Summary of Skills

Age 8-10 - Concept 5: Math

Unit 1: Place Value to 1,000,000

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

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

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.

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

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

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

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

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

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