Mathematics Toolkit
Curriculum Guidance Materials & Resources
Grade 3-8 Mathematics Testing Program Guidance, Pre-March/Post March
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Number Sense and Operations |
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Band Performance Indicator |
Pre- MarchTesting
/Post-March Testing |
Number Systems
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Grade 3 |
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3.N.1
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Skip count by 25’s, 50’s, 100’s to 1,000 |
Pre-March |
3.N.2
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Read and write whole numbers to 1,000 |
Pre-March |
3.N.3
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Compare and order numbers to 1,000 |
Pre-March |
3.N.4
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Understand the place value structure of
the base ten number system:
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand |
Pre-March |
3.N.5
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Use a variety of strategies to compose and decompose three-digit numbers |
Pre-March |
3.N.6
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Use and explain the commutative property of addition and multiplication |
Pre-March |
3.N.7
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Use 1 as the identity element for multiplication |
Pre-March |
3.N.8
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Use the zero property of multiplication |
Pre-March |
3.N.9
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Understand and use the associative property of addition |
Pre-March |
3.N.10
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Develop an understanding of fractions as part of a whole unit and as parts of a collection |
Pre-March |
3.N.11
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Use manipulatives, visual models, and illustrations to name and represent
unit fractions (1/2, 1/3, 1/4, 1/5, 1/6 and 1/10 ) as part of a whole or a
set of objects |
Pre-March |
3.N.12
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Understand and recognize the meaning of numerator and denominator in the
symbolic form of a fraction |
Pre-March |
3.N.13
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Recognize fractional numbers as
equal parts of a whole |
Pre-March |
3.N.14
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Explore equivalent fractions(½,
⅓, ¼) |
Post-March |
3.N.15
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Compare and order unit fractions (½, ⅓, ¼) and find their approximate
locations on a number line |
Post-March |
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Grade 4 |
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4.N.1 |
Skip count by 1,000’s |
Pre-March |
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4.N.2 |
Read and write whole numbers to 10,000 |
Pre-March |
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4.N.3 |
Compare and order numbers to 10,000 |
Pre-March |
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4.N.4 |
Understand the place value structure of the base ten number system:
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
10 thousands = 1 ten thousand |
Pre-March |
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4.N.5 |
Recognize equivalent representations for numbers up to four digits and
generate them by decomposing and composing numbers |
Pre-March |
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4.N.6 |
Understand, use, and explain the associative property of multiplication |
Pre-March |
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4.N.7 |
Develop an understanding of fractions as locations on number lines and as
divisions of whole numbers |
Post-March |
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4.N.8 |
Recognize and generate equivalent fractions (halves, fourths, thirds,
fifths, sixths, and tenths) using manipulatives, visual models, and
illustrations |
Post-March |
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4.N.9 |
Use concrete materials and visual models to compare and order unit
fractions or fractions with the same denominator (with and without the use
of a number line) |
Post-March |
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4.N.10 |
Develop an understanding of decimals as part of a whole |
Post-March |
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4.N.11 |
Read and write decimals to hundredths using money as a context |
Post-March |
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4.N.12 |
Use concrete materials and visual models to compare and order decimals
(less than 1) to the hundredths place in the context of money |
Post-March |
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Grade 5 |
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5.N.1 |
Read and write whole numbers to millions |
Pre-March |
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5.N.2 |
Compare and order numbers to millions |
Pre-March |
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5.N.3 |
Understand the place value structure of the base ten number system:
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
10 thousands = 1 ten thousand
10 ten thousands = 1 hundred thousand
10 hundred thousands = 1 million |
Pre-March |
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5.N.4 |
Create equivalent fractions, given a fraction |
Pre-March |
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5.N.5 |
Compare and order fractions including unlike denominators (with and
without the use of a number line)
Note: Commonly used
fractions such as those that might be indicated on ruler, measuring cup,
etc. |
Pre-March |
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5.N.6 |
Understand the concept of ratio |
Pre-March |
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5.N.7 |
Express ratios in different forms |
Pre-March |
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5.N.8 |
Read, write, and order decimals to thousandths |
Pre-March |
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5.N.9 |
Compare fractions using <, >, or = |
Pre-March |
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5.N.10 |
Compare decimals using <, >, or = |
Pre-March |
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5.N.11 |
Understand that percent means part of 100, and write percents as fractions
and decimals |
Pre-March |
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Grade 6 |
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6.N.1 |
Read and write whole numbers to trillions |
Pre-March |
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6.N.2 |
Define and identify the commutative and associative properties of addition
and multiplication |
Pre-March |
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6.N.3 |
Define and identify the distributive property of multiplication over
addition |
Pre-March |
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6.N.4 |
Define and identify the identity and inverse properties of addition and
multiplication |
Pre-March |
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6.N.5 |
Define and identify the zero property of multiplication |
Pre-March |
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6.N.6 |
Understand the concept of rate |
Pre-March |
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6.N.7 |
Express equivalent ratios as a proportion |
Pre-March |
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6.N.8 |
Distinguish the difference between rate and ratio |
Pre-March |
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6.N.9 |
Solve proportions using equivalent fractions |
Pre-March |
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6.N.10 |
Verify the proportionality using the product of the means equals the product
of the extremes |
Pre-March |
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6.N.11 |
Read, write, and identify percents of a whole (0% to 100%) |
Pre-March |
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6.N.12 |
Solve percent problems involving percent, rate, and base |
Pre-March |
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6.N.13 |
Define absolute value and determine the absolute value of rational numbers
(including positive and negative) |
Pre-March |
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6.N.14 |
Locate rational numbers on a number line (including positive and negative) |
Pre-March |
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6.N.15 |
Order rational numbers (including positive and negative) |
Pre-March |
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Grade 7 |
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7.N.1 |
Distinguish between the various subsets of real numbers (counting/natural
numbers, whole numbers, integers, rational numbers, and irrational numbers) |
Pre-March |
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7.N.2 |
Recognize the difference between rational and irrational numbers (e.g.,
explore different approximations of
π) |
Pre-March |
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7.N.3 |
Place rational and irrational numbers (approximations) on a number line and
justify the placement of the numbers |
Pre-March |
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7.N.4 |
Develop the laws of exponents for multiplication and division |
Pre-March |
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7.N.5 |
Write numbers in scientific notation |
Pre-March |
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7.N.6 |
Translate numbers from scientific notation into standard form |
Pre-March |
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7.N.7 |
Compare numbers written in scientific notation |
Pre-March |
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Grade 8 |
NONE |
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Number Theory
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Grade 3 |
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3.N.16
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Identify odd and even numbers |
Pre-March |
3.N.17
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Develop an understanding of the properties of odd/even numbers as a result
of addition or subtraction |
Pre-March |
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Grade 4 |
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4.N.13
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Develop an understanding of the properties of odd/even numbers as a result
of multiplication |
Pre-March |
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Grade 5 |
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5.N.12 |
Recognize that some numbers are only divisible by one and themselves
(prime) and others have multiple divisors (composite) |
Pre-March |
5.N.13
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Calculate multiples of a whole number and the least common multiple of two
numbers |
Pre-March |
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5.N.14 |
Identify the factors of a given number |
Pre-March |
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5.N.15 |
Find the common factors and the greatest common factor of two numbers |
Pre-March |
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Grade 6 |
None |
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Grade 7 |
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7.N.8 |
Find the common factors and greatest common factor of two or more numbers |
Pre-March |
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7.N.9 |
Determine multiples and least common multiple of two or more numbers |
Pre-March |
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7.N.10 |
Determine the prime factorization of a given number and write in exponential
form |
Pre-March |
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Grade 8 |
NONE |
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Operations
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Grade 3 |
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3.N.18
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Use a variety of strategies to add and subtract 3-digit numbers (with and
without regrouping) |
Pre-March |
3.N.19
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Develop fluency with single-digit multiplication facts |
Assess Post- March for above
5 x 10. In context |
3.N.20
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Use a variety of strategies to solve multiplication problems with factors
up to 12 x 12 |
Post-March |
3.N.21
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Use the area model, tables, patterns, arrays, and doubling to provide
meaning for multiplication |
Pre-March |
3.N.22
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Demonstrate fluency and apply single-digit division facts |
Assess Post- March for above
50 divided by 10 and grade 3 for below 50 divided by 10. In context |
3.N.23
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Use tables, patterns, halving, and manipulatives to provide meaning for
division |
Post-March |
3.N.24
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Develop strategies for selecting the appropriate computational and
operational method in problem solving situations |
Pre-March |
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Grade 4 |
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4.N.14 |
Use a variety of strategies to add and subtract numbers up to 10,000 |
Pre-March |
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4.N.15 |
Select appropriate computational and operational methods to solve problems |
Pre-March |
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4.N.16 |
Understand various meanings of multiplication and division |
Pre-March |
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4.N.17 |
Use multiplication and division as inverse operations to solve problems |
Pre-March |
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4.N.18 |
Use a variety of strategies to multiply two-digit numbers by one-digit
numbers (with and without regrouping) |
Pre-March |
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4.N.19 |
Use a variety of strategies to multiply two-digit numbers by two-digit
numbers (with and without regrouping) |
Post-March |
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4.N.20 |
Develop fluency in multiplying and dividing multiples of 10 and 100 up to
1,000 |
Pre-March |
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4.N.21 |
Use a variety of strategies to divide two-digit dividends by one-digit
divisors (with and without remainders) |
Pre-March |
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4.N.22 |
Interpret the meaning of remainders |
Pre-March |
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4.N.23 |
Add and subtract proper fractions with common denominators |
Post-March |
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4.N.24 |
Express decimals as an equivalent form of fractions to tenths and
hundredths |
Post-March |
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4.N.25 |
Add and subtract decimals to tenths and hundredths using a hundreds chart |
Post-March |
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Grade 5 |
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5.N.16 |
Use a variety of strategies to multiply three-digit by three-digit
numbers
Note: Multiplication by anything greater
than a three-digit multiplier/ multiplicand should be done using
technology. |
Pre-March |
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5.N.17 |
Use a variety of strategies to divide three-digit numbers by one- and
two-digit numbers
Note: Division by anything greater
than a two-digit divisor should be done using technology. |
Pre-March |
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5.N.18 |
Evaluate an arithmetic expression using order of operations including
multiplication, division, addition, subtraction and parentheses |
Pre-March |
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5.N.19 |
Simplify fractions to lowest terms |
Pre-March |
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5.N.20 |
Convert improper fractions to mixed numbers, and mixed numbers to improper
fractions |
Pre-March |
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5.N.21 |
Use a variety of strategies to add and subtract fractions with like
denominators |
Pre-March |
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5.N.22 |
Add and subtract mixed numbers with like denominators |
Pre March |
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5.N.23 |
Use a variety of strategies to add, subtract, multiply, and divide
decimals to thousandths |
Pre-March |
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Grade 6 |
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6.N.16 |
Add and subtract fractions with unlike denominators |
Pre-March |
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6.N.17 |
Multiply and divide fractions with unlike denominators |
Pre-March |
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6.N.18 |
Add, subtract, multiply and divide mixed numbers with unlike denominators |
Pre-March |
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6.N.19 |
Identify the multiplicative inverse (reciprocal) of a number |
Pre-March |
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6.N.20 |
Represent fractions as terminating or repeating decimals |
Pre-March |
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6.N.21 |
Find multiple representations of rational numbers (fractions, decimals, and
percents 0 to 100) |
Pre-March |
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6.N.22 |
Evaluate numerical expressions using order of operations (may include
exponents of two and three) |
Pre-March |
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6.N.23 |
Represent repeated multiplication in exponential form |
Pre-March |
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6.N.24 |
Represent exponential form as repeated multiplication |
Pre-March |
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6.N.25 |
Evaluate expressions having exponents where the power is an exponent of one,
two, or three |
Pre-March |
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Grade 7 |
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7.N.11 |
Simplify expressions using order of operations Note: Expressions may
include absolute value and/or integral exponents greater than 0. |
Pre-March |
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7.N.12 |
Add, subtract, multiply and divide integers |
Pre-March |
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7.N.13 |
Add and subtract two integers (with and without the use of a number line) |
Pre-March |
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7.N.14 |
Develop a conceptual understanding of negative and zero exponents with a
base of ten and relate to fractions and decimals (e.g., 10-²
= .01 = 1/100) |
Pre-March |
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7.N.15 |
Recognize and state the value of the square root of a perfect square (up to
225) |
Pre-March |
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7.N.16 |
Determine the square root of non-perfect squares using a calculator |
Pre-March |
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7.N.17 |
Classify irrational numbers as non-repeating/non-terminating decimals |
Pre-March |
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Grade 8 |
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8.N.1 |
Develop and apply the laws of exponents for multiplication and division |
Pre-March |
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8.N.2 |
Evaluate expressions with integral exponents |
Pre-March |
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8.N.3 |
Read, write, and identify percents less than 1% and greater than 100% |
Pre-March |
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8.N.4 |
Apply percents to: Tax, percent increase/decrease, simple interest, sale
price, commission, interest rates, and gratuities |
Pre-March |
Estimation
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Grade 3 |
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3.N.25
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Estimate numbers up to 500 |
Post-March
for numbers past 200 |
3.N.26
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Recognize real world situations in which an estimate (rounding) is more
appropriate |
Post-March |
3.N.27
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Check reasonableness of an answer by using estimation |
Pre-March |
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Grade 4 |
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4.N.26 |
Round numbers less than 1,000 to the nearest tens and hundreds |
Pre-March |
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4.N.27 |
Check reasonableness of an answer by using estimation |
Pre-March |
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Grade 5 |
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5.N.24 |
Round numbers to the nearest hundredth and up to 10,000 |
Pre-March |
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5.N.25 |
Estimate sums and differences of fractions with like denominators
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Pre-March |
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5.N.26 |
Estimate sums, differences, products, and quotients of decimals |
Pre-March |
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5.N.27 |
Justify the reasonableness of answers using estimation |
Pre-March |
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Grade 6 |
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6.N.26 |
Estimate a percent of quantity (0% to 100%) |
Pre-March |
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6.N.27 |
Justify the reasonableness of answers using estimation (including rounding) |
Pre-March |
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Grade 7 |
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7.N.18 |
Identify the two consecutive whole numbers between which the square root of
a non-perfect square whole number less than 225 lies (with and without the
use of a number line) |
Pre-March |
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7.N.19 |
Justify the reasonableness of answers using estimation |
Pre-March |
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Grade 8 |
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8.N.5 |
Estimate a percent of a quantity, given an application |
Pre-March |
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8.N.6 |
Justify the reasonableness of answers using estimation |
Pre March |
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Key to number: |
3.N.16
3 = 3rd Grade
N = Number Sense & Operations
16 = Performance Indicator number |
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