Welcome to
5th Grade
math Night!
Samantha Clegg and Jacklyn Gelman
Tonight’s Agenda
� Common Core Areas of Focus� Standards of Mathematical Practice� Conceptual Knowledge + Operational
Skills� Algorithms and do some math� Parent Resources
Self Assessment!
� Take a moment to read each of the concepts listed
� Put an X next to the concepts you feel confident about
5th Grade Critical Areas
� Extending division to 2-digit divisors, integrating decimals into the place value system and developing understanding of all operations with decimals to hundredths.
� Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).
� Developing understanding of volume.
1.
Standards of
Mathematical Practice
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in
repeated reasoning.
2.
Procedural vs.
Conceptual
Understanding
Conceptual Understanding:
Way students show thinking
Ability to justify answers
Understand the “why” behind the process
Procedural Knowledge vs. Conceptual Understanding
Procedural Knowledge:
Find answer using a particular method
Steps to find an answer
Memorization of operations without meaning
Knowing how something happens
“Conceptual understanding in mathematics means that students understand which ideas are
key...and that they grasp the heuristic value of those ideas. They are thus better able to use them
strategically to solve problems – especially non-routine problems…”
Grant Wiggins
“
Education is not the learning of facts, but
the training of the mind to think.
- albert Einstein
3.
Multiplication Strategies
Area Model Multiplication and
Partial Products
15 x 13
Multiplication Flow
Area Model for Multiplication
Partial Products
Basic Multiplication
Facts
Traditional Multiplication
(Conceptually)
4.
Division Strategies
Area Model Division
4
345 / 4
Partial Quotients
1, 385 / 34 1, 385 34
Traditional Division
1, 385 / 5 1, 385- 1 0
38- 35
35- 35
5
277Students are not required to talk through problems
like this each time they solve, only to build
understanding in the beginning!
Division Flow
Area Model for Division
Partial Quotients
Traditional Division
Basic Division Facts
Given someone directions to your house or directions to another location?
When you gave those directions, did you provide the shortcuts you take? Or, did you try to keep them on the main roads since they don’t know the area?
The shortcut may be faster! But, sometimes we have to take the long way until we get to know the area. After a few times in the area, then we’re ready for the shortcut.
Have you ever?
Previously math has been seen as a set of
rules and procedures to memorize in order to
calculate quickly and accurately.
Unfortunately, this eliminated the need to
understand the mathematical relationships
that provide the foundation for the rules.
Throughout 3rd and 4th
grade, students have only
experienced situations where
multiplication creates a
larger product.
5.
Multiplication of
Decimals
Multiplication of
Decimals Flow
Whole number x Decimal
larger than 12 x 1.4
Decimal in tenths x decimal in
tenthsEx: 0.3 x 0.4
Whole number x decimal
2 x 0.4
Decimal x decimal
Ex: 1.3 x 1.4Ex: 4.25 x 3.7
Using the base 10 blocks we can
model multiplication with decimals
The Flat = 1 whole
● Build 2 groups of 1● Build 2 groups of 0.2 ● Build 2 groups of 1.2
Standard of Mathematical Practice # 4
Model with Mathematics!
Multiplication of Decimals
Multiplication of Decimals
0.7 x 0.4
0.7 OF 0.4
2.6 x 1.2
Estimation: 3 x 1 = 3
2 6 x 1 22 0 0 4 0 6 0 1 23 1 2.
Multiplication of
Decimals Algorithm Flow
Visual Models Algorithms ● Partial Products● Estimation with
Partial Products
Base Ten Blocks
Whole number x Decimal
larger than 12 x 1.4
Decimal in tenths x decimal in
tenthsEx: 0.3 x 0.4
Whole number x decimal
2 x 0.4
Decimal x decimal
Ex: 1.3 x 1.4Ex: 4.25 x 3.7
6.
Division of Decimals
Division of Decimals Flow
Decimal in tenths divided by
decimal in tenths0.6 / 0.2
Decimal divided by decimal
2.6 / 1.2
Decimal divide by a whole
number2.5 / 3
Division of Decimals
3 352 . 2 - 3 05 - 3 22 - 21 12 - 12
1 1 7 4
We can use the same traditional division algorithm with decimals!
Estimation = 300 / 3 = 100.
Division of Decimals
0.3 35.22
Why is it that when you divide by a decimal, you can simply just move the decimal?
Standard of Mathematical Practice #3 Construct viable arguments and critique the reasoning of others
Division of Decimals
What patterns do you see? Standard of Mathematical Practice #8
Look for and express regularity in repeated reasoning!
Division of Decimals
0.3 35.22
Now that I know I can multiply both numbers by the same multiple of 10 and get the same quotient, I can use that to make my divisor a whole number!
7.
Multiplication of
Fractions
Multiplication of
Fractions Flow
Multiply a fraction by a whole
number
Multiply a fraction by a
fraction
Multiply a whole number by a fraction
Visual Models
Algorithm Visual Models
Algorithm Visual Models
Algorithm
Multiplication of Fractions
¾ x 1 ¾ x 2Think.. 3/4 of 1 whole
Use the commutative property - we can think of this as 1 group of 3/4 !
Multiplication of Fractions
Fill in the grid to show ¾ of �
Multiplication of Fractions
Fill in the grid to show ¾ of �
Multiplication of Fractions
6/20!
Multiplication of Fractions
3 x 2 = 64 5 20
We really just multiplied the
numerators and denominators!
Connecting Representations
A. ⅔ x ½ B. ½ x � C. � x ⅔
Multiplication of
Fractions Flow
Multiply a fraction by a whole
number
Multiply a fraction by a
fraction
Multiply a whole number by a fraction
Visual Models
Algorithm Visual Models
Algorithm Visual Models
Algorithm
8.
Division of Fractions
Division of Fractions
Connecting visual models to the
inverse operation of multiplication
Learn to multiply by the inverse when dividing
fraction.
Dividing unit fractions and whole
numbers using visual models.
Division of Fractions
Unit Fraction Divided by a Whole Number2 students are going to share ½ pound of candy. What is each
student’s share?
Each student will get 1/4 of a pound of candy!
1/2
Division of Fractions
Whole Number Divided by a Unit FractionMrs. Smith has 2 pounds of chocolate. She is going to sell the chocolate in ½
pound packages at the bake sale. How many packages will she make?
½ lb
½ lb
½ lb
½ lbMrs. Smith will have 4 packages to sell.
Division of Fractions
Whole Number Divided by a Unit Fraction
½ lb
½ lb
½ lb
½ lb
¼ In both situations
we really just multiplied by the
reciprocal
12 2 = 14 2 = 4 1
2
12 = 1
4 12 x 2 x 2 = 4
Division of Fractions
Connecting visual models to the
inverse operation of multiplication
Learn to multiply by the inverse when dividing
fraction.
Dividing unit fractions and whole
numbers using visual models.
Parent Resources
� Math Resources and Tutorials
� Located on any of the school websites!
Post Assessment!
� Turn back to the front page.
� Put a check next to the concepts you NOW feel more confident about!
We’d LOVE your Feedback!
Please fill out the google form using the QR code or website.
THANK YOU!!