The Math Team is working on an
“EBook”
A work in Progress!!!!!!!!
Being Created for YOU!
This resource is being developed by math topic
and grade level span. Each topic will include:
At your request we are sharing:
• Addition
• Subtraction
One of the richest ways to assess early
counting is with sorting sets.
Invite the child to sort a set of (25 to
30) objects that can be sorted in more
than one way, like color and shape.
After the materials have been sorted,
ask some counting and amount
comparison questions.
• How did you decide which ones belong
together?
• Which group has the fewest (the least)?
– How many? (How is the child counting and keeping track?)
• Which group has the most?
– How many? (How is the child counting and keeping track?)
• Do any groups have the same amount?
• Can you put these things into groups in another
way?
Materials:
20 to 30 small objects - shells, bottle tops, buttons, barrettes, keys etc.
---------------------------------------------------------------------------------Ask the student if some of the objects are alike in some way. Discuss
likenesses and differences.
Have the student put the objects into groups based upon some likeness.
Ask the child to identify the groups.
Have the child count the objects in each group and compare the amounts.
Which group has the least? The most? Do any have the same number?
Can the objects be grouped in a different way?
Materials:
• Pasta - penne and/or rigatoni (hollow pasta)
• Yarn (with tape wrapped tightly around one end to create a needle
effect)
• Tie one piece of pasta to the end of the necklace so that the rest of
the pieces stay on.
________________________________________________________
Explain to the student that this necklace is a counting necklace and
each piece of pasta needs to be counted once and only once as it’s
placed on the necklace.
Ask how many pieces of pasta the necklace should include.
Offer the possibility of a pattern 2 penne, 2 rigatoni etc. to create a
total of (10).
Discuss the importance of saying a counting word only when a piece
of pasta is added to the necklace.
Materials:
• A calculator
• Counting objects such as cubes or pennies
Explain to the student that they will press a number on the
calculator and then count out that number of cubes,
pennies, or whatever counting object is being used.
You may wish to continue the conversation by asking the
child to show a group with fewer objects and a group
with more objects than the number on display. Discuss
the amount comparisons.
• Offer fewer objects to be sorted.
• Provide frequent opportunities for sorting and
counting real objects.
• Ask the child to move each item as it is counted.
• Emphasize the language of amount comparisons
– More, same number, less or fewer
• Make the grouping distinctions clear
– Example: different colors and sizes of plastic teddy
bears
When young children are confronted with
addition situations or are solving addition
problems, they naturally begin by counting all of
the objects in the problem.
Children directly model the problem with
objects or with their fingers and count to combine
the quantities in the problem. This counting
behavior is referred to as “counting all”.
Denise had 4 cookies. Her grandmother gave
her 3 more. How many cookies does Denise
have now?
* Numbers of items are adjusted as needed.
After a period of time, which differs for
individual children, it’s typical that “counting all” is
replaced with more efficient strategies. Usually
the first strategy to follow counting all is “counting
on”.
Counting on generally begins from the first
number given in the problem. Gradually
students realize, or are led to the conclusion, that
it is more efficient to count on from the larger
number. Counting on is useful with small
numbers like 1, 2 and 3.
• Alvin had four
crayons and Lashana
gave him two more.
How many crayons
does Alvin have now?
• 4 +1 is 5
5 +1 is 6
Beginning subtraction develops along with - rather than
after - addition.
Like addition, students begin to understand subtraction
by directly modeling situations that describe the action taking something away from a group. Using objects as
concrete evidence of the action helps the child keep
track of the action and also helps the adult to see what
the child is thinking.
Unlike addition, more sophisticated strategies relating to
subtraction take longer to develop.
For example counting back is more challenging than
counting on. It is important that initial subtraction work
begin right away and be connected with addition.
Addition involves putting parts of a group together into a
whole, early subtraction involves removing or separating
parts of the whole. This is an important relationship for
students to understand.
Mark had 10 presents. He gave
2 presents to children at a
homeless shelter. How many
presents does Mark have left?
* Numbers can be changed as
appropriate. Use real objects.
It is important for students to use the strategies
that they have acquired to begin to calculate
mentally, as we often do in real life situations.
Present a short problem to the children and ask
them to solve it by visualizing and thinking about
it in their heads.
•
•
•
•
•
Counting On from first and then larger number
Plus one, minus one
Plus two, minus two
Use a known fact: 3+3=6
Doubles & Inverse of Double
4+4=8 so 8-4=4
• Counting Back
• Make a Ten
• Using known facts to help determine unknown
facts i.e.: I know; 3+3=6 so 3+4=7 and 7-4=3
• Observe the student as he/she is solving
problems. Which strategies are already being
used? Does the student understand the
operation? Are they able to keep track of the
numbers?
• Ask the student how they solve problems. This
often provides insight into their thinking.
• Together, determine which facts are already
known (which ones are “the easy ones”) and
discuss why those are easy.
• Set goals for the next learning target that
acknowledge strategies that are comfortable to
the student. Discuss the next logical strategy
that the student would like to practice to increase
efficiency. Add that strategy to the learning
target.
• Use games and contextual problems (it helps to
include the student’s name in the problems).
Provide lots of practice in the target range and
use the numbers that are already comfortable,
as well as a low percentage of challenge
numbers.
Young students have to grasp the understanding that our
numbers are arranged in groups of tens (or hundreds, or
thousands) to help us count large quantities. We can
either count all or we can count the collections of groups
of tens, hundreds, thousands etc.
Ten is simultaneously 10 ones and 1 group of ten. This
is a complex idea for young learners.
Children need to encounter principles of the base-ten
number system to understand the significance of
grouping by tens. This is the heart of place value.
Ten frames help
students to
systematically develop
sums to ten and to think
about groups of ten.
The arrangements help
develop habits of
noticing 5s and tens as
children count in more
than one way.
Elise has 4 cards of
stickers. There are
10 stickers on each
card. She also has 6
more stickers. How
many stickers does
she have in all?
Use a 1-100 wall chart and remove some numbers. Ask
students to replace the number where it belongs in the
chart.
Discuss the patterns as the numbers are
replaced. For example how did a student know that 16
wasn’t 61? What is the difference between these
numbers?
1
2
3
4
5
11
12
13
14
15
21
22
24
25
33
34
31
6
7
8
9
10
17
18
19
20
26
27
28
29
30
35
36
37
38
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
62
63
64
65
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
94
95
96
97
98
99
Think of a number and describe it by
* decomposing the number in some way.
Give a clue and allow students to use number charts or
other materials to help them solve the riddle.
* Decomposing a number refers to taking a number apart into smaller
numbers.
–
–
–
–
I have 14 ones and 3 tens, what am I?
I have 22 tens and 15 ones, what am I?
I have 1 ten and 7 ones, what am I?
I have 900 tens and 90 ones, what am I?
Place 36 objects on the table and
ask the student to estimate how
many there are.
(Was the estimate reasonable?)
Ask about how many groups of ten
could be made with the objects?
(Did the student understand the
question?)
Have the student put the objects
into groups of ten and ask if the
student has an idea of how many
there are altogether.
If the child says no, ask how they
could find out.
(Did the child need to start over and
count the objects one by one? Or did
she count by tens and then count on
the extra six?)
After the child has determined
that there are 36 objects, ask
the student to write the number
36.
Underline the 3 in 36 and ask
what that digit or number in 36
means when you look at the
objects. Does the student tell
you that this stands for 30 or 3
groups of ten? If not ask if she
can show you where that
amount is in the objects.
Underline the 6 in the 36 and
ask what digit or number this
stands for in the number 36.
Can the student explain that it
is 6 ones or show you with the
materials?
Use small erasers or lima beans and ask the
student to take a handful that is as near to ten
(or twenty) as possible.
Have the child count the objects in an efficient
way. Students may decide to count by twos or
by fives.
Have the student determine how far they were
from the target number. How many more will be
needed or how many extras were there?
• Provide context for larger numbers.
• Have students use individual number charts to
clearly keep track of what is happening with the
numbers as quantities increase and decrease.
• Avoid rote procedures for trading (even with
manipulatives).
• Have students create groups of ten to represent
quantities.
• Include estimation in problem solving with larger
numbers.
Dear Central Region Friends,
You are you are the first to see this initial work.
Please help us continue to think about our product.
What would you call our efforts (careful now)…
I mean name this product?
• Ebook?!
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