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MAT-04.NO.NF.01

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

MAT-04.NO.NF.02

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

MAT-04.NO.NF.03

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

MAT-04.NO.NF.04

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

MAT-04.NO.NF.05

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Fractions

• MAT-03.NO.NF.02 Represent and understand a fraction as a number on a number line.
• MAT-03.NO.NF.03 Represent equivalent fractions using visual representations and number lines.
• MAT-03.NO.NF.04 Recognize whole numbers as fractions and express fractions that are equivalent to whole numbers.
• MAT-03.NO.NF.05 Compare fractions of the same whole having the same numerators or denominators, using symbols >, <, and = by reasoning about their size. (Fractions should be limited to denominators of 2, 3, 4, 6, and 8 and should not exceed the whole.)
• MAT-04.NO.NF.01 Express equivalent fractions with a denominator of 10 and a denominator of 100 to generate a decimal notation.
• MAT-04.NO.NF.02 Explain and demonstrate how a mixed number is equivalent to a fraction greater than one and how a fraction greater than one is equivalent to a mixed number using visual fraction models and reasoning strategies (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.03 Generate equivalent fractions using numerical representations, visual representations, and number lines (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.04 Demonstrate how equivalent fractions are generated by multiplying a fraction equivalent to 1 or the properties of multiplication (proper and improper fractions limited to 2, 3,4, 5, 6, 8, 10, 12, and 100).
• MAT-04.NO.NF.05 Compare and order fractions having unlike numerators or denominators. Record comparisons using symbols >, <, = and justify using a visual fraction model (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.01 Generate equivalent forms of commonly used fractions and decimals (e.g., halves, fourths, fifths, tenths).
• MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic and mathematical problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
• MAT-06.NO.NS.02 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
• MAT-07.NO.NS.02 Recognize common fractions and decimal equivalencies up to a denominator of 10. Convert a rational number to a decimal using technology.

MAT-04.NO.NF.06

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

• MAT-04.NO.NF.06 Solve authentic word problems by adding and subtracting fractions and mixed numbers with like denominators (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.03 Solve authentic word problems by adding and subtracting fractions and mixed numbers with unlike denominators using a visual fraction model and/or equation.
• MAT-06.NO.O.02 Add and subtract fractions and decimals up to the hundredth place, including in authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-12.NO.04 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.
• MAT-12.AR.05 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system analogous to rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.
• MAT-12.NO.06 Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Understand the hierarchal relationships among subsets of the complex number system.

MAT-04.NO.NF.07

 4th Grade (MAT) Targeted Standard    (NO) Number and Operations  (NF) Factions Learners will understand fractions and equivalency to represent, compare, and perform operations of fractions and decimals.

Progressions

Multiplying and Dividing Fractions

• MAT-04.NO.NF.07 Solve problems by multiplying fractions and whole numbers using visual fraction models (proper and improper fractions limited to denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100).
• MAT-05.NO.NF.02 Explain why multiplying a given number by a fraction greater than one results in a product greater than the given number and explain why multiplying a given number by a fraction less than one results in a product smaller than the given number.
• MAT-05.NO.NF.04 Solve authentic word problems by multiplying fractions and mixed numbers using visual fraction models and equations.
• MAT-06.NO.O.03 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.
• MAT-07.NO.O.02 Add, subtract, multiply, and divide non-negative fractions in multi-step problems, including authentic problems.
• MAT-08.NO.O.02 Add, subtract, multiply, and divide rational numbers using strategies or procedures.
• MAT-09.NO.02 Perform basic operations of simple radical expressions to write a simplified equivalent expression.
• MAT-12.NO.03 Demonstrate that the sum or product of two rational numbers is rational, that the sum of a rational number and an irrational number is irrational, and that the product of a nonzero rational number and an irrational number is irrational.