Transcript Redelivery of Session 1 for grades K-2

“Education is the key to unlock the
golden door of freedom.”
George Washington Carver
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Model, read, and write place value in word,
standard, and expanded form for numbers (N-1E)
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)
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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) (A2-M) (A-3-M)
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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?
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.
Children must be aware of two
components of fractions:
1. The number of parts
2. The equality of the parts
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(equal size, but not necessarily shape)
See attachment: Questions to Help Students Reason About
Fractions as Numbers (Front and Back)
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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.
 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.
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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.
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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
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What number is halfway between zero and
one?
What number is halfway between zero and
one-half?
What other numbers are the same as onehalf?
What number is ¼ more than ½?
What number is 1/6 more than ½?
What number is 1/6 less than one?
cont.
Navigating Through Number and Operations
Lynne Tullos,
LDOE 2010
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If the square = 2/5, draw 1 whole
Lynne Tullos,
LDOE 2010
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If this piece = 3/5 unit
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How much of a unit is this piece =?
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Draw the unit piece.
Lynne Tullos,
LDOE 2010
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How can you tell which fraction is larger?
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What must you consider?
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What strategies can you use?
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Notations for money are the first thing to
come to mind.
$127.95 means 127 dollars and some part of
another dollar.
The decimal point separates the dollars from
the parts of a dollar.
Type a number plus another number and
then continuously hit the = button to see
the pattern.
See attachment: Calculator Pattern Pieces (front and back)
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 354. 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)
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)
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
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
Highlight the numbers on a hundreds chart in a visual pattern and have
students identify the numerical pattern.
Here are some examples:
1. 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
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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
◦ 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.
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See Attachment: Clock Face
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
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
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
1.Seeing Students’ Knowledge of Fractions
2.Creating, Naming, and Justifying Fractions