1. “Education is the key to unlock the golden door of freedom.”
Redelivery of the 1st of 4 content workshops for this school year ( ) (Making Fit for Pre-K to 2nd grades) By: Wanda Rougeau and Tracee Spring (Midway Elementary) La-STEM Math Academies for ENFA and LA Educators “Transforming Numbers & Operations and Algebra Instruction in Grades 3-5”
“Education is the key to unlock the golden door of freedom.”
George Washington Carver

2. N&NR GLEs for 3rd, 4th, and 5th Grades
Model, read, and write place value in word, standard, and expanded form for numbers (N-1- E)
Read, write, compare, and order whole numbers using symbols (i.e., <, =, >) and models (N-1-E) (N-3-E)
Use region and set models and symbols to represent, estimate, read, write, model, compare, order, and show understanding of fractions and equivalents through twelfths (N-1-E) (N-2-E)
Differentiate between the terms factor and multiple, and prime and composite (N-1-M)
Give decimal equivalents of halves, fourths, and tenths (N-2-E) (N-1-E)

3. Algebra GLEs for 3rd, 4th, and 5th Grades
Use the symbols <, >, and � to express inequalities (A-1-E)
Identify and create true/false and open/closed number sentences (A-2-E)
Find unknown quantities in number sentences by using mental math, backward reasoning, inverse operations (i.e., unwrapping), and manipulatives (e.g., tiles, balance scales) (A- 2-M) (A-3-M)

4. Good Questions To Ask (Grades 1 -2)
A number has been rounded off to 20; what might the number be?
How many numbers can you write with 8 in the tens place?
How many numbers can you make using the digits 1,2, and 3 if you can only use each digit once?
How many ways can you rename 65 as the sum of smaller numbers?

5. Grades Pre-K to 2
Let’s skip-count by 5’s starting with one of the following numbers: (7, 11, 13, etc.) Create a skip counting pattern starting at 2 that someone else can continue. A number was shown as a set of dots. Part of the pattern is shown below. What might the number be and how do you know? Number generator: use a deck of cards. Pull 2 or 3 different numbers and have the students make as many numbers as they can with the digits.

6. Show your thinking

7. Fair Shares Children must be aware of two components of fractions:
The number of parts
The equality of the parts
(equal size, but not necessarily shape)
See attachment: Questions to Help Students Reason About Fractions as Numbers (Front and Back)

8. 5 Main Interpretations of Fractions
Fractions as parts of wholes or parts of sets
A unit is partitioned equally into equivalent parts.
Fractions as the result of dividing two numbers
The quotient- meaning results when a number of objects are shared by a set number.
Fractions as the ratio of two quantities
Compares a part to a whole.
Fractions as operators
A fraction acts on another number by stretching or shrinking it.
Fractions as measures
The length marked on a number line or subunits.
NOTE: equal parts and equal size pieces (but not necessarily
identical shapes) are ESSENTIAL when dealing with fractions.

9. Research indicates:
Using models is critical in understanding fractions.
Younger grades are better at this than later grades.
Models help clarify what is being written symbolically.
Sometimes it helps to do the same activity with different models.

10. 1. Area or Region Model
This is the place we usually begin for MOST students but students have to understand what we mean by AREA.
Area models involve sharing something that can be cut into smaller parts.
Circular models are good about emphasizing the amount that remains but not very good when the fractions move beyond ½, 1/3, ¼, 1/5 or when we have to operate with fractions.

11. 2. Measurement or Length Model
Length is the critical factor in this model-- instead of the area of the unit
The number line is significantly more sophisticated that most other models
Each number represents a distance to the labeled point from zero

12. Helping Students Reason About Fractions as Numbers
What number is halfway between zero and one?
What number is halfway between zero and one-half?
What other numbers are the same as one- half?
What number is ¼ more than ½?
What number is 1/6 more than ½?
What number is 1/6 less than one?
cont.

13. Set Model
Navigating Through Number and Operations

14. Draw a small square on your paper.
Lynne Tullos, LDOE 2010
If the square = 2/5, draw 1 whole

15. Look at your Pattern Pieces
Lynne Tullos, LDOE 2010
If this piece = 3/5 unit
How much of a unit is this piece =?
Draw the unit piece.

16. REMEMBER To Ask Children
Lynne Tullos, LDOE 2010
How can you tell which fraction is larger?
What must you consider?
What strategies can you use?

17. Modeling Decimals
Notations for money are the first thing to come to mind.
$ means 127 dollars and some part of another dollar.
The decimal point separates the dollars from the parts of a dollar.

18. Decimals Make Cents!

19. Activities

20. Calculator Pattern Puzzles
Type a number plus another number and then continuously hit the = button to see the pattern.
See attachment: Calculator Pattern Pieces (front and back)

21. Calculator Wipe-out
Give all students a calculator. Tell them a number to
type into the calculator. The number should be at least
a 2 digit number. Have them change one digit in the
number. For example: Tell the students to input the
number Then tell them to change the 5 to a zero.
They should subtract 50 from the number. Students get
a better understanding of the value of each digit in
a number.
See attachment: Activity 4 Calculator Wipe-Out
(make fit for your grade level)

22. Place Value Strategies
Number Riddles Using
Place Value Strategies
Give students the number riddle cards. Have them separate
them by odd and even. Then, have them put the numbers
In order from least to greatest. Make up number riddles using
place value strategies.
Example riddle: I am a number with a 5 in the tens place. I
am an even number. I am a number that is between 200 and 300.
The number could be 250, 252, 254, 256, or 258.
See attachments: Activity 6 – Number Riddles Using Place Value Strategies (front and back) and Unit 1 Activity 6 Number Riddles Cards (make fit for your grade level)

23. Sum are Odd, Sum are Even
Students should already have an understanding of odd and even
numbers.
Discuss with students whether or not the sum of 2 even numbers
Is odd or even. Accept all answers.
Start with small 1 digit numbers, then have them predict with 2 and 3
digit numbers. Do the same with odd/odd and even/odd. Discuss
with the students why this is true.
See attachment: Activity 11 – Sum are Odd, Sum are Even

24. Venn Diagram What’s my Rule?
Venn Diagram #1 – Think of a rule. For example, numbers with a 2 in the
ones place. Have the students call out numbers. If the number fits the
rules, write it in the circle. If they do not fit the rule, write it outside the
circle. Continue until the students figure out the rule.
Number smaller than 10
Venn Diagram #2 – Same as above, except there is a rule for each circle in
the diagram and numbers might fall in the middle because they fit both
rules. For example – Multiples of 2 might go in A and multiples of 3 might
in B. The number 6 would fall in the middle.
See attachments: Activity 5 – What’s my rule? and Unit 4 Activity 5 Venn
Diagrams

25. Hundreds Chart Find the Pattern
Highlight the numbers on a hundreds chart in a visual pattern and have
students identify the numerical pattern.
Here are some examples:
Start with 2 and color in every other number (counting by 2’s)
Pre-K/K – white red white red skipping # let students discover this
2. Start with 1 and color in every number below it in a diagonal direction.
(color in 12, 23, 34, 45, 56, etc.) The number pattern would be +11.
See attachment: Patterns on 100s Charts

26. Taking an Hour for Clock Fractions
Engage students by asking questions such as:
How many minutes in an hour?
How many minutes after the hour is it when the minute hand is pointing to the 6?
See Attachment: Clock Face

27. Clock Fractions See Attachment: Clock Face
What are some ways you can use to find this?
This leads to discussing 30 minutes out of 60 is ½ of an hour
How many minutes after the hour is it when the minute hand is pointing to the 3?
Since we were ½ way around the clock showed 30 min., we must be ½ of 30, or 15 minutes.
The clock hand divides the clock into 4 parts so 15 minutes must be ¼ of the clock.
See Attachment: Clock Face

28. Clock Activity Reproduce the clock on colored paper. Cut it out.
Cut out another circle on a different colored sheet of
paper. Make sure the circle is the same size as the
clock. Cut a slit to the center of the clock and the center
of the circle. Use the clock to represent fractions such as
a quarter past, half past, half of an hour, three quarters of an
hour, etc.
See Attachment: Clock Face

29. Fractions on Grids
Have students divide grids into different numbers of equal parts as determined by teacher. Have them count the squares to determine a fraction and a fraction of a number depending on the number of squares in the grid provided. The whole will change.
See attachments: Activity 1 – Fractions on Grids and Unit 7, Activity 1, Fractions on Grids

30. Double Number Line
Use the double number lines to show a fraction of a number. Have students use the unlabeled
Side to predict the fraction of a number. For example, “what is half of 10?” The students put the paper clip where they think half of 10 would be and then turn it over to see the answer.
See attachments: Double Number Lines and 12-cm Number Lines

31. make fit for your grade level.
Read both of the
Following articles:
Seeing Students’ Knowledge of Fractions
2.Creating, Naming, and Justifying Fractions
See ACTIVITY PACKET
and
make fit for your grade level.