(NS) Number Sense Learners will expand their knowledge of the number system to create connections and solve problems within and across concepts.
MAT-06.NO.NS.01 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines, including authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
MAT-00.NO.NBT.02 Compare two numbers between 1 and 20 using words greater than, less than, or equal to.
MAT-01.NO.NBT.02 Compare two two-digit numbers using symbols >, <, and =. Justify comparisons based on the number of tens and ones.
MAT-02.NO.NBT.02 Compare two three-digit numbers using symbols >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
MAT-03.NO.NBT.01 Compare two four-digit numbers using symbols, >, <, and =. Justify comparisons based on the value of thousands, hundreds, tens, and ones.
MAT-04.NO.NBT.02 Compare two numbers to the millions place and decimals to the hundredths place, using symbols >, <, and =. Justify comparisons based on the value of the digits.
MAT-05.NO.NBT.02 Compare two decimals to thousandths using symbols >, <, and =. Justify comparisons based on the value of the digits.
MAT-06.NO.NS.01Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines in authentic 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.01 Describe the absolute value of a number as its distance from zero on a number line.
MAT-08.NO.NS.01 Compare and classify real numbers within the real number system.
MAT-08.NO.NS.02 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line diagram, and estimate the value of irrational expressions involving one operation.
MAT-08.NO.NS.03 Use scientific notation to represent very large or very small quantities. Interpret scientific notation generated by technology. Compare and order numbers in scientific and standard notation.
MAT-09.AR.06 Solve linear equations and inequalities (to include compound inequalities) in one variable.
MAT-09.AR.08 Graph the solution set to a two-variable system of linear equations. Create and graph the solution set to a two-variable system of linear inequalities in context.
MAT-09.AR.09 Solve absolute value equations and inequalities in one or two variables.
MAT-12.AR.09 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.
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.01Explain 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.
Proficiency Scale