# Math Scope and Sequence

This page provides a high-level overview of the skills and facts that are covered in our math curriculum.

## Age 5-7

### Semester 1

#### Unit 1: Number Sense 1-20 (27 days)

Counting, ordering and comparing numbers, creating number bonds, making 10, recognizing patterns, learning skip counting

#### Unit 2: Geometry (14 days)

Exploring two-dimensional and three-dimensional shapes, understanding shape attributes, forming halves and quarters

#### Unit 3: Addition and Subtraction to 10 (14 days)

Adding and subtracting to 10, counting coins, using an abacus, number line, and counters

#### Unit 4: Data and Graphing (13 days)

Collecting and representing data, using tally marks and tally graphs, creating pictographs and bar graphs

#### Unit 5: Addition and Subtraction to 20 (17 days)

Understanding mathematical properties, adding three numbers, reading and writing in mathematical language, learning addition and subtraction problem-solving strategies

### Semester 2

#### Unit 6: Time (14 days)

Exploring the concept and measurement of time, learning both digital and analog formats, reading and writing time to the ½ hour, sequencing time, and relating time to daily activities

#### Unit 7: Place Value (27 days)

Representing two-digit and three-digit numbers, understanding tens and ones place value, sequencing and comparing numbers to 120, adding and subtracting larger numbers

#### Unit 8: Measurement (17 days)

Exploring linear measurement using nonstandard units, introducing the measurement of weight, temperature, and volume

#### Unit 9: Addition to 100 (17 days)

Synthesizing skills for adding and subtracting within 100, adding two-digit numbers, adding multiples of ten, adding a one-digit number to a two-digit number, developing mental math strategies

#### Unit 10: Skills Review (6 days)

Reviewing addition and subtraction, fact fluency within 10, place value, linear measurement, and basic geometric shapes and attributes

## Age 6-8

### Semester 1

#### Unit 1: Number Sense

Number patterns, mathematical language, greater than, less than, equal to, odd and even numbers

#### Unit 2: Addition and Subtraction / Fact Power!

Fluency in addition and subtraction to 20, fact power, arrays, commutative property of addition, doubles, fact families

#### Unit 3: Geometry

2D and 3D shapes, sides, angles, vertices, faces, edges, halves, quarters, thirds, tessellations, tangrams

#### Unit 4: Place Value I

Place value to the thousands, skip counting by 10s and 100s, composing tens, carrying

### Semester 2

#### Unit 5: Measurement: Length

US Customary System, metric system, selecting units

#### Unit 6: Place Value II

Adding and subtracting two-digit and three-digit numbers, borrowing, sequencing and comparing three-digit numbers

#### Unit 7: Telling Time

Telling time to 5 minutes, AM and PM, using time to communicate and plan

#### Unit 8: Money

Coins and bills up to $5, money problems

#### Unit 9: Data and Graphing

Collecting and displaying data, graphing up to four categories, pictographs, bar graphs, line plots, using data to draw conclusions

#### Unit 10: Skills Review

Review place value to 1000, addition and subtraction within 1000, linear measurement using standard units, geometric shapes, time, money, and graphing

## Age 7-9

### Semester 1

#### Unit 1: Multiplication and Division I

Multiplication strategies; commutative property of multiplication; multiples of 2, 3, 4, 5, and 10; multiplication problem solving; division; multiplication and division fact families

#### Unit 2: Place Value

Review of three-digit place value, numbers to 10,000, rounding, using rounding to estimate sums and differences, adding and subtracting four-digit numbers

#### Unit 3: Measurement

Telling time to the minute, elapsed time, weight, volume

#### Unit 4: Multiplication and Division II

Multiplication and division facts; multiples of 6, 7, 8, and 9; associative and distributive properties of multiplication; multiplication and division problem solving

### Semester 2

#### Unit 5: Area and Perimeter

Plane shapes review, calculating perimeter and area, solving perimeter and area problems

#### Unit 6: Fractions

Introduction to fractions, fraction parts, division and groups, fractions on number lines, equivalent fractions, fraction problem solving

#### Unit 7: Geometry

Parallel, intersecting, and perpendicular lines; attributes of quadrilaterals; dividing shapes; geometric problem solving

#### Unit 8: Graphing Data

Data collection; reading and creating pictographs, bar graphs, line plots

#### Unit 9: Skills Review

Reviewing multiplication and division, fractions, perimeter and area, and geometry

## Age 8-10

### Semester 1

#### Unit 1: Place Value to 1,000,000

Place value to the millions place; comparing, rounding, adding, and subtracting large numbers; rounding to estimate

#### Unit 2: The Four Operations

Addition and subtraction problem solving, review of multiplication and division, multiples and factors, prime and composite numbers, working with equations

#### Unit 3: Geometry

Points, lines, line segments, and rays; classifying, measuring, and adding angles; using a protractor; classifying triangles; symmetry

#### Unit 4: Multi-Digit Multiplication

Multiples of 10, 100, 1000, and above; multi-digit multiplication using arrays, area models, and the standard multiplication algorithm

### Semester 2

#### Unit 5: Fractions

Identifying, creating, and naming fractions and mixed numbers; comparing, decomposing, and simplifying fractions; adding and subtracting fractions and mixed numbers with like denominators; solving fraction word problems

#### Unit 6: Multi-Digit Division

Long division, division with remainders, division problem solving

#### Unit 7: Decimals

Identifying, reading, writing, and comparing decimal numbers; decimal place value; relating fractions and mixed numbers to decimals; decimals on a number line; converting decimals to fractions

#### Unit 8: Measurement

Customary and metric units; converting units of length, weight, and capacity; review of time, perimeter, and area; measurement problem solving

#### Unit 9: Skills Review

Reviewing multi-digit multiplication and division, geometry, fractions, decimals, customary and metric measurement, and area and perimeter

## Age 9-11

### Semester 1

#### Unit 1: Place Value: Million to Thousandths

Place value from thousandths to millions, comparing and rounding decimal numbers, working with powers of 10 and Roman numerals

#### Unit 2: The Four Operations

Adding, subtracting, multiplying, and dividing whole numbers and decimals; understanding mathematical expressions, order of operations, and prime factorization

#### Unit 3: Measurement

Conversion and problem solving with time as well as metric and customary units of length, mass/weight, and capacity

#### Unit 4: Adding and Subtracting Fractions

Finding equivalent fractions, comparing and ordering fractions, adding and subtracting fractions and mixed numbers with like and unlike denominators, solving fraction word problems

### Semester 2

#### Unit 5: Multiplying Fractions

Using a variety of models to understand fraction multiplication; multiplying fractions and mixed numbers; finding fractional area

#### Unit 6: Geometry

Identifying and classifying polygons, reviewing types of graphs, creating and interpreting graphs on a coordinate plane

#### Unit 7: Dividing Fractions

Exploring the concept of fraction division, solving division problems involving whole numbers and unit fractions

#### Unit 8: Volume

Finding perimeter and area; using models to explore volume; finding the volume of cubes and rectangular prisms; solving word problems involving perimeter, area, and volume

#### Unit 9: Skills Review

Reviewing concepts including operations of fractions and decimals; finding the volume of rectangular prisms; and working with coordinate graphs

## Age 10-12

### Semester 1

#### Unit 1: Operations

Adding, subtracting, multiplying, and dividing whole numbers and decimals; working with factors, multiples, exponents, and order of operations

#### Unit 2: Integers and Rational Numbers

Reviewing fraction addition, subtraction, and multiplication; solving fraction division problems; understanding negative numbers; plotting coordinates and drawing shapes on a coordinate plane

#### Unit 3: Ratios and Percentages

Exploring algebraic expressions; working with mathematical properties; simplifying expressions and finding equivalent expressions

#### Unit 4: Algebraic Expressions

Exploring algebraic expressions; working with mathematical properties; simplifying expressions and finding equivalent expressions

### Semester 2

#### Unit 5: Algebraic Equations

Solving one-step and two-step algebraic equations; exploring inequalities, two-variable equations, and dependent and independent variables

#### Unit 6: 2D Geometry

Working with angles and triangles; finding the area of polygons and circles; creating scale drawings

#### Unit 7: 3D Geometry

Using nets to create 3D shapes; solving surface area and volume problems; working with cross sections

#### Unit 8: Statistics

Using nets to create 3D shapes; solving surface area and volume problems; working with cross sections

#### Unit 9: Skills Review

Reviewing operations with decimals and fractions; plotting on the coordinate plane; ratio and percentage; algebraic equations and inequalities; and area, volume, and surface area