In Grade 5, students encounter new components in math problems for Common Core Standards, such as brackets and parentheses. Certain concepts introduced in earlier grades, such as working with fractions and decimals, are more specialized and are used in multiplication and division. Students also continue to look at representations of data and take their first steps in graphing points on a coordinate plane.

Common Core Standards for Grade 5 math call for a focus on three key areas:

• Fractions: Students develop fluency with multiplying fractions and a conceptual understanding of the procedures used to multiply fractions.

• Division: Students hone their skills in division by dividing by two-digit divisors and developing an understanding of decimal fractions and the place values of numbers that come after the decimal point.

• Volume: Grade 5 math introduces the concept of the volume of three-dimensional objects.

## Operations and algebraic thinking

Mathematical calculations are extended in this domain. Students discover how to complete expressions that include brackets, parentheses, and other symbols in order to grasp the order of operations. The order of operations rules govern the sequence in which you perform operations (such as addition, subtraction, and multiplication) in multi-operation equations. The order goes like this:

• Parentheses and exponents

• Multiplication and division

• Addition and subtraction

For example, in this equation

(4 × 2) + 32 – (9 ÷ 3)2 × 5 =

you perform the operations in the following sequence:

1. Operations in parentheses first, which gives you:

(8) + 32 – (3)2 × 5 =

2. Exponents, which gives you:

(8) + 9 – 9 × 5 =

3. Multiplication, which gives you:

(8) + 9 – 45 =

4. Addition, which gives you:

17 – 45 =

5. Subtraction, which gives you the final result:

-28

In addition to order of operations, students are introduced to patterns with more than one rule, and they graph pairs of numbers from a pattern on a coordinate plane.

Practice solving problems that require multiple operations to reinforce your child’s understanding of the order of operations. Help him come up with a way to remember the order of operations so that he doesn’t get confused when working problems.

Don’t let your child get lost in the new details. Help him understand how symbols such as brackets and parentheses are used in the order of operations so that he stays on track.

## Number and operations in base ten

Grade 5 math applies the concept of place value to decimals. Students see that each place is 1/10 of the place to the left, and students are challenged to add, subtract, multiply, and divide by numbers with decimals to the thousandths place.

Write a series of numbers that includes decimals up to the thousandths place. Ask your child to explain the value of each place in the number, including comparing the value of the place held by digits within the same number. Then give her a multi-digit number, such as 23.45, and ask her to tell you how many tenths and hundredths there are.

This encourages your child to develop a deeper understanding of the relationship between the places.

## Number and operations: Fractions

In Grade 5, students take another look at adding and subtracting with mixed numbers (a whole number with a fraction) and fractions that have different denominators, including their use in word problems. Students also discover how to multiply and divide fractions by other fractions, including in real-world situations where fractions are used.

Practice adding and subtracting mixed numbers and fractions that have different denominators. Continue using everyday objects to represent fractions. Be sure to represent the whole number in a mixed number with whole unit(s) of the objects so that your child begins to understand that the mixed number is a whole number added to a fraction.

## Measurement and data

Students begin to convert units into other units (for example, feet into inches) and are able to do so in real-world problems. Volume is added as a characteristic of solid figures, and students explore various ways to measure volume in rectangular prisms with edges represented by whole numbers.

Convert units of measure by using a ruler or other tool to measure a rectangular object, such as a large book. Then have your child convert inches into feet. You can use the formulas for volume (volume = length × width × height, or volume = base × height) to find the volume of the same object. Ask your child to describe what volume represents for each object measured.

## Geometry

Students graph points on a coordinate plane and identify the location and use of the X axis and Y axis when graphing an ordered pair. They find out how to solve real-world problems by graphing ordered pairs in the first quadrant (when both numbers are positive).

They also use characteristics of shapes to classify them into one or more categories with other similar shapes. For example, students may be asked to explain how a square can be a rectangle and a rhombus at the same time (even though a rhombus is not a rectangle).

Help your child get comfortable with the coordinate plane by practicing graphing various sets of ordered pairs. Reinforce the use of the X axis and Y axis by asking your child to explain why she places the points in the ordered pairs in particular locations. Look for graphs in newspapers and magazines and ask your child to explain what the graph shows.