Fractions, Multiplication, and Division

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 Welcome! 
O Thank you for coming!
O Please sign in.
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
Grade
Standard
Required Fluency
K
K.OA.5
Add/subtract within 5
1
1.OA.6
Add/subtract within 10
2
2.OA.2
2.NBT.5
Add/subtract within 20
Add/subtract within 100
3
3.OA.7
3.NBT.2
Multiply/divide within 100
Add/subtract within 1000
4
4.NBT.4
Add/subtract within 1,000,000
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
2-Digit Addition
10
Data
5
2-Digit Subtraction
11
Geometry &
Fractions Concepts
6
3-Digit Addition &
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
work/answers
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
addition.
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.
Addition Charts
Adding Zeros: Identity
property of Addition
Count on strategy: +/- 1
and 2
Adding Doubles
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
O Max made
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 
Addition Words
Subtraction Words
Add
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
O Third Grade-FSA
SAT- The Math portion of the SAT is auditory.
Questions are read aloud to students.
FSA- Third Grade
Sample Page
Looking ahead
to Third Grade…
O Upon entering third grade, your child should have
1.
2.
3.
4.
5.
show mastered:
Adding/subtracting with regrouping
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.
Third Grade FOCUS
Here are some strategies
that will help your child
get ready for third grade.
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
O www.dadeschools.net
O www.iReady.com
O www.ixl.com
O www.thinkcentral.com
O www.brainpopjr.com
Contact me with questions
Email:
[email protected]

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