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Math Toolkit Time!
Using Manipulatives to Help Students Develop
Common Core Math Mastery
Jacqueline Burns, Global Mathematics Consultant
Today’s Overview
• 10.00 – 12.00 Math Toolkit Time: Using Manipulatives to Help Students Develop
Number Sense
• 12.00 – 12.45 Lunch
• 12.45 – 01.30 Curriculum Mapping with the Common Core Math
• 01.30 – 01.50 Coffee Break
• 01.50 – 02.30 Alpha Math Presentation
• 02.30 – 03.00 Closing, Certificate Distribution, and Prizes
Session Agenda
• Introduction & Norms
• Importance of Manipulatives
• PISA
• Whole number computation and math tools (+, −, ×, ÷)
• Mini-lesson creation
• Fraction sense
• Math tool exploration
• Mini-lesson creation
• Debrief
• Q&A
Our Norms
• Be present both physically and
mentally.
• Listen to, and make room for, the
ideas of others.
• Share your knowledge and
wisdom.
• Table side topics.
• Exercise mobile phone etiquette.
What PISA15 Says About Math
Globally, and in Lebanon
From https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf
Mathematics performance among PISA 2015 participants
Country
Mean
performance
score
Share of top
performers in at least
one subject (Level 5
or 6)
Share of low achievers
in all three subjects
(below Level 2)
Singapore 564 15.3% 13.0%
Lebanon 396 2.5% 50.7%
Solving Basic Facts: Partner Work
The Student’s Hat
Work on the problems, using
manipulatives to concretely
model the solution.
The Teacher’s Hat
Consider student abilities:
Direct modeling,
counting, derived
facts, recall
PROBLEMS
5 + 7 = ?
12 – 5 = ?
4 + ? = 11
5 x 7 = ?
56 ÷ 8 = ?
PROBLEM DIRECT MODELING COUNTING DERIVED FACTS RECALL
5 + 7 = ?
Join Result
Unknown
Makes a set of 5 counters and a set
of 7 counters. Pushes the two sets
together and counts all the
counters.
Counts “5 [pause], 6, 7, 8, 9, 10, 11,
12,” extending a finger with each
count. “The answer is 12” [The
counting sequence may also begin
with the larger number]
“Take 1 from the 7 and give
it to the 5. That makes 6 + 6,
and that’s 12.”
5 plus 7 is 12.
12 – 5 = ?
Separate Result
Unknown
Makes a set of 12 counters and
removes 5 of them. Then counts
the remaining counters.
Counts back “12, 11, 10, 9, 8
[pause], 7. It’s 7.” Uses fingers to
keep track of the numbers of steps
in the counting sequence.
“12 take away 2 is 10, and
take away 3 more is 7.”
12 take away 5 is 7.
4 + ? = 11
Join Change
Unknown
Makes a set of 4 counters. Makes
a second set of counters, counting
“5, 6, 7, 8, 9, 10, 11,” until there is
a total of 11 counters. Counts the
7 counters in the second set.
Counts “4 [pause], 5, 6, 7, 8, 9, 10,
11,” extending a finger with each
count. Counts the 7 extended
fingers. “It’s 7.”
“4 + 6 is 10 and 1 more is 11.
So it’s 7.”
4 and 7 make 11.
5 x 7 = ?
Makes 7 groups of 5 counters and
counts them all.
5, 10, 15, 20, 25, 30, 35 5 times 5 is 25 and 10 more
is 35.
5 times 7 is 35.
56 ÷ 8 = ?
Counts out 56 counters. Pulls out
groups of 8 until 7 groups are
made.
8, 16, 24, 32, 40, 48, 56 8 times 8 is 64. 8 less is 56.
So that’s 7.
8 x 7 is 56.
Children’s Strategies for Solving Basic Facts
With, or Without Manipulatives?…
That is the Question
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.
Learning through the
Standards for Mathematical Practice
Create a Mini-Lesson
Create a mini-lesson that involves the use of at least
one math manipulative
• CCSS-M
• Standard(s) for Mathematical Practice
• Interdisciplinary connection/s
• Independent/pair/small group/whole group?
• How will students communicate mathematically?
• Identify the manipulative/s and other tools.
Manipulatives
for
Consideration
• Counters
• Connecting cubes
• Base ten counters
• Number line
• Random number
generator
(number cubes)
• Spinners
Need Interactive and eResources?
• http://www.debbiewaggoner.com/math.html
• http://http://www.readtennessee.org/
• http://www.corestandards.org
• https://ccgpsmathematicsk-5.wikispaces.com/
• http://www.k-5mathteachingresources.com/
• http://www.insidemathematics.org
Jacqueline Burns
USA | UAE
Global Mathematics Consultant
Jacqueline@GlobalMathConsultants.com
Twitter: @GlobalMath411
WhatsApp: +971 56 4166150

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Alpha Math Presentation

  • 1. Math Toolkit Time! Using Manipulatives to Help Students Develop Common Core Math Mastery Jacqueline Burns, Global Mathematics Consultant
  • 2. Today’s Overview • 10.00 – 12.00 Math Toolkit Time: Using Manipulatives to Help Students Develop Number Sense • 12.00 – 12.45 Lunch • 12.45 – 01.30 Curriculum Mapping with the Common Core Math • 01.30 – 01.50 Coffee Break • 01.50 – 02.30 Alpha Math Presentation • 02.30 – 03.00 Closing, Certificate Distribution, and Prizes
  • 3. Session Agenda • Introduction & Norms • Importance of Manipulatives • PISA • Whole number computation and math tools (+, −, ×, ÷) • Mini-lesson creation • Fraction sense • Math tool exploration • Mini-lesson creation • Debrief • Q&A
  • 4. Our Norms • Be present both physically and mentally. • Listen to, and make room for, the ideas of others. • Share your knowledge and wisdom. • Table side topics. • Exercise mobile phone etiquette.
  • 5. What PISA15 Says About Math Globally, and in Lebanon From https://www.oecd.org/pisa/pisa-2015-results-in-focus.pdf Mathematics performance among PISA 2015 participants Country Mean performance score Share of top performers in at least one subject (Level 5 or 6) Share of low achievers in all three subjects (below Level 2) Singapore 564 15.3% 13.0% Lebanon 396 2.5% 50.7%
  • 6. Solving Basic Facts: Partner Work The Student’s Hat Work on the problems, using manipulatives to concretely model the solution. The Teacher’s Hat Consider student abilities: Direct modeling, counting, derived facts, recall PROBLEMS 5 + 7 = ? 12 – 5 = ? 4 + ? = 11 5 x 7 = ? 56 ÷ 8 = ?
  • 7. PROBLEM DIRECT MODELING COUNTING DERIVED FACTS RECALL 5 + 7 = ? Join Result Unknown Makes a set of 5 counters and a set of 7 counters. Pushes the two sets together and counts all the counters. Counts “5 [pause], 6, 7, 8, 9, 10, 11, 12,” extending a finger with each count. “The answer is 12” [The counting sequence may also begin with the larger number] “Take 1 from the 7 and give it to the 5. That makes 6 + 6, and that’s 12.” 5 plus 7 is 12. 12 – 5 = ? Separate Result Unknown Makes a set of 12 counters and removes 5 of them. Then counts the remaining counters. Counts back “12, 11, 10, 9, 8 [pause], 7. It’s 7.” Uses fingers to keep track of the numbers of steps in the counting sequence. “12 take away 2 is 10, and take away 3 more is 7.” 12 take away 5 is 7. 4 + ? = 11 Join Change Unknown Makes a set of 4 counters. Makes a second set of counters, counting “5, 6, 7, 8, 9, 10, 11,” until there is a total of 11 counters. Counts the 7 counters in the second set. Counts “4 [pause], 5, 6, 7, 8, 9, 10, 11,” extending a finger with each count. Counts the 7 extended fingers. “It’s 7.” “4 + 6 is 10 and 1 more is 11. So it’s 7.” 4 and 7 make 11. 5 x 7 = ? Makes 7 groups of 5 counters and counts them all. 5, 10, 15, 20, 25, 30, 35 5 times 5 is 25 and 10 more is 35. 5 times 7 is 35. 56 ÷ 8 = ? Counts out 56 counters. Pulls out groups of 8 until 7 groups are made. 8, 16, 24, 32, 40, 48, 56 8 times 8 is 64. 8 less is 56. So that’s 7. 8 x 7 is 56. Children’s Strategies for Solving Basic Facts
  • 8. With, or Without Manipulatives?… That is the Question
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  • 12. 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. Learning through the Standards for Mathematical Practice
  • 13. Create a Mini-Lesson Create a mini-lesson that involves the use of at least one math manipulative • CCSS-M • Standard(s) for Mathematical Practice • Interdisciplinary connection/s • Independent/pair/small group/whole group? • How will students communicate mathematically? • Identify the manipulative/s and other tools. Manipulatives for Consideration • Counters • Connecting cubes • Base ten counters • Number line • Random number generator (number cubes) • Spinners
  • 14. Need Interactive and eResources? • http://www.debbiewaggoner.com/math.html • http://http://www.readtennessee.org/ • http://www.corestandards.org • https://ccgpsmathematicsk-5.wikispaces.com/ • http://www.k-5mathteachingresources.com/ • http://www.insidemathematics.org
  • 15. Jacqueline Burns USA | UAE Global Mathematics Consultant Jacqueline@GlobalMathConsultants.com Twitter: @GlobalMath411 WhatsApp: +971 56 4166150