between
251 and 260
Exponents and Scientific Notation
- Evaluate powers with a
negative exponent
New
Vocabulary in this Range: none
New
Signs and Symbols: none
RIT scores between
261 and 270
Percents
- Change a percent to a
fraction (including mixed numbers)
Square Roots
- Understand properties
of square roots
Irrational Numbers
- Define irrational
numbers
New
Vocabulary in this Range: infinite non-repeating decimal
New
Signs and Symbols: none
RIT scores between
271 and 280
Exponents and Scientific Notation
- Evaluate power of zero
- Identify the lowest
common multiple of numbers in their prime factored state
Set
Notation
- Use inequalities to
represent set notation
New
Vocabulary in this Range: none
New
Signs and Symbols: none