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