 #### CURRICULUM

What your child will be learning in kindergarten mathematics

In kindergarten, your child will focus primarily on two important areas. The ﬁrst is learning numbers and what numbers represent. The second is addition and subtraction. Students will also learn to identify and work with shapes. Activities in these areas include:

• Counting how many objects are in a group and comparing the quantities of two groups of objects

• Comparing two numbers to identify which is greater or less than the other

• Understanding addition as putting together and subtraction as taking away from

• Adding and subtracting very small numbers quickly and accurately

• Breaking up numbers less than or equal to 10 in more than one way (for example, 9=6+3, 9=5+4)

• For any number from 1 to 9, finding the missing quantity that is needed to reach 10

• Representing addition and subtraction word problems using objects or by drawing pictures

• Solving addition and subtraction word problems involving numbers that add up to 10 or less or by subtracting from a number 10 or less

In grade one, students will work with whole numbers and place value—including grouping numbers into tens and ones as they learn to add and subtract up through 20. Students will also use charts, tables, and diagrams to solve problems. Activities in these areas will include:

• Quickly and accurately adding numbers together that total up to 10 or less and subtracting from numbers up through 10

• Understanding the rules of addition and subtraction (for example, 5+2=2+5)

• Solving word problems that involve adding or subtracting numbers up through 20

• Understanding what the different digits mean in two-digit numbers (place value)

• Comparing two-digit numbers using the symbols > (more than), = (equal to), and < (less than)

• Understanding the meaning of the equal sign (=) and determining if statements involving addition and subtraction are true or false (for example, which of the following statements are true? 3+3=6, 4+1=5+2)

• Adding one- and two-digit numbers together

• Measuring the lengths of objects using a shorter object as a unit of length

• Putting objects in order from longest to shortest or shortest to longest

• Organizing objects into categories and comparing the number of objects in different categories

• Dividing circles and rectangles into halves and quarters

• In grade two, students will extend their understanding of place value to the hundreds place. They will use this place value understanding to solve word problems, including those involving length and other units of measure. Students will continue to work on their addition and subtraction skills, quickly and accurately adding and subtracting numbers up through 20 and also working with numbers up through 100. They will also build a foundation for understanding fractions by working with shapes and geometry. Activities in these areas will include:

• Quickly and accurately adding numbers together that total up to 20 or less or subtracting from numbers up through 20

• Solving one- or two-step word problems by adding or subtracting numbers up through 100

• Understanding what the different digits mean in a three-digit number

• Adding and subtracting three digit numbers

• Measuring lengths of objects in standard units such as inches and centimeters

• Solving addition and subtraction word problems involving length

• Solving problems involving money

• Breaking up a rectangle into same-size squares

• Dividing circles and rectangles into halves, thirds, or fourths

• Solving addition, subtraction, and comparison word problems using information presented in a bar graph

• Writing equations to represent addition of equal numbers

In grade three, students will continue to build their concept of numbers, developing an understanding of fractions as numbers. They will learn the concepts behind multiplication and division and apply problem-solving skills and strategies for multiplying and dividing numbers up through 100 to solve word problems. Students will also make connections between the concept of the area of a rectangle and multiplication and addition of whole numbers. Activities in these areas will include:

• Understanding and explaining what it means to multiply or divide numbers

• Multiplying all one-digit numbers from memory (knowing their times table)

• Multiplying one-digit numbers by multiples of 10 (such as 20, 30, 40)

• Solving two-step word problems using addition, subtraction, multiplication, and division

• Understanding the concept of area

• Relating the measurement of area to multiplication and division

• Understanding fractions as numbers

• Understanding and identifying a fraction as a number on a number line

• Comparing the size of two fractions

• Expressing whole numbers as fractions and identifying fractions that are equal to whole numbers (for example, recognizing that 3⁄1 and 3 arethe same number)

• Measuring weights and volumes and solving word problems involving these measurements

• Representing and interpreting data

In grade four, your child will use addition, subtraction, multiplication, and division to solve word problems, including problems involving measurement of volume, mass, and time. Students will continue to build their understanding of fractions—creating equal fractions, comparing the size of fractions, adding and subtracting fractions, and multiplying fractions by whole numbers. They will also start to understand the relationship between fractions and decimals. Activities in these areas will include:

• Adding and subtracting whole numbers up to 1 million quickly and accurately

• Solving multi-step word problems, including problems involving measurement and converting measurements from larger to smaller units

• Multiplying and dividing multi-digit numbers

• Extending understanding of fractions by comparing the size of two fractions with diﬀerent numerators (top numbers) and diﬀerent denominators (bottom numbers)

• Creating equal fractions (3⁄4 = 3x2⁄4x2 = 6⁄8)

• Adding and subtracting fractions with the same denominator

• Building fractions from smaller fractions (3⁄8 = 1⁄8+1⁄8+1⁄8)

• Connecting addition and subtraction of whole numbers to multiplying fractions by whole numbers

• Connecting addition of fractions to the concept of angle measurement

• Representing and interpreting data

• Converting fractions with denominators of 10 or 100 into decimals

• Locating decimals on a number line

• Comparing decimals and fractions using the symbols > (more than), = (equal to), and < (less than)

In grade ﬁve, students will build their understanding of the place value system by working with decimals up to the hundredths place. Students will also add, subtract, and multiply fractions, including fractions with unlike denominators. They will continue to expand their geometry and measurement skills, learning the concept of volume and measuring the volume of a solid ﬁgure. Activities in these areas will include:

• Quickly and accurately multiplying multi-digit whole numbers

• Dividing numbers with up to four digits by two digit numbers

• Using exponents to express powers of 10 (in 102, 2 is the exponent)

• Reading, writing, and comparing decimals to the thousandths place

• Adding, subtracting, multiplying, and dividing decimals to the hundredths place

• Writing and interpreting mathematical expressions using symbols such as parentheses. For example, “add 8 and 7, then multiply by 2” can be written as 2× (8+7).

• Adding and subtracting fractions with unlike denominators (bottom numbers) by converting them to fractions with matching denominators

• Multiplying fractions by whole numbers and other fractions

• Dividing fractions by whole numbers and whole numbers by fractions

• Analyzing and determining relationships between numerical patterns

• Measuring volume using multiplication and addition

In grade six, your child will learn the concept of rates and ratios and use these tools to solve word problems. Students will work on quickly and accurately dividing multi-digit whole numbers and adding, subtracting, multiplying, and dividing multi-digit decimals. Students will extend their previous work with fractions and decimals to understand the concept of rational numbers—any number that can be made by dividing one integer by another, such as ½, 0.75, or 2. Students will also learn how to write and solve equations—mathematical statements using symbols, such as 20+x = 35—and apply these skills in solving multi-step word problems. Activities in these areas will include:

• Understanding and applying the concepts of ratios and unit rates, and using the correct language to describe them (for example, the ratio of wings to beaks in a ﬂock of birds is 2 to 1, because for every 2 wings there is 1 beak)

• Building on knowledge of multiplication and division to divide fractions by fractions

• Understanding that positive and negative numbers are located on opposite sides of 0 on a number line

• Using pairs of numbers, including negative numbers, as coordinates for locating or placing a point on a graph

• Writing and determining the value of expressions with whole-number exponents (such as 15+32)

• Identifying and writing equivalent mathematical expressions by applying the properties of operations. For example, recognizing that 2 (3+x) is the same as 6+2x

• Understanding that solving an equation such as 2+x = 12 means answering the question, “What number does x have to be to make this statement true?”

• Representing and analyzing the relationships between independent and dependent variables

• Solving problems involving area and volume

In grade seven, students will further develop their understanding of rates and ratios, using tables, graphs, and equations to solve real-world problems involving proportional relationships. Students will also work on quickly and accurately solving multi-step problems involving positive and negative rational numbers—any number that can be made by dividing one integer by another, such as ½, 0.75, or 2. Additionally, students will expand their knowledge of geometry and apply the properties of operations to solve real world problems involving the measurement of multi-dimensional objects. Activities in these areas will include:

• Determining whether two quantities are in a proportional relationship and using knowledge of rates, ratios, proportions, and percentages to solve multi-step problems

• Identifying the unit rate of change (the constant rate at which the value of a variable changes) in tables, graphs, equations, and verbal descriptions

• Calculating the unit rates associated with ratios of fractions, including quantities measured in different units (for example, the ratio of ½ a mile for every ¼ of an hour means that you travel 2 miles in an hour)

• Solving problems using equations to find the value of one missing variable

• Applying the properties of operations to generate equivalent mathematical expressions

• Solving multi-step word problems by adding, subtracting, multiplying, and dividing positive and negative rational numbers in any form (including whole numbers, fractions, or decimals)

• Understanding that numbers cannot be divided by 0

• Converting rational numbers to decimals using long division

• Describing situations in which positive and negative quantities combine to make 0

• Finding the area of two-dimensional objects and the volume and surface area of three-dimensional objects