# Summary of Skills

Age 9-11 - Concept 5: Math

## Unit 1: Place Value: Million to Thousandths

### Math

• Compare and order large numbers
• Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons
• Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10
• Read and write decimals to thousandths using base-ten numerals, number names, and expanded form
• Read and write numbers from 1,000,000 to thousandths using base-10 numerals, number names, and expanded form
• Read and write Roman numerals
• Read, write, and compare decimals to thousandths
• Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left
• Use place value understanding to round decimals to any place
• Use whole-number exponents to denote powers of 10

## Unit 2: Four Operations

### Math

• Add and subtract multi-digit numbers
• Add, subtract, multiply, and divide decimals to hundredths
• Express a whole number as a product of its prime factors
• Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors
• Fluently multiply multi-digit whole numbers using the standard algorithm
• Solve problems
• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols
• Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them

## Unit 3: Measurement

### Math

• Connect objects and appropriate units of measurement
• Convert among different-sized standard measurement units within a given measurement system
• Convert between units of time
• Distinguish between units of measurement
• Identify equivalent measurements
• Identify equivalent units of measurement (for example, 12 inches = 1 foot)
• Identify equivalent units of time
• Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8)
• Use conversions in solving multi-step, real world problems
• Use conversions to solve real-world problems
• Use operations on fractions to solve problems involving information presented in line plots

## Unit 4: Adding and Subtracting Fractions

### Math

• Add and subtract fractions with like and unlike denominators (including mixed numbers)
• Compare fractions with different numerators and denominators
• Convert between improper fractions and mixed numbers
• Decompose a fraction into fraction parts (ex. 3/5=1/5+1/5+1/5)
• Determine common denominators when working with unlike denominators
• Distinguish types of fractions (unit fractions, mixed numbers, non-simplified fractions, simplified fractions, improper fractions)
• Recognize and generate equivalent fractions
• Solve word problems involving addition and subtraction of fractions referring to the same whole

## Unit 5: Multiplying Fractions

### Math

• Add, subtract, and multiply fractions
• Apply and extend previous understandings of multiplication to multiply a fraction (including mixed numbers) or whole number by a fraction (including mixed numbers)
• Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction
• Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction (including mixed numbers)
• Compare the size of a product to the size of one factor on the basis of the size of the other factor
• Convert between improper fractions and mixed numbers
• Discover the fraction multiplication algorithm
• Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case)
• Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number
• Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths
• Interpret multiplication as scaling (resizing)
• Interpret the product (a/b)× q as a parts of a partition of q into b equal parts
• Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas
• Solve real world problems involving fractional areas
• Solve real world problems involving multiplication of fractions
• Solve real world problems involving multiplication of fractions and mixed numbers, including fractional areas
• Use area models to show fraction multiplication

## Unit 6: Geometry

### Math

• Distinguish regular and irregular polygons
• Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
• Identify and classify triangles
• Identify parts of polygons
• Read, interpret, and create graphs
• Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation
• Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category
• Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)
• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates

## Unit 7: Dividing Fractions

### Math

• Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions
• Divide multi-digit numbers and decimals using the standard algorithms
• Explore patterns related to division and fractions
• Interpret division of a unit fraction by a non-zero whole number, and compute such quotients
• Interpret division of a whole number by a unit fraction, and compute such quotients
• Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions by using visual fraction models and equations to represent the problem

## Unit 8: Volume

### Math

• Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems
• Create rectangular prisms using cubes
• Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths (l × w × h = V)
• Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems
• Identify and construct rectangular prisms
• Make rectangular prisms with specific dimensions using centimeter cubes
• Measure volume by counting unit cubes
• Recognize volume as an attribute of solid figures and understand concepts of volume measurement
• Relate volume to the operations of multiplication and addition
• Solve real and mathematical problems involving perimeter and area

## Unit 9: Skills Review

### Math

• Add, subtract, multiply, and divide decimals to hundredths
• Add, subtract, multiply, and divide fractions with like and unlike denominators (including mixed numbers)
• Apply the formulas V = l (×) w (×) h and V = b (×) h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems
• Apply the order of operations (PEMDAS)
• Compare fractions with different numerators and denominators (< > =)
• Convert among different-sized standard measurement units within a given measurement system
• Convert between improper fractions and mixed numbers
• Distinguish regular and irregular polygons
• Distinguish types of fractions (unit fractions, mixed numbers, non-simplified fractions, simplified fractions, improper fractions)
• Find the perimeter and area of given shapes
• Identify equivalent units of measurement
• Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8)
• Read and write decimals to thousandths using base-ten numerals, number names, and expanded form
• Read, write, and compare decimals to thousandths
• Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation
• Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)
• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates
• Use operations on fractions to solve problems involving information presented in line plots
• Use place value understanding to round decimals to any place
• Use whole-number exponents to denote powers of 10