Using Manipulatives to Help Students Develop Common Core Math Mastery

1. Math Toolkit Time!
Using Manipulatives to Help Students Develop
Common Core Math Mastery
Jacqueline Burns, Global Mathematics Consultant
11 March 2017
Bahrain

2. Today’s Objectives
• Increase awareness of the purpose and benefits of using math manipulatives for
students to develop conceptual understanding
• Work with tools and explore teaching and learning strategies to help students
understand numbers less than one
• Broaden awareness of and access to a variety of high quality resources to support
teaching and learning of mathematics

3. Session Agenda
9:00am – 9:45am Math Toolkit Time
Using Manipulatives to Help Students Develop Common Core Mastery
9:45-10:30am Alpha Math
10:30-10:45am Coffee Break
10:45-11:15am e-Alpha
11:15-12:00pm Digging Deeper: Numbers less than One
Teaching and learning experiences with quantity and numbers less than one
12:00pm – 1:00pm Lunch
1:00pm – 2:45pm Resources and Tools for 21st Century Teaching & Learning
Exemplar tasks, websites, and strategies for today's classroom
2:45pm – 3:00pm Closing and Certificates

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. Math Facts about Bahrain
Bahrain is actually an archipelago of 33 islands.
The largest, on which many people live, is 55km long by
18km wide and areas such as Sitra and Muharraq are
actually separate islands.
Bahrain’s flag used to be the largest flag in the world,
setting a Guinness world record in 2004 at 169.5m long and
97.1m wide. The five red points signify the five pillars of
Islam. The oldest known Bahraini flags were plain red. In
1820, the island signed a treaty with the UK and a white
stripe was added to the flag to indicate the truce. In 1932,
a serrated edge was added to distinguish Bahrain’s flag
from those of its neighbours. The flag originally had 28
white points, but this was reduced to eight in 1972 and five
in 2002.
Source: http://www.timeoutbahrain.com/aroundtown/features/40006-25-amazing-bahrain-facts

6. More Math Connections
in Bahrain
Bahrain World Trade Centre is the first skyscraper in
the world to integrate wind turbines into its design.
Each turbine is 29m in diameter and their capacity is
675kw of wind power production. The 240m-tall tower
has won several international awards including the
LEAF (Leading European Architects’ Forum) award for
best use of technology in a large scheme.
The British School of Bahrain holds the world record
for the largest simultaneous coin toss. As part of
World Maths Day in 2010, 1,117 staff and students
took part in the toss which made it into the Guinness
Book of Records.

7. Why use manipulatives?
Concrete.
The “doing” stage using
concrete objects to model
problems
Representational.
The “seeing” stage using
representations of the objects
to model problems
Abstract.
The “symbolic” stage using
abstract symbols to model
problems

8. 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 = ?

9. 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 5 groups of 7 counters and
counts them all.
7, 14, 21, 28, 35 or
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.
Source: https://catalyst.uw.edu/gopost/conversation/ekazemi/117145
Children’s Strategies for Solving Basic Facts

10. Create a Mini-Lesson
Components for the Mini-Lesson
• at least one math manipulative
• CCSS-M (math standard)
• Standard(s) for Mathematical Practice
• Interdisciplinary connection/s
• Independent/pair/small group/whole
group?
• How will students communicate
mathematically?
Manipulatives for
Consideration
• Counters
• Connecting cubes
• Base ten counters
• Number line
• Random number generator
(number cubes)
• Spinners

11. 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

12. “The difficulty with fractions (including decimals and
percents) is pervasive and is a major obstacle to
further progress in mathematics. . .”
—Report of the National Math Panel, March 2008
Fraction Sense

13. What are some of the biggest challenges
students face with fractions?

14. In One Minute…
• write down everything that comes to mind when you think about or see
5
8

15. Now, in one minute…
• write down everything that comes to mind when you think about or see
9

16. Compare Your Responses
• What similarities do you see?
• What differences do you see?
• Any surprises or insights?

17. The Progression of Fractions
NF Standards, Grades 3-5

18. Prior knowledge through the lens of geometry

19. Develop understanding of fractions
• 3.NF1 Understand a fraction 1/b as a quantity formed by 1 part
when a whole is portioned into b equal parts: understand a
fraction a/b as the quantity formed by a parts of size 1/b.

20. TASK:
Locate 1 on the number line. Label the point.
Be exact as possible.
While it is not necessary to name all of the intervals on the number line, many students
may do so .

21. TASK:
Locate 1 on the number line. Label the point.
Be exact as possible.
While it is not necessary to name all of the intervals on the number line,
many students may do so .

22. Other Helpful Considerations for Understanding
Fractions
• Fraction Basic Vocabulary (denominator)
• 2 is pronounced “half”
• 3 is pronounced “third”
• 4 is pronounced “fourth” (or “quarter”)
• 5 is pronounced “fifth”
• 6 is pronounced “sixth”
• 7 is pronounced “seventh”
• 8 is pronounced “eighth”
• 9 is pronounced “ninth”
• 10 is pronounced “tenth,” and so on.
• Where do we see and use fractions
in our daily lives?
• Support Strategy: The use of
pictures provides students with
realia for understanding
fractions
• Wholes vs. Holes
• Use visual images that support
all learners for understanding
this concept.

23. Equivalent Fractions
• The meaning of fraction equivalence
• The equivalence of whole numbers and fractions
• Explaining fraction equivalence in general

24. Adjectives vs. Nouns
(Adapted from Kathy Richardson, NCTM 2008)
• Young children initially consider numbers as adjectives or descriptors
• 9 bears
• 6 cookies
• 20 students
• Eventually, they come to understand numbers as nouns or concepts
9 is …
• half of 18,
• It is 1 less than 10,
• It is 4.5 doubled,
• It is 3 squared,
• It is the square root of 81,
• ………..?

25. Adjectives vs. nouns (continued)
• Students need opportunities to transition from considering fractions as adjectives
1/2 of a pizza
3/4 of an hour
2/3 of a cup
• to considering them as nouns
5/8 is…
a little more than 1/2, but less than 1
It is 3/8 less than 1
It is equivalent to 10/16
It is twice 5/16
It is half of 1¼
……………?

26. Which is bigger . . .
𝟏
𝟑
𝒐𝒓
𝟏
𝟖
?
Source - https://www.youtube.com/watch?v=g0nuomCCu9A

27. It’s Your Turn!
Create a Lesson that supports, develops, reinforces, applies
or extends understanding of fractions
Components for the
Mini-Lesson
• at least one math manipulative
• CCSS-M (math standard)
• Standard(s) for Mathematical
Practice
• Interdisciplinary connection/s
• Independent/pair/small
group/whole group?
• How will students communicate
mathematically?

28. 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

29. Interactive Resources and eResources
• http://nrich.maths.org/
• www.illustrativemathematics.org
• http://achievethecore.org/category/854/mathematics-lessons
• National Library of Virtual Manipulatives
• https://illuminations.nctm.org
• K-2 Algebra Placement Assessments
• http://www.mathplayground.com/math_manipulatives.html
• https://www.pbslearningmedia.org/asset/mgbh_int_balance/
• Plickers
• Alpha Math Grade 1, Grade 2, Grade 3, Grade 4, and Grade 5

30. Closing
• Processing, Next Steps, Reflections, Questions
"The essence of mathematics is not to make simple things
complicated, but to make complicated things simple."
– Stan Gudder, American mathematician
• Written reflection: Write one action you will take as a result
of today’s exploration of algebraic thinking.

31. Questions?

32. Thank you!
EM: JacquelineBurns@gmail.com
WhatsApp: +971 56 4166150
Twitter: @GlobalMath411