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# The 4 Major Math Concepts Your Kids Learn in Grades 5-6

From ratios to equations, this quick refresher on your kids' math will also help you provide support at home.
on May 24, 2016

There can be quite a jump in math knowledge from fifth grade to sixth grade, and I like to think of it as crossing a bridge. The more we can connect the bridge, the better our children will feel about themselves in middle school. Fifth grade is a culmination of all that students have learned at the elementary level, while sixth grade can be seen as the starting point for middle school. And no matter how your child’s middle school works, there is a distinct connection between these grades. The more comfortable children are with these concepts by the end of sixth grade, the more they’ll be equipt for middle school.

Here are four of the major math concepts your child will cover in fifth and sixth grade:

1. Number System. In fifth grade, students focus on adding, subtracting, multiplying, and dividing whole numbers, fractions, and decimals. Your kid will become fluent with computing these types of numbers and understanding the relationship between them. Students should also be able to use these numbers in real-world scenarios. In sixth grade, kids continue their understanding of these numbers, and are also introduced to negative numbers. They will begin to identify rational numbers and integers on a number line as well as compare them. Using models will greatly improve your child’s understanding of these concepts.

• Recognize and calculate using fractions and decimals in the real world. For example, have your child figure out the discount from a sale; the amount of tax while shopping; find the tip of a bill, or explain sports stats.
• Use fraction bars to compute (adding, subtracting, multiplying, or dividing).

Image courtesy: LearnZillion

• Find examples of positive and negative numbers in the real world (temperature, distance, sea-level, etc.) and use models to help understand the relationship between them.

Image courtesy: The positive impact of Math

2. Ratios. Students will use their knowledge of fractions and decimals in fifth grade to reason ratio and rate problems in sixth grade. Kids will need to connect their understanding of multiplication and division with real-world problems using ratios. They will use models (diagrams, table, double number lines, etc.) to help them make these connections and solve unit rate problems. Students will also learn about percents and how they match up with fractions and decimals.

• Find examples of ratios in the real world. For example, “The ratio of wings to beaks in the birdhouse at the zoo was 2:1, because for every 2 wings there was 1 beak.”
• Use models to help understand ratio and rate problems:

Image courtesy: Mr. Pratt's 6th Grade Class

Image courtesy: nzmaths.

• Create real-world problems using ratio understanding. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.”

3. Expressions & Equations. Students start to distinguish the difference between an expression and an equation. They use variables to represent an unknown number in both expressions and equations. Fifth and sixth graders follow the appropriate order of operations to solve problems, including parentheses and exponents. Your children are beginning to read, interpret, and write expressions and equations, as well as solving one-variable equations.

• Distinguish between an expression and an equation, and understand the meaning of the equal sign:

Expression: 4y + 2
Equation: 4y + 2 = 14

• Solve problems using the acronym of PEMDAS:

Image courtesy: coolmath.com

• Read and write expression with ease: Subtract n from 8" as 8 - n.
• Create and solve real-world problems using variables. For example, "It costs \$100 to rent the skating rink plus \$5 per person. Write an expression to find the cost for any number (n) of people. What is the cost for 25 people? Answer: 100 + 5n; so for 25 people = 100 + 5(25) = 225."

4. Geometry: Students continue classifying figures into categories based on their properties. Your child will learn to find the area of triangles and some quadrilaterals. They will learn to calculate the volume of 3-D figures using whole numbers and fractional edges. Students begin to use represent real-world problems by graphing points on the coordinate plane.

• Understand the difference between finding area of a 2-D figure versus finding the volume of a 3-D figure. Point out different objects and ask if your kid would find the area or volume of that figure. For example, "Would you find the area oro volume of that backyard?" Or, "Would you find the area of volume of that swimming pool?"
• Use appropriate vocabulary when describing different polygons and geometric properties. For example, "What are parallel lines?"  Answer: "Two lines on a plane that never meet. They are always the same distance apart."
• Use their third grade learning on understanding how to find the area of a rectangle or to find the read of a triangle:

Image courtesy: The University of Georgia Department of Math Education

• Develop an understanding of the coordinate plane and begin to plot points using real-world scenarios (using graph paper). For example, “On a map, the library is located at (-2, 2), the city hall building is located at (0,2), and the high school is located at (0,0). Represent the locations as points on a coordinate grid with a unit of 1 mile.”

Don't worry if these concepts feel a little intimidating at first. Remember, you haven't been taking yearly math classes that build on each other like your children have. (At first, it may even feel like your chidren understand it better than you do!)

But that's the point of our "Major Math Concepts" blog series. We want you endowed with understanding these math concepts as well. You may get a jump start on your kids' learning, you may keep pace with them, but either will help you connect more with your child on what is often a challenging subject.

Have any questions about these concepts or any other questions on your child’s math? Submit them to Jennifer here so she can consider answering in an upcoming blog. Or share them with us on the Scholastic Parents Facebook Page.

Featured photo credit: © Oktay Ortakcioglu/iStockphoto