### Fractions, Multiplication, and Division

``` Welcome! 
O Thank you for coming!
Past and Present…
O In the past, Math instruction focused on
computation.
O Now, Math instruction focuses on
APPLICATION through the use of critical
thinking skills, higher order thinking and
depth of knowledge in order to
solve/analyze multi-step problems.
Fluency By Grade level
Standard
Required Fluency
K
K.OA.5
1
1.OA.6
2
2.OA.2
2.NBT.5
3
3.OA.7
3.NBT.2
Multiply/divide within 100
4
4.NBT.4
5
5.NBT.5
Multi-digit multiplication
6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
At school…
Mathematics Teaching Practices:
1 – Establish Mathematics Goals to Focus on Learning.
2 – Implement Tasks that promote reasoning and
problem solving.
3 – Use and connect mathematical representations.
4 – Facilitate meaningful mathematical discourse.
5 – Pose purposeful questions.
6 – Build procedural fluency from conceptual
understanding.
7 – Support productive struggle in learning
mathematics.
8 – Elicit and use evidence of student thinking.
Math series
Student textbook & practice book
Math Chapters- Topic Breakdown
Chap.
Topic
Chap.
Topic
1
Number Concepts
7
Time & Money
2
Numbers to 1,000
8
Length in
Customary Units
3
Basic Facts &
Relationships
9
Length in Metric
Units
4
10
Data
5
2-Digit Subtraction
11
Geometry &
Fractions Concepts
6
Subtraction
During instruction students …
O Use the textbook
O Use manipulatives and math tools
O Use their Math Journals to explore/write about:
O
O
O
O
O
“Essential Question, Problem of the Day, justify their
Use task cards, anchor sheets
Participate in “Math Talks” and cooperative
learning groups
Math drills
Computer programs for enrichment/remediation
Whole Group/Small group/Independent
instruction
Three types of
Mathematical understanding- CPR
O
Conceptual -- What do students need to
know?
O
Procedural -- What do students need to
do?
O
Representational -- What do students
need to show?
How can we get our students
to UNDERSTAND math?
O Students can understand Math
by: building FLUENCY and
using STRATEGIES.
3 Elements of Fluency
O Accuracy (Correctness)
O Efficiency (Quick retrieval of
facts both written and oral.)
O Flexibility (Use of strategies
to help with recall.)
O Reading/Writing capability also play a major
role.
Prerequisites
O Before children can
conceptually understand
addition and subtraction facts
they must first have one-toone correspondence,
conservation of numbers, and
they must know the counting
sequence.
Counting Sequence
O Knowing the counting sequence is
as simple as knowing what number
comes next. Just because a child
knows the counting sequence does
not mean that they understand
numbers, but it is an important step
in the development of numbers.
One-to-one Correspondence
O Understanding that one item is represented by a unique count.
Conservation of Number
O The final item counted tells the number in the group. Seven items
are counted so there are seven items in the group.
Why learn strategies?
O Students can develop fluency with their addition
and subtraction facts if they memorize strategies
such as: the Doubles facts & the Tens facts. The
rest of the facts can be derived using strategies.
O Efficient use of strategies leads to a better
understanding of numbers, and the properties of
O Better conceptual understanding promotes long
lasting procedural understanding and ultimately
results in quick retrieval of all facts. That is the goal.
Quick retrieval of all facts.

Strategies that
promote
understanding…
“Teachable” moments for parents:
Using a hundreds chart to
practice counting patterns.
Count on strategy: +/- 1
and 2
Doubles +/- 1
How does it work?
O 6 + 6 = 12 so,
O 6 + 7 = 13 because
O 6 + 6 + 1 = 12 + 1 = 13
Or
O 7 + 7 = 14 so,
O 6 + 7 = 13 because
O (7 - 1) + 7 = 14 – 1 = 13
Make a ten
Add tens and ones
Adding tens and ones places an emphasis on place value
and expanded form.
How does it work?
8 + 6 = 14
Use a visual model to promote
“Cardinality”. Cardinality is recognizing a number by
the configuration – no counting needed.
8 + (2 + 4) = 14
Decompose 6 into 2 and 4
(8 + 2) + 4 = 14 Use the Associative Property to make a
ten with 8 and 2
10 + 4 = 14
Now the number is in expanded form
and place value makes it easy to add.
Subtraction
O Think addition when
solving subtraction
problems.
Fact families and related math facts.
O 9 – 5 = 4 because
O5 + 4 = 9
Equal Groups
O Sarah has three
pages of stickers.
There are four
stickers on each
page. How many
stickers are there?
Array Model
three rows of
tiles. He put
four tiles in
each row. How
many tiles are
there?
 What to Do When
Teaching Basic Facts
O Develop conceptual understanding using
O
O
O
O
O
O
O
O
strategies
Ask students to self-monitor
Focus on self-improvement
Drill in short time segments
Work on facts over time
Involve families
Make practice/drill enjoyable
Use technology
Emphasize the importance of quick recall of facts
 More “to Do-s”…
O Practice makes BETTER!
O Use manipulatives, anchor sheets, & task
cards.
O SHOW YOUR WORK!
O Explain your answer. Know the “WHY”
Attack Word Problems with
CUBES…
C
U
B
E
S
Circle the numbers
Underline important words/math vocabulary
Box the question
Evaluate the information
Solve the problem
 Build Math Vocabulary 
Subtraction Words
Plus
All together
Total
Combine
Gets
More join
Sum
Difference
Minus
Subtract
Less
How many more?
How much more?
How many were left?
 What Not to Do When
Teaching Basic Facts
O Don’t use lengthy drilling
O Don’t proceed through the facts in order from
0 to 9
O Don’t move to memorization too soon
O Don’t use facts as a barrier to good
mathematics
Remediation
O Focus on reasoning strategies
O Recognize that more drill will not work
O Provide hope
O Inventory the known and unknown facts
O Diagnose strengths and weaknesses
O Build in success
O Provide engaging activities
TESTING
O Second Grade- SAT
SAT- The Math portion of the SAT is auditory.
Questions are read aloud to students.
Sample Page
O Upon entering third grade, your child should have
1.
2.
3.
4.
5.
show mastered:
Telling time
Counting money
Estimating 10-100
Math operations
Start practicing multiplication BEFORE the third grade
school year; during the summer.
Promote good study habits.
Here are some strategies
Multiplying Zeros
Multiply by 1: Multiplicative
Identity
Multiply by 2: Doubling
2 x 8 = 8 + 8 = 16
Multiply by 10
Multiply by 5
Division
O Think
multiplication
when
solving division
problems.
O 24 ÷ 6 =
O 6 x __ = 24
Resource Websites
O www.flstandards.org