Summary of Skills

Age 8-10 - Concept 5: Math

Unit 1: Place Value to 1,000,000

Math

  • Apply rounding to telling time
  • Compare two multi-digit numbers based on meanings of the digits in each place
  • Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm
  • Order and compare multi-digit numbers
  • Read and write multi-digit whole numbers
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form
  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right
  • Use place value understanding to round multi-digit whole numbers to any place

Unit 2: The Four Operations

Math

  • Assess the reasonableness of answers
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding
  • Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number
  • Determine whether a given whole number in the range 1-100 is prime or composite
  • Find all factor pairs for a whole number in the range 1-100
  • Find products and quotients
  • Fluently add and subtract multi-digit whole numbers using the standard algorithm
  • Identify multiples and factors
  • Identify properties of multiplication
  • Interpret division problems in words and symbols
  • Recognize and apply patterns
  • Recognize that a whole number is a multiple of each of its factors
  • Represent problems using equations with a letter standing for the unknown quantity
  • Represent verbal statements of multiplicative comparisons as multiplication equations
  • Represent word problems using equations with a letter standing for the unknown quantity
  • Solve equations
  • Solve word problems posed with whole numbers and having whole-number answers
  • Solve word problems posed with whole numbers and having whole-number answers using the four operations

Unit 3: Geometry

Math

  • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size
  • Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines
  • Identify geometric elements in two-dimensional figures
  • Identify line-symmetric figures and draw lines of symmetry
  • Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts
  • Recognize angle measure as additive
  • Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement
  • Recognize right triangles as a category, and identify right triangles
  • Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Unit 4: Multi-Digit Multiplication

Math

  • Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number
  • Fluently multiply within 100
  • Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations
  • Recognize and apply patterns
  • Recognize that a whole number is a multiple of each of its factors
  • Solve multistep word problems posed with whole numbers and having whole-number answers

Unit 5: Fractions

Math

  • Add and subtract fractions that have the same denominators
  • Add and subtract mixed numbers with like denominators
  • Add fractions that have the same denominators
  • Apply and extend previous understandings of multiplication to multiply a fraction by a whole number
  • Compare two fractions with different numerators and different denominators
  • Decompose a fraction into a sum of fractions with the same denominator
  • Identify, create, and name fractions
  • Identify, create, and name mixed numbers
  • Recognize and generate equivalent fractions
  • Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators
  • Solve word problems involving multiplication of a fraction by a whole number
  • Subtract fractions that have the same denominators
  • Understand a fraction a/b with a > 1 as a sum of fractions 1/b
  • Understand addition and subtraction of fractions as joining and separating parts referring to the same whole
  • Write fractions in their simplest form

Unit 6: Multi-Digit Division

Math

  • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division
  • Interpret division problems in words and symbols
  • Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted

Unit 7: Decimals

Math

  • Add and subtract fractions that have the same denominators
  • Compare two decimals to hundredths by reasoning about their size
  • Convert decimals to fractions
  • Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100
  • Identify, read, and write decimal numbers
  • Locate decimals on a number line
  • Recognize and generate equivalent fractions
  • Record the results of comparisons with the symbols >, =, or <, and justify the conclusions
  • Use decimal notation for fractions with denominators 10 or 100

Unit 8: Measurement

Math

  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems
  • Know relative sizes of measurement units within one system of units
  • Make a line plot to display a data set of measurements in fractions of a unit
  • Solve problems involving addition and subtraction of fractions by using information presented in line plots
  • Use area to determine perimeter and vice versa
  • Use multiplication and division to convert between units of measurement
  • Use multiplication and division to convert between units of time
  • Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money
  • Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit and vice versa

Unit 9: Skills Review

Math

  • Add and subtract fractions that have the same denominators
  • Apply the area and perimeter formulas for rectangles
  • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size
  • Compare two decimals to hundredths by reasoning about their size
  • Compare two fractions with different numerators and different denominators
  • Compare two multi-digit numbers based on meanings of the digits in each place
  • Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines
  • Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors
  • Identify line-symmetric figures and draw lines of symmetry
  • Know relative sizes of measurement units within one system of units
  • Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers
  • Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form
  • Recognize and generate equivalent fractions
  • Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators
  • Understand concepts of angle measurement
  • Use decimal notation for fractions with denominators 10 or 100
  • Use place value understanding to round multi-digit whole numbers to any place
  • Within a single system of measurement, convert between measurement units