Grade 6 Fractions & Decimals Study Guide

Grade 6 Fractions and Decimals Study Guide

Relate improper fractions to mixed numbers and mixed numbers to improper fractions

-Example questions: Write 1 4/8 as an improper fraction. Write 29/9 as a mixed number fraction. We learned a formula for doing these conversions.

Compare and order mixed number and improper fractions

-For example, you may be given a number line from 0 to 2 and be asked to order the following fractions from least to greatest: 1 ¾, 9/8, and 3/2. 

-Know how to use symbols to represent greater than, equal to, or less than (< = >).

Represent ratios in a variety of ways (using the word ‘to’, using the symbol ‘:’, as a fraction, and by drawing pictures.

-Example question: represent the ratio 2:6 in two other ways (2 to 6, 2/6)

-Know how to write a ratio based on a picture (for example, 6 bats and 3 balls = 6:3).

-Understand that a ratio can be written either way (for example, balls to bats (3:6) or bats to balls (6:3).

Know how to find equivalent ratios

-For example, to find an equivalent ratio to 3:6, simply multiply both numbers by 2 (6:12)

Know how to relate fractions, decimals, and percents

-For example, 40/100, .40, and 40% all represent the same amount. 

-Be able to represent decimals, fractions, and percentages on a 10 x 10 (hundreds) grid

-Be able to determine what percent is shaded from a pictorial representation (for example, 4 of 8 sections of a pizza are shaded, what percent is shaded?).

-Be able to convert a decimal or a fraction to a percent (for example, to find the percent of 4/50, multiply the numerator and denominator by 2 so that the denominator is 100 (A = 8%). If you cannot make the denominator out of 100, remember the formula (numerator x 100 divided by the denominator = %). 

Vocabulary

Numerator – The top number in a fraction, this number tells how many equal parts are counted.

Denominator – The bottom number in a fraction (remember, D = Down). This number tells how many equal parts are in 1 whole.

Mixed Number Fraction – Has a whole number part and a fraction part (example: 1 ½).

Improper Fraction – Shows an amount greater than one whole (example: 7/2).

Ratio – Comparison of two quantities with the same unit. 

Grade 5 Fractions & Decimals Study Guide

Grade 5 Fractions and Decimals Study Guide

Be able to represent fractions with pictures and write a fraction based on a picture.

Example question: Draw a picture to show the fraction 4/8 (the student could draw 8 birds and circle 4 of them, or they could draw a bar split into 8 sections with 4 shaded – these are just 2 of many examples).

Understand tenths, hundredths, and thousandths

-For example, in 0.456, the 4 is in the tenths place value, the 5 is in the hundredths, and the 6 is the thousandths. Students are expected to know how to read this as “four hundred fifty six thousandths.”

Be able to represent decimals and fractions on a 10 x 10 (hundred) grid

Relate decimals to fractions and fractions to decimals

-Example questions: Write the fraction 3/10 as a decimal. Write the decimal .35 as a fraction.

-Be able to write an equivalent fraction from a decimal and an equivalent decimal from a fraction

Understand equivalent fractions and decimals

-For example: 0.04, 0.040, 0.0400, 0.04000 all represent an equivalent fraction

-3/4, 75/100, 6/8, and 0.75 are also all equivalent

Be able to compare and order fractions and decimals

Example question: Order the following decimals from least to greatest: 5.087, 5.102, 5.09

-Know how to use symbols to represent greater than, equal to, or less than (< = >)

-Know how to use benchmarks on a number line to compare and order fractions

Know how to convert decimal numbers to a different unit of measurement

-Remember: KHDMDCM

-For example: A horse is 5.81 meters long. How many centimeters is that?

Be able to add and subtract decimals and use estimation strategies

-Example questions: Add: 3.467 + 5.393. Subtract: 18.265 – 6.98. Estimate the sum: 4.8 + 3.293 (you would choose a rounding strategy to round the two numbers and then add – be prepared to explain what estimation strategy was used)

Relate fractions and decimals to division

-For example, the division sentence 5 divided by 3 can be written as 5/3.

-Know how to divide and represent the answer’s remainder as a fraction

-For example, 5 divided by 3 would equal 1 whole and 2/3  

Vocabulary

Numerator – The top number in a fraction, this number tells how many equal parts are counted.

Denominator – The bottom number in a fraction (remember, D = Down). This number tells how many equal parts are in 1 whole.

Sum – Answer to an addition problem.

Difference – Answer to a subtraction problem.

Grade 6 Multiplication and Division Study Guide

Grade 6 Multiplication and Division with Decimals Study Guide

Solve problems involving whole numbers and decimal numbers.

Represent Decimal Numbers: Be able to represent a decimal number in a place value chart, expanded form, standard form, and word form. Refer to your problem slips for a review.

Demonstrate an understanding of multiplication and division of decimals (1-digit whole number multipliers and 1-digit whole number divisors).

·       For example, know how to multiply 2.936 x 4 by first estimating, then multiplying without the decimal, and finally, putting the decimal back on to the product using your estimation to help you.

·       Example 2: know how to divide 7.938/2 by dividing without the decimal point (using long division), and then adding the decimal point by placing it according to how many digits are before the decimal point in the dividend.

Know how to divide a decimal less than 1 by a whole number, such as 0.0860/5. You will need to remember the process for how to divide until there is no decimal (adding a 0 to the remainder).

Be able to estimate products and quotients using rounding strategies like front-end estimation (5.81 x 7 would be changed to 5 x 7), decimal benchmarks (5.81 is closer to 6 than to 5, so you would round to 6 x 7), and compatible numbers.

Be able to create and solve word problems involving multiplication and division with decimal numbers.

Understand the following language:

Product – The answer to a multiplication problem.

Quotient – The answer to a division problem.

Divisor – The smaller number in a division problem, the one in which the larger number is being divided into. For example, in the division problem 18/4, 18 is the number being divided by the divisor 4.

Dividend – The larger number in a multiplication problem, the one that is being divided (18 in the example above).

Grade 5 Multiplication and Division Study Guide

Grade 5 Multiplication and Division Study Guide

1) Know how to use strategies to find the answer to multiplication facts up to 9 x 9.

·      Use Repeated Doubling: For example, to find 8 x 4, you can use doubling from an easier fact. 8 x 2 = 16; doubling the product (16) gives you 32, which is the answer to 8 x 4).

·      Skip Counting: For example, to find 5 x 5, you can skip count 5, 5 times.

·      Use Known Facts: For example, if you known 6 x 6 = 36, you can use that fact to help you find 6 x 7.

2) Know how to use strategies to find the answer to 2-digit by 1-digit division.

• Related Multiplication Facts: To find 72 ÷ 8, think 8 times what number is 72? If you know that 8 x 9 = 72, then 72 ÷ 8 = 9.
• Halving: To find 64 ÷ 4, you could think 64 ÷ 2 = 32, and then divide it by 2 again to get 32 ÷ 2 = 16. You can also do Repeated Halving. For example, to find 96 ÷ 8, you could first divide 96 by 2 which is 48, and then divide it by 2 again which is 24, and then divide it by 2 one more time which is 12. Therefore 96 ÷ 8 = 12.
• Repeated Subtraction: This is kind of like the opposite of skip counting. To find 18 ÷ 6 I can keep subtracting 6 from 18 until I get to 0. The amount of times I had to subtract 6 is my answer. 18 – 6 = 12 – 6 = 6 – 6 = 0. So 18 ÷ 6 = 3.
• Understanding how to write a related multiplication and division fact. For example, the related facts for 9 x 2 = 18 include: 2 x 9 = 18, 18/2 = 9 and 18/9 = 2. Know how to use these related facts to solve a problem (use your knowledge of 7 x 4 = 28 to find 28/ 7 =?)

3) Demonstrate an understanding of multiplication (2- or 3-digit by 1-digit) to solve problems by using a strategy that works for you, such as:

• Using personal strategies for multiplication
• Using the traditional algorithm.
• Using cross multiplication. 
• Using lattice multiplication.
• Applying the distributive property (this property lets you multiply a sum by breaking down the numbers into their place values, multiplying them separately, and then adding the products). For example, to multiply 14 x 7, the student could multiply the tens (10 x 7) and then the ones (4 x 7), and then add the two numbers).

4) Apply mental mathematics strategies for multiplication, such as:

• Removing and then re-adding zero (for example, to find the answer to 700 x 30, multiply 7 x 3 and add the three 0’s). * Know how to multiply with multiples of 10 up to 1000.

5) Demonstrate an understanding of division (3-digit by 1-digit), and interpret remainders to solve problems.

• Remember the steps for long division, use the family trick (Dad = divide, Mom = multiply, Sister = subtract, Brother = bring down, Rover = Repeat or remainder) to help you! Know how to multiply to check your answer.

6) Remember a variety of estimation strategies to solve products (examples: front end rounding, rounding to the nearest ten, nearest hundred, and using compatible numbers). 

Understand the following language:

Product – The answer to a multiplication problem.

Quotient – The answer to a division problem.

Divisor – The smaller number in a division problem, the one in which the larger number is being divided into. For example, in the division problem 18/4, 18 is the number being divided by the divisor 4.

Dividend – The larger number in a multiplication problem, the one that is being divided (18 in the example above).