Teach To One Roadmaps - Math Skills

# 5th Grade

## Target the precise skills and concepts each student needs.

We’ve developed a system of organizing the 300 skills a student must learn cumulatively in order to be Algebra-ready. The skills and concepts covered in *Teach to One Roadmaps *allow students to gain unlearned, prerequisite skills while still advancing at grade level.

Browse the skills and concepts covered in each grade level below.

## Grade 5

### Multiplying and Dividing Large Numbers

- I will fluently multiply multi-digit whole numbers using the standard algorithm.
- I will divide large whole numbers by whole numbers with two or more digits and explain remainders within context.

### Understanding Volume

- I will understand volume and measure it using unit cubes.
- I will develop and use a formula for finding the volume of rectangular prisms.
- I will solve real world and mathematical problems involving additive volume and right rectangular prisms.

### Numerical Expressions

- I will use the order of operations, including parentheses, to evaluate numerical expressions involving whole numbers.
- I will write expressions to record operations with numbers, and interpret numerical expressions without evaluating them.

### Adding & Subtracting Unlike Fractions

- I will add and subtract fractions with unlike denominators.
- I will add and subtract mixed numbers with unlike denominators.
- I will solve problems by adding and subtracting fractions and mixed numbers with unlike denominators.

### Data Displays

- I will make line plots to display a data set measured in fractions and use operations with fractions to solve problems involving the data set.

### Dividing Fractions

- I will interpret fractions as division of the numerator by the denominator and solve whole number division problems leading to answers in the form of fractions or mixed numbers.
- I will divide whole numbers by unit fractions in real world and mathematical problems.
- I will divide unit fractions by whole numbers in real world and mathematical problems.
- I will solve word problems involving division between unit fractions and whole numbers.

### Fraction Equivalence

- I will simplify fractions to lowest terms.

### Multiplying Fractions

- I will multiply whole numbers by fractions.
- I will find the area of a rectangle with fractional side lengths.
- I will develop and use an algorithm for multiplying fractions.
- I will multiply mixed numbers.
- I will interpret multiplication as scaling.

### Coordinate Plane

- I will use a pair of perpendicular lines, called axes, to define a coordinate system and locate points using coordinates.
- I will solve real-world problems by plotting and interpreting points in the first quadrant of the coordinate plane.
- I will generate two numerical patterns using two given rules, graph ordered pairs of corresponding terms on a coordinate plane, and identify apparent relationships between corresponding terms.

### Decimal Operations

- I will add and subtract decimals using a variety of strategies.
- I will multiply a decimal by a whole number using a variety of strategies.
- I will multiply a decimal by a decimal using a variety of strategies.
- I will divide a decimal by a whole number using a variety of strategies.
- I will divide a decimal by a decimal using multiple strategies.

### Decimal Place Value

- I will understand the value of a single digit in a multi-digit number and explain the relationship between the digits.
- I will read and write decimal numbers using base ten numerals, number names, and expanded form.
- I will compare and order decimals using the math symbols <, >, and =.
- I will use rounding rules to round numbers to the ones place and decimal place values.

### Classifying Shapes

- I will classify and draw triangles by their angles and sides.
- I will classify and draw quadrilaterals by their angles and sides.

### Powers of 10

- I will explain patterns in the number of zeros in the products when multiplying whole numbers by 10; 100; and 1,000.
- I will explain patterns about multiplying or dividing decimal numbers by powers of ten.

### Unit Conversions

- I will identify and convert among customary units of length, capacity, and mass/weight.
- I will identify and convert among metric units of length, capacity, and mass/weight.
- I will solve real world and mathematical problems involving operations with decimal numbers that require unit conversions.

## Grade 4

### Decimal Place Value

- I will compare decimals using models.

### Addition & Subtraction

- I will add large whole numbers.
- I will subtract large whole numbers.

### Basic Multiplication

- I will identify and use the distributive property of multiplication over addition, relating it to area models.
- I will identify and use the distributive property of multiplication over addition, relating it to area models.
- I will make sense of multiplicative comparisons.

### Multiplication and Division Fundamentals

- I will multiply 2-digit by 2-digit numbers using area models to represent partial products.
- I will multiply large whole numbers by one-digit whole numbers using area models to represent partial products.
- I will divide large whole numbers by one-digit whole numbers and explain remainders within context.

### Understanding Area

- I will recognize area as additive and find the area of polygons composed of rectangles.

### Whole Numbers

- I will read and write whole numbers up to millions using base-ten numerals, number names, and expanded form.
- I will round whole numbers to the nearest ten, hundred, or thousand.
- I will compare whole numbers up to millions.

### Basic Algebraic Thinking

- I will solve word problems involving operations with whole numbers.
- I will generate a number or shape pattern that follows a given rule and identify features of the pattern.
- I will define, identify, and use the commutative and associative properties of addition and multiplication.
- I will identify all the factors of a given whole number and identify prime and composite numbers.

### Comparing Fractions

- I will compare and order fractions using the math symbols <, >, and =.

### Decomposing Fractions

- I will add and subtract fractions with like denominators.
- I will understand a fraction as a multiple of a unit fraction.
- I will recognize and generate equivalent products of fractions and whole numbers.
- I will decompose a fraction or mixed number into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.
- I will add and subtract mixed numbers with like denominators.

### Fraction Equivalence

- I will use fraction equivalence to add fractions with denominators of 10 and 100.
- I will understand decimals are part of a whole and express decimals as fractions to tenths or hundredths.
- I will create equivalent fractions and explain fraction equivalence.

### Representing Fractions

- I will add and subtract fractions with like denominators using models.

### Geometry Fundamentals

- I will identify and classify lines, line segments, rays, and angles.
- I will identify and draw intersecting, perpendicular, and parallel lines.
- I will draw and measure angles and classify angles as acute, obtuse, right, and straight.

## Grade 3

### Addition & Subtraction

- I will add numbers within 1000 using a variety of strategies.
- I will subtract numbers within 1000 using a variety of strategies.

### Basic Multiplication

- I will multiply one-digit whole numbers by multiples of 10.
- I will calculate and list multiples of whole numbers.

### Multiplication and Division Fundamentals

- I will understand multiplication and know multiplication facts up to 10 times 10.
- I will interpret division as equal shares and know division facts with one-digit numbers.
- I will determine an unknown whole number in a multiplication or division equation.

### Understanding Area

- I will calculate the perimeter of regular or irregular polygons and solve problems involving perimeter.
- I will understand the concept of area and find area of figures by counting square units.
- I will develop and use a formula for finding the area of rectangles.

### Basic Algebraic Thinking

- I will solve two-step word problems using all four operations.

### Comparing Fractions

- I will compare fractions with the same numerator or denominator.

### Fraction Equivalence

- I will recognize and generate equivalent fractions using visual models.
- I will recognize and generate fractions and whole numbers that are equivalent.

### Representing Fractions

- I will describe fractions using numbers, words, and pictures.
- I will represent fractions on a number line.

## Grade 2

### Data Displays

- I will read and interpret different types of graphs.

### Addition & Subtraction

- I will find sums and differences within 100 and represent them on the number line.

### Whole Numbers

- I will read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.

### Representing Fractions

- I will partition shapes and describe the shares using halves, thirds, and fourths.