October 23, 2014
OPENING VIDEO:
Escalator Problem.webloc
We don't want our children to feel this way when
presented with a problem.
Mental Math: Every teacher should be doing it 10 minutes a day (not necessarily in math class,
but throughout the day)...
*As you open your page (instead of saying open to page 34, say open to page 38-4)
*Write the date as a math problem (Oct. 15+8, 2014)
*When the kids line up, tell them how many kids you see in front of you in a math
equation, ask them how many kids are in line by what you say)
*Ask them the number of stairs they are going up/down in a math equation
*Ask them how many more minutes there are left of class by saying we have 30+5
minutes left before special.
Problem Solving:
It is not problem solving if they know what operation to do right away. Problem solving
should consist of a "struggle" so to speak. They should have to think, plan, figure out, rework,
etc...
First step should be to write the question into a statement (full sentence) with a blank where
their answer will go so they know what their target is. Make sure the label is there. Do this for
every single problem that has words with a question at the end.
example: If the question reads, "How many erasers will be left in the end?" the first step
is for the student to write, " There will be _____ erasers left in the end."
*Heuristics: Different ways to solve problem"
Act it Out:
Integer chips: Make a square with 8 dots (3 dots on each side) (p.7)
(p.8&9) Sticks: Change the shape into 3 squares
Change the house to face the other direction
Take the 5 sticks and 6 sticks and make 9 (+9, 4+5, NINE, 9 formed with sticks)...many
ways to make 9.
colored squares with before, after, between (p.7)
By teaching a strategy with several examples, doesn't mean that you are giving them the
answer. You need to model how to do it and give them the confidence and competence to
solve.
Looking for Patterns:
Win by getting to 20 game (p.11)
can count by 1s or 2s only and whoever says 20 wins. Do not ever let students know
the strategy. Write it in their journal when they think they know....but do not let them tell other
kids. Look for the pattern. When do you know you have won?
Making a Systematic List (p.10)
# of nephews
1
2
3
4
(mult. of 4) + 5
9
13
17
21
(mult. of 6) - 3
3
9
15
21
So, the list/chart shows us that Miss Romero has 4 nephews. The least number of pieces of
candy she has is 21.
Digit tiles 0-9 (p.11)
tiles 1-5 make a lowercase t and rows and columns need to have the same sum.
pattern: sums are 8,9,10 and the center #s are 1,3,5
tiles 2-6
pattern: sums are 11,12,13 and the center #s are 2,4,6
tiles 3-7
pattern: sums are 14,15,16 and the center #s are 3,5,7
Working backward (p.14):
C7A + 6B9 = 1544 (solve for the letters)
Important things to do at home:
math facts
time
money
measurement
math facts!!! yes, said it twice!!
The math facts need to be done at home, we do not have enough time to do this during a day
and they are crucial to every child's math progress.
Guess and Check (US most used strategy) p.15:
Look for strategy to start. It should not be random guesses.
p.15 multiplication example
p.16 open book problem: If the product of 2 open pages is 20, then the pages must be 4/5 so
the even # has to be on the left throughout the book. So, to get a product of 240 is impossible.
Guess/Check: 14x15=210 (too low) Next option would be 16/17=too high.
Simplify the Problem (p.18)
Add the numbers 1 to 10.
1
2
3
4
5
6
7
8
9
10
To do this, make partners of 11 (10+1, 9+2, etc). You will have 5 partners of 11. 11x5=55
Add the numbers 1 to 100
Use the same strategy as above to get the sum.
Card Game for making 10!! This was something the instructor did that strayed from the agenda.
We discussed this as being a basic stumbling block for so many kids.
One person picks a card from the deck and then the dealer sets out cards in rows, when
the dealer sees a partner of 10, they cover both addends and keep moving on until the end of
the deck. Then, collect the piles that have a top card that partners with an addend of 10. What
is left will match the card the person pulled from the deck to start. This was a great game, and
the students are going to want to get faster and faster with it. She doesn't tell them what she is
doing, she does it each day and eventually a student will pick up on what she is doing and then
they tell her privately. Once she knows they have it, she makes sure they can do it and then
they are a leader of it as well.
Box Car and One Eyed Jacks- website for ideas and manipulatives.
Singapore math support (www.singaporemathsupport.com) website and facebook....she will
send us the other material from her other conference. Sherri Adler, LLC
Dyscalculia: Does exist. Look at those kids who do not have any idea of math sense. If the
number is 427, it might mean 274, 742, etc... We need to really look at those kids in the upper
grades that lack any sort of number sense at all. Start digging, what is it that they can do?
What can't they do? How are they seeing numbers? What does a number mean to them?
Model Drawings:
Singapore math is centered around this. Kids should be making the models, not simply
filling them in. Model Drawing works in about 80% of problems.
Practice drawing yourself and use friendly numbers to model.
Give them models at their computational level (start with problems below their grade
level so they build confidence with models).
Grading scale that she recommends: 1 pt for accurate model, 1 pt for question mark, 1 pt for
computation, 1 pt for the complete sentence. All of the sentence needs to be done
correctly...spelling, punctuation, capital letters, etc since they are copying the words from the
problem (Do the sentence before they start the problem- she emphasized this a ton!).
Should not start until at least 2nd grade so they have proportionate drawings. 8 should
be about 2x the size of the 4...without the number sense, they can't do this correctly. You do
not want them to start this concept too early and have wrong models that are hard to switch
later.
Provide practice of multiple examples of similar problems to allow students to achieve
mastery and improve confidence.
Be consistent in how you present your models. You don't want to change it each time,
the kids need to see the same thing each time. Write your numbers on top of the model all the
time OR write them under the model all the time (doesn't matter, just keep consistent)
Model Drawings are ONE type of way to solve problems. If they can solve the problems
without them, let them.
*We should NOT testing the strategy, we are testing the concept. We give them strategies to
help them be successful. Let them use whatever works for them when assessing their ability to
master a standard.
Part/Whole model: 5 examples on pg. 37.
Allow the kids to do it their way (if they want to add two numbers first then subtract, let them. If
they want to subtract the first number and then the second, let them.
Comparison model: starts at the bottom of p.37.
If they finish quickly an idea is to ask them to make another problem from this information. If
they can't, help them to see that they could find the total weight of the two dogs with a model.
**We did all the models at the seminar and she said she was very flexible with how they were
done. If a child can see two numbers that have to be worked with first and then that answer is
used in a second step, let the kids do it however they see it (2 steps or 3). Some kids will see
things as a subtraction problem with a missing part and others see it as addition. Let them see
it their way, just make sure they can tell you what they are thinking. She said that the higher
kids may not put the ? in, but she really pushes for this, but if you can see a child gets the
concepts and they are getting the right answers, then maybe a 1:1 discussion about not taking
away that point is ok. For most, the ? helps the students see if their answer should be greater
or less than the original and it is very important that they put it there.
Be careful with underlining words like more than, lighter than, etc in a word problem....
these words can mean add or subtract, depending on the situation and how it is worded. Don't
have them circle these words. Talk about the problem and how they know what they are being
asked to do. Ex: Will my answer get bigger or smaller than this number here? How do you
know?
Side note: teach +/- together because of the relationship. Three types of subtraction
5 take away 3 (something is disappearing)
Part/Whole: I have 5 apples. 3 of them are red. How many of them are yellow?
Comparison: I have 3 red apples and 2 yellow apples, how many more red than yellow do I
have?
Talk about it like this: 5 minus 3 or 3 less than 5 or 3 fewer than 5
Any problem that gets difficult: LIST the words with numbers (get them out of the paragraph
form)
put words/names into the story problems (instead of nursery X
call it Kelly's nursery)
Work Station ideas for using manipulatives: Foam sheets (absorbs noise and keeps things on
the desk more easily). Put a felt piece down on desk and this is a noise reduction idea as well.
It rolls up easily and stores in a small place.
Side note to help build number sense: Skip counting by 2s, 3s (should be able to do 3s by the
end of first grade without any excuse), 5s, 10s.
**Above level kids, have them skip count by numbers...NOT multiples of that number. Ex: skip
count by 3s starting at 2.
Magic Thumb game: ex: count by 2s starting from 14. When my thumb is up, you are counting
up, when I switch to down, you count down by 2s.
By 3s: "Talk to the hand"....they say 1,2 with hand over mouth then uncover to say 3, cover for
4,5 and take hand away for 6...keep going on this. Say the two behind the hand quieter and
quieter, eventually they won't need to say them and they will hear the pattern.
Decomposing numbers is crucial. Kids need to know how to break up numbers, especially
within 10.
**Rekenrek app (FREE) on ipad. You can move it just like a real rekenrek that you might not
have in your classroom. She is big on using these as a tool for manipulating numbers.
Dominoes Game: Set up a square with 2 on each side. Touch each set of "pips" and count
them as you touch (1-6 then start over at 1). When one set of pips is the same as the number
you are saying, you get it. Don't give them anymore rules. There are things that will happen
such as the pattern is the same and you aren't getting a new number (stuck at a stand
still)...what else could we do (ask the kids...don't answer it for them). Start at a new spot,
rearrange your dominoes, etc. Strategy will be for kids to figure out where they have to start in
order to get one. Once kids gain number sense and plan ahead, they will see where they want
to start once they get to a stand still in order to pick up a domino.
Singapore math: Doesn't teach steps...that defeats the purpose of problem solving. They need
to do it how they see it. Let the kids figure it out themselves!!
p.111-115-Math Journals: "Just do it" is her motto on journals (they need to be done)...this
should be used for differentiation. You can have a section for vocabulary, a section of word
problems, fact practice, etc. These should be pulled out when a child finishes early...DO NOT
SILENT READ A BOOK WHEN THEY ARE DONE MATH... do math. Staple (glue, put in
binder, etc) things in to their journals that they need to work on for their level. These are best
done in 3-ring binders because they need to have things go in and out. Don't let them get
stagnant, make them new so they don't get bored.
p.115 (start showing how to use models with graph paper)
Multiple game: Bizz Buzz (multiples of __ say bizz, multiples of ___ say buzz, and multiples of
both say bizz buzz) Students stand in a line and you can choose to start anywhere you want
and go in any direction. Numbers are said aloud.
Salute game: addition/subtraction
dealer hands each player one card and they put it on their head...only being able to see
the other person's card. The dealer says the sum and each player has to figure out what they
have for a card that is against their forehead. The first person to say the number correctly is the
new dealer.
Bullwinkle game: opposite than Salute game...put antlers up above head, back to back and
dealer gives sum. Now you have to guess what is on the other person's antlers. First person to
answer correctly is the new caller.
p.51-74 has CCSS vocabulary and discussion of the 8 mathematical practices (each one is
done in kid friendly terms in the form of "I will...."
p.75-85 Gives you some great math language to use in the classroom as well as some great
question stems you can use to help move your children into more independent thinkers/workers.
How can you help your students get going when you are stuck? How can you help them when
they've become frustrated? What can you ask a student who finishes quickly? How can you
guide your children to explain their answers? How can you redirect your students when their
mathematical thoughts aren't on target, need clarification, or need some guidance.
p.93-102 Math Anxiety
Strategies for reducing math anxiety (parents, teachers, and students can help with math
anxiety). This section gives many ideas of how to help students who have true math anxiety...it
is real and we need to be aware of it and have empathy for these students in order for them to
be able to move forward. There are references on these pages as well.
p. 103-110 Mental Math
Examples of mental math-strings on p.105-106
Strategies for multiplication/dividing by 4 and 5 (5 for when you get to tougher numbers is neat
for kids who are able to do basic computation well).
Mental Math Links to Activities on p.108-110
Great Ideas to give to parents...and teachers:
People buy books for gifts...why not a math book??
p.118-135 Full of book titles with author, grade level appropriateness, math concept, and a brief
description.
p.136-137 Some sites that she likes (websites, apps, FB pages) She said the Granite School
District one has awesome vocabulary lists.
p.138-144 Activities to do on a 100 chart
CLOSING VIDEO:
Kid Snippet.webloc
This is what we often do for kids who aren't understanding. Getting closer, changing our voice,
getting louder, telling them over and over, etc isn't going to fill in their gaps. They need to be
given different strategies until they can see why it works.