# Summary of Skills

Age 10-12 - Concept 5: Math

## Unit 1: Operations with Whole Numbers and Decimals

### Math

- Apply the properties of operations to generate equivalent expressions
- Express natural numbers as factors
- Find common multiples of two whole numbers
- Find the greatest common factor of two whole numbers less than or equal to 100
- Find the least common multiple and greatest common factor of two given whole numbers
- Find the least common multiple of two whole numbers
- Find the prime factorization of composite numbers
- Fluently add and subtract multi-digit decimal numbers using the standard algorithm for each operation
- Fluently add and subtract multi-digit whole numbers using the standard algorithm for each operation
- Fluently divide multi-digit decimals using the standard algorithm
- Fluently divide multi-digit whole numbers using the standard algorithm
- Fluently multiply and divide multi-digit decimal numbers using the standard algorithm for each operation
- Fluently multiply and divide multi-digit whole numbers using the standard algorithm
- Fluently multiply multi-digit decimals using the standard algorithm
- Fluently multiply multi-digit whole numbers using the standard algorithm
- Identify a natural number as prime or composite.
- Identify multiples of whole numbers
- Identify numbers as prime or composite
- Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations)
- Use divisibility rules to determine if a dividend can be evenly divided by a divisor
- Use exponential notation to solve problems
- Use standard algorithms to add, subtract, multiply, and divide multi-digit decimal numbers
- Use the distributive property of multiplication to correctly factor algebraic expressions
- Use the distributive property of multiplication to correctly factor numerical expressions
- Use the distributive property of multiplication to correctly multiply expressions
- Use the distributive property of multiplication to multiply and factor expressions
- Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)
- Write and evaluate numerical expressions involving whole-number exponents

## Unit 2: Integers and Rational Numbers

### Math

- Apply an understanding of the coordinate plane to analyze and solve problems
- Draw polygons in the coordinate plane and calculate simple lengths and distances
- Fluently add and subtract fractions with unlike denominators (including mixed numbers)
- Fluently divide unit fractions by whole numbers and whole numbers by unit fractions
- Fluently multiply a whole number or a fraction by a fraction
- Interpret and compute quotients of fractions
- Plot rational numbers on number lines
- Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions
- Solve real-world problems involving multiplication of fractions and mixed numbers
- Solve word problems involving addition and subtraction of fractions
- Understand and solve problems involving inequalities
- Understand and solve problems involving ordering and absolute value of rational numbers
- Use positive and negative numbers and number lines to describe real-world situations
- Use the coordinate plane to plot coordinates, draw simple figures, and calculate simple distances
- Use visual models and equations to represent and solve fraction division word problems

## Unit 3: Ratios, Rates, and Percentages

### Math

- Calculate and compare unit prices
- Find a part when given the whole amount and the percent of the whole the part represents
- Find a percent of a quantity as a rate per 100
- Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means to multiply 30/100 by the given quantity)
- Find a whole amount when given a part and the percent of the whole the part represents
- Find the percent that a part represents when given the whole amount and a part
- Manipulate and transform units appropriately when multiplying or dividing quantities
- Solve real-world and mathematical problems involving percents
- Solve unit rate problems including those involving unit pricing and constant speed
- Understand and describe ratios
- Understand and describe unit rates
- Use rate and rate reasoning, along with double number lines, to solve real-world and mathematical problems
- Use ratio and rate reasoning to solve real-word and mathematical problems
- Use ratio and rate reasoning to solve real-world and mathematical problems
- Use ratio and rate reasoning to solve real-world problems
- Use ratio and rate reasoning, along with tables, tape diagrams, double number lines, and graphs, to solve real-world and mathematical problems.
- Use ratio reasoning to convert measurement units

## Unit 4: Algebraic Expressions

### Math

- Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
- Apply mathematical operations and properties (e.g., commutative, associative, and distributive properties) to generate equivalent expressions.
- Apply rules for exponents to write and evaluate expressions.
- Correctly use the order of operations when evaluating expressions and formulas.
- Evaluate expressions for specific numerical values of their variables (e.g., evaluate formulas).
- Identify equivalent expressions.
- Identify the parts of an algebraic expression using mathematical terms (e.g., sum, term, product, factor, quotient, coefficient).
- Recognize parts of an algebraic expression as a single entity
- Recognize parts of an algebraic expression as a single entity.
- Recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3.
- Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
- Understand a rational number as a point on the number line.
- Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).
- Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.
- Understand what it means for two expressions to be equivalent.
- Use positive and negative numbers to represent quantities in real-world contexts.
- Use strategies to add and subtract expressions with rational coefficients.
- Write algebraic expressions from verbal descriptions.
- Write, read, and evaluate expressions in which letters (i.e., variables) stand for numbers.