# 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