The Math Team is working on an

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The Math Team is working on an EBook

• A work in Progress!!!!!!!!
• Being Created for YOU!

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This resource is being developed by math topic
and grade level span. Each topic will include
Topic Information
Assessments/Sample Activities
Ideas for Extra Support
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At your request we are sharing

• Addition
• Subtraction

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Early Counting

• 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.

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Sorting and Counting 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?

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Sorting and Counting

• 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?

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Pasta Necklaces - Counting 1 to 1 practice

• 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 its 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.

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Calculator Numbers and Counting

• 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.

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If students have difficulty with sorting and
counting

• 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

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Beginning Addition Directly Models - Counts All

• 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.

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Early Addition - Direct Modeling

• Denise had 4 cookies. Her grandmother gave her
  3 more. How many cookies does Denise have now?
• Numbers of items are adjusted as needed.

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Early Addition

• After a period of time, which differs for
  individual children, its 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.

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Counting On

• 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

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Beginning Subtraction Directly Models Taking Away

• 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.

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Beginning Subtraction Directly Models Taking Away

• 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.

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Early Subtraction Direct Modeling

• 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.

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Calculate Mentally

• 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.

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As Students Mature Beyond Direct Modeling They
use a Variety of Strategies

• Counting On from first and then larger number
• Plus one, minus one
• Plus two, minus two
• Use a known fact 336
• Doubles Inverse of Double
• 448 so 8-44
• Counting Back
• Make a Ten
• Using known facts to help determine unknown facts
  i.e. I know 336 so 347 and 7-43

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If a student is having difficulty with facts to 10

• 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.

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If a student is having difficulty with facts to 10

• 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 students 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.

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Critical Importance of Grouping by Tens

• 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.

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Visual Cues Ten Frames

• 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.

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Contexts for Multi-Digit Problems

• 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?

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Mystery Number

• 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 wasnt 61? What is the
  difference between these numbers?

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1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 17 18 19 20
21 22 24 25 26 27 28 29 30
31 33 34 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
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Number Riddles

• 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?

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Assessment for Early Place Value Understandings

• 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?)

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Assessment for early understanding of place value

• 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?

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Estimating Ten or Twenty

• 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?

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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.
If a student is having difficulty with
early place value

• 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.

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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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