Dear 5th Grade Families,
We would like to provide you with additional support and resources to help your child at
home with math during 3rd quarter. As you know, we have transitioned to the Common
Core Math Standards. We hope this letter is helpful in supporting your child in math at
home. Please don’t hesitate to contact your child’s teacher with questions.
What are the “Common Core Standards?”
They are standards designed to create clear, consistent expectations for what all students
should learn at each grade level to prepare them for college and career. These standards
help ensure that all students are receiving a high quality education consistently, from school
to school and state to state. These MATH standards stress conceptual understanding. This
‘new’ way of teaching and learning builds a strong foundation for our students.
Resources
*Google/YouTube – search the standard number (ex. 5.NF.3) in Google or YouTube to locate
videos, examples, worksheets, etc.
*Websites:
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•
•
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http://www.corestandards.org
http://illustrativemathematics.org/
http://learnzillion.com/
http://www.khanacademy.org/
http://www.azed.gov/standards-practices/mathematics-standards/
*Help your child memorize basic facts (addition, subtraction, multiplication, division)
*Discuss/explain and “do” real life math
What is your 5th Grade student learning in 3rd quarter?
Numbers and Operations in Base Ten
• Multiply decimals to the hundredths. (5.NBT.7)
o Example 1: Find the product of 0.3 x 0.4
Visual Model:
The double shaded
part is the product.
The answer is .12
or 12 hundredths
o Example 2: Find the product of 3.7 x 0.8
Place Value Model:
• Divide whole numbers and decimals to the hundredths. (5.NBT.7)
o Example 1: Divide 0.72 by 8
There are 8 groups. Each group of
8 has 0.09 in it.
The quotient (answer) is 0.09
o Example 2: Divide a decimal by a decimal using visual models
o Example 3: Decimal divided by a decimal (long division style)
Students use place
value to get a
decimal out of the
divisor position.
Students would use the
standard algorithm (long
division) to solve this
problem.
Numbers and Operations – Fractions
• Interpret a fraction as division of the numerator by the denominator (i.e. ¾ = 3 ÷4)
(5.NF.3)
o Example: Peter and his three friends are going to share three pepperoni pizzas
at Peter's birthday party. If they share the pizzas equally, what fraction of a
whole pizza does each person get?
• Multiply a fraction by a whole number. (5.NF.4a)
• Multiply a fraction by a fraction (5.NF.4a)
o Example 1: Use a visual fraction model to solve
= The circle represents product
of the two fractions
o Example 2: Solve the multiplication problem using equation form (standard
algorithm)
Multiply across the numerator and
1 3 13
3
=
=
then the denominator
2 8
28
16
• Solve real-world problems by multiplying a mixed number by a fraction or a whole
number (5.NF.6)
o Example 1: Kate has 1 ½ lbs of candy and she ate ¾ of her total candy. How
much did she eat?
The shaded part
This part is crossed off because
1 3
1
represents ¾ of the 1 ½.
we only need 1 ½ lbs!
1 × =1
2 4
8
Draw a picture:
If you look at “one whole piece”, you will see that it is divided into 8 total
pieces. Therefore, the answer is 9/8 or 1 1/8.
o Example 2: Same word problem from above, but using the standard algorithm
for multiplying mixed numbers.
1 × = × =
9
1
=1
1 3
8
8
1 =
2 2
• Find the area of a rectangle with fractional side lengths. (5.NF.4b)
o Example:
• Divide whole numbers by unit fractions and unit fractions by whole numbers and
create a representation or model to explain the quotient. (5.NF.7 a, b, and c).
o Vocabulary: Unit Fractions are fractions with a 1 in the numerator and any other
number in the denominator. Common Unit Fractions include:
o Example 1: Divide by 4. (Problem ÷ 4) Draw a model to solve.
1
8
Each piece is worth 1/8. Therefore the answer is 1/8.
We take ½ and divide it into 4
pieces. We are trying to
determine what each piece is
worth.
o Example 2: 3 ÷ Find the quotient. Draw a model to solve.
1. Draw three whole bars
2. Cut each whole box into fourths (because we are dividing by ¼)
3. Count how many total pieces there are now (12)
4. 3 ÷ = 12
, , , , , , .
• Recognize that multiplying by a number greater than one whole results in a larger
product while multiplying by a number less than one whole results in a smaller product.
(5.NF.5a and b)
o Example: Determine if the FIRST (given) number is greater than or less than the
product of the following two numbers:
×4
Two ways to solve this problem: Draw a picture or solve the equation
Students will be expected to EXPLAIN their reasoning!
Answer: I think that product of 2/3 and 4 will be greater than 2/3 because when I use a
picture to show 2/3 of 4, I get 8/3, which is 2 2/3. 2 2/3 is greater than 2/3.