Helping with Math at Home
Ideas for Parents
Workshop Handout Masters
(Click on title to access PDF)
1
Handout 2
Handout 3
Handout 4
Handout 5
Handout 6
Handout 7
Handout 8
Handout 9
Handout 10
Handout 11
Handout 12
Handout 13
Handout 14
Handout
What Can Parents Do . . .
Practicing Numerical Reasoning
Multiples of 5 Dominoes Game
Blackline Master of Double-6 Domino Set
The Game of Skunk
Thinking About Skunk
Pig/Get to Zero
Math Games for Family Fun
X/O Problem
Parents as Questioners
Helping Your Child with Mathematics
But I Don't Have Time to Wait for You to Learn!
Research Brief
Feedback Form
Workshop
Handout
Masters
(English)
What Can Parents Do . . .
. . . as an Adult?
Parent as
a Learner
• continue to learn
and be a learner of
mathematics
• recognize that
mathematics is an
important tool for
making sense of the
world around you
. . . as a Parent?
• investigate and play
with numbers
• attend parent math
nights
• pay attention to
experiences that
impact your child’s
attitudes about
mathematics
• involve your child in
the measuring and
comparing that you do
at home
• look for information
that comes home
about your school’s
mathematics program
• use games to support
mathematical thinking
• become familiar with
mathematics as it is
taught in your child’s
classroom
• do mental arithmetic
and share strategies
• be curious about how
you and others solve
problems
• ask questions to
understand your
child’s thinking
• broaden your
understanding of what
mathematics is
• be curious about how
your child solves
problems
• find out about
current research in
mathematics teaching
and learning
Parent as a
Communicator
• recognize that learning
and understanding
mathematics depends
on communication
(listening, talking,
and writing)
• learn to examine
and explain your
own thinking
. . . for Your Child
at School?
• learn what math is all
about for your child
• recognize that new
discoveries are still
being made in
mathematics
Parent as a
Researcher
. . . with Your Child
at Home?
• share information with
your child about how
you use mathematics
• display a positive
disposition about
mathematics
• investigate with
your child his or
her mathematical
questions
• explore with your
child the best time
and place to do
homework
• talk with your child
about the importance
of mathematics in
his or her life
• explore the many ways
to approach solving
problems
• be clear about your
expectations for
homework
• ask questions
about your child’s
mathematics program,
both the goals and
how it is taught
• find out about roles
for parents in the
mathematics program
at your child’s school
• find a way to let the
school know what you
want for your child’s
mathematical
education
• become a
knowledgeable
advocate for good
mathematics education
• find ways to show
enthusiasm about
mathematics
Handout 1
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 1
Handout 2
Practicing Numerical Reasoning
Directions: Solve these problems
mentally without using paper and
pencil.
95 – 38 =
18 × 26 =
7 × 8 is 56. If someone did not know
this multiplication fact, how could
he think about it? Write as many
ideas as you can.
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
HANDOUT 2
Helping with Math at Home: Ideas for Parents
Handout 3
Multiples of 5 Dominoes Game
You Will Need
A double-six set of dominoes (the game is more challenging if you play
with a double-nine set of dominoes).
Object of the Game
Play each tile so that the “end sums”—numbers at the ends of the domino train—add up to 5 or a multiple of 5. Maintain cumulative scores for
each player. The highest score wins.
How to Play
Set all dominoes face down in a “kitty.” Each player takes seven dominoes from the kitty.”
The player with the highest double plays first.
After each play, players add the end sums—sum of the numbers at each
ends of the domino train. If the player scores (the sum of the numbers is
5 or a multiple of 5), the player records the sum and continues to play
another domino and gets to play again until the end sum is not a multiple of 5. Cumulative scoring is recorded after each tile is played.
The next player then puts his tiles in play.
Players who do not have a domino that can be played when it is their
turn must draw single dominoes from the kitty until they pick a domino
that can be played.
The game is over if a player plays all of the dominoes in his or her hand.
The player who plays the last domino also receives the sum of all of the
other dominoes remaining in the other players’ hands.
The player with the most points at the end is the winner.
Note: An electronic version of the game of dominoes is available on AOL
(games).
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 3
Handout 4
Blackline Master of Double-6
Domino Set
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
HANDOUT 4
Helping with Math at Home: Ideas for Parents
Handout 5
The Game of Skunk
You Will Need
◆ two or more players (more than five is best)
◆ two dice
Object of the Game
Determine at what point in rolling the dice it is best to save your cumulative score. The highest score wins.
How to Play
Each player writes Skunk in big letters on a paper. The game involves five
rounds, one round for each letter in Skunk.
First, everyone stands up for the letter S. The dice are rolled (for example,
shows a 6). Each standing player has a choice—either sit down and take
those points and record them under the letter S or continue standing for
another roll of the die.
Players can stand as long as they want for additional rolls of the die, adding the new roll for their current sum for that letter. A player must choose
to sit down and keep his or her sum before a roll, not after. The die is
rolled for a particular letter until no one is left standing.
But beware! Anyone still standing when a 1 is rolled (on either die) loses
all points and receives a score of 0 for that letter.
A new round (for example, for the next letter K) begins after either roll of
a 1 or everyone has chosen to sit down to preserve their score. After the
five rounds, players add their scores, and the highest total wins.
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 5
Handout 6
Thinking About Skunk
Choice vs. Chance
1. Skunk is a game that involves both choice and chance.
◆ What part of Skunk involves choice?
◆ What part of the game involves chance?
2. List some other games you know.
◆ Which games involve mostly choice?
◆ Which games involve mostly chance?
Rate each game on a scale of 1 to 10 with
1 = pure chance 5 = chance/choice about equal 10 = pure choice
3. In life many things happen. Some are the result mostly of chance or
“luck,” and others mostly result from choices or decisions you make.
Think about some things that happened recently in your life.
◆ List two things that happened to you mainly due to chance.
◆ List two things that happened mostly because you made a choice.
Investigate the Following in Depth
1. Rolling a 1 in Skunk is a disaster. To get a better score it is useful to know, on
average, how many good rolls happen in a row before a 1 or double-1
comes up.
◆ Decide on a way to find this out. Carry out your plan and describe the
results.
2. In Skunk, when a 1 does not come up, what is the average score on a single
roll of a pair of dice?
◆ Decide on a way to find this out. Carry out your plan and describe the
results.
3. What are some strategies that could be used to play Skunk?
Describe a “play-it-safe” strategy.
Describe a “risky” strategy.
Estimate the kinds of scores each strategy would be likely to produce.
Play Skunk using each of your strategies and keep a record of your
scores.
◆ How well do your results agree with what you expected.
◆ Why should these strategies be tested in many games?
◆
◆
◆
◆
Adapted from Choice and Chance in Life, by D. Brutlag. EDC, 1993. Used with permission.
From Helping
with Math
at Home:
IdeasIdeas
for Parents.
2006.. Portsmouth,
Portsmouth,NH:
NH:Heinemann.
Heinemann.
© 2006 by Mathematics Education Collaborative
from Helping
with Math
at Home:
for Parents
HANDOUT 6
Helping with Math at Home: Ideas for Parents
Handout 7
Pig
You Will Need
◆ two or more players
◆ two dice
How to Play
The goal is to be the first player to reach 100. On your turn, roll the dice and
determine the sum. You can either stop and record that sum or continue rolling
and add the new sums together. Roll the pair of dice as many times as you
choose. Again, when you decide to stop, record the current total for your score
(and add it to your previous score).
But beware! If you roll a 1 on exactly one die, your turn ends and 0 is your
recorded score for that turn. And, if you roll double 1s, your turn ends and your
entire score is set back to 0.
Adapted from About Teaching Mathematics by Marilyn Burns. Copyright © 2000 by Math Solutions Publications. Reprinted with permission. All rights reserved.
Get to Zero
You Will Need
◆ two or three players
◆ three dice
How to Play
First, on a sheet of paper, each player needs to write the players’ names and the
number 999 under them.
A player rolls the three dice, then arranges the three numbers (for example, 2, 3,
5) in some order (for example, 235, 352, 532, and so on) and subtracts that
3-digit number from 999. The other players also should subtract as a check.
The players take turns, rolling the die to make their special number and continuing to subtract. The winner is the first player to reach 0, but they must get to
0 exactly.
At any time, a player may choose to roll only one or two dice, instead of three
dice. If the only numbers a player can make are larger that his remaining score,
the player loses his turn.
See About Teaching Mathematics (Math Solutions Publications, 2000) for additional games that support arithmetical skills.
Adapted from Burns, Marilyn, The Math Solution. Not in print.
From
Helping
with Math atEducation
Home: Ideas
for Parents.from
2006.
Portsmouth,
NH: Heinemann.
© 2006
by Mathematics
Collaborative
Helping
with Math
at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 7
Handout 8
Math Games for Family Fun
Compiled by Ruth Parker
Mathematics Education Collaborative
E-mail: [email protected]
Website: mec-math.org
Parents have asked me to recommend some good games that encourage math
play at home. It’s a question I love to be asked. How math is experienced in the
home has a big impact on how children do with math at school. As the “math
auntie” of quite a few nieces and nephews, I’m always looking for challenging
and fun math games—games that engage children in mathematical reasoning
and help them experience the compelling nature of a good math challenge. I’ve
polled my nieces and nephews and can offer some of our favorites (most are
available in toy stores and in price range $5 to $15).
Set: A card game of logic and visual perception that can be enjoyed by the
whole family (ages 6 to adult). Adults . . . be forewarned that it can be humbling to play this game with youngsters.
Tangos: A game that focuses on spatial relationships that will provide challenges to the whole family, young and old alike.
Mastermind: A game of logic that can be enjoyed by both children and adults.
Look for a version of Mastermind for younger children (ages 6 and up).
Cribbage: A card game that’s played on a pegged board and is wonderful for
developing skill in adding series of small numbers. The game is enjoyable
for children of all ages.
Dominoes: A game of strategy and numbers that can be played with children
as young as 4 years of age as a number recognition game, and yet the regular game of dominoes is challenging for adults as well.
Mancala: An African stone game of logic that is challenging for adults but
can be adapted to meet the needs of children ages 5 and up.
Equate: A game for reinforcing computation with whole numbers, decimals,
and fractions. I haven’t played this yet, but my nieces and nephews tell me it
is challenging and fun.
Checkers/Chess: Great games for developing skill with logical reasoning.
We hope you find these math games as fun as we do. Curl up with your favorite
kid(s) and enjoy playing math. Please let us know if you have other favorites to
add to the list.
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
HANDOUT 8
Helping with Math at Home: Ideas for Parents
Handout 9
X/O Problem
You have three cards marked as
follows:
◆ one card with an X on both sides
◆ one card with an O on both sides
◆ one card with an X on one side
and an O on the other
Suppose all three of these cards are
in a bag. You reach into the bag,
randomly draw a card, and you are
looking at an X.
Is it more likely that the other side
will show an O? An X? Or, are both
equally likely?
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 9
Handout 10
Parents as Questioners
Mathematical investigations present new and sometimes unexpected mathematical situations, so the teacher cannot have taught the way to solve the problem in advance. The student needs to apply prior knowledge in ways that make
sense to the situation. There may be many paths to follow and many outcomes,
depending on the problem; the student must make his or her own plan for
finding a solution.
Parents can assist their children to be independent problem solvers by becoming guides or questioners. They do not need to know how to solve the problem
themselves, but can help the students think through the problem and make a
realistic plan for solving it.
USE FREELY any questions that will help students think about the way they are
tackling the problem:
◆
◆
◆
◆
◆
◆
◆
What have you tried?
Is there another way to look at the problem?
Can you explain this to me?
What makes sense so far?
Is there another way to think about it?
Is this like any other problem that you have worked on in any way?
What is it you are trying to do/solve/find out?
USE SPARINGLY those questions that tend to direct students’ thinking:
◆
◆
◆
◆
◆
◆
◆
How might you organize this?
Can you make a table of your results?
Can you see any patterns?
Have you tried smaller (or simpler) cases?
How can you start?
Have you checked to see that the solution works?
What would happen if . . . ?
AVOID any hint or question referring to the particular problem:
◆
◆
◆
◆
◆
Do you recognize square numbers?
Explore it like this . . .
Why not try three counters?
That’s not quite what I had in mind . . .
No, you should . . .
Adapted from Shell Centre for Mathematical Education's Problems with Pattern and Numbers (1984, 2001, see www.mathshell.com)
From Helping
with Math
at Home:
IdeasIdeas
for Parents.
2006.. Portsmouth,
Portsmouth,NH:
NH:Heinemann.
Heinemann.
© 2006 by Mathematics Education Collaborative
from Helping
with Math
at Home:
for Parents
HANDOUT 10
Helping with Math at Home: Ideas for Parents
Handout 11
Helping Your Child
with Mathematics
Be a Learner Yourself
◆
◆
◆
◆
◆
Learn to play with numbers using mental arithmetic.
Play mathematical games at home that involve problem
solving.
Notice when you use mathematics in your everyday life
and share this with your child.
Demonstrate that you value persistence.
Get to know the research on math education.
Be a Researcher
◆
◆
◆
◆
◆
Become a question poser.
Be curious about your child’s thinking when he or she is
doing math.
Be a thoughtful listener.
Ask questions that help you understand your child’s
thinking.
Know that teaching by telling is not how people learn
mathematics.
Be a Communicator
◆
◆
◆
Recognize how important talking and writing are to
learning mathematics.
Talk with your child about the many ways to think about
a math problem.
Encourage diverse ways of solving problems.
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 11
Handout 12
But I Don’t Have Time to Wait
for You to Learn!
Reflections on What It Really Means to Raise Expectations
Kathy Richardson
Math Perspectives Teacher Development Center
Bellingham, WA 98228-9418
www.mathperspectives.com
During this time in education when the emphasis is on high expectations and accountability, it is
essential that we stop and reflect on what this means in the lives of individual children. The need
to be successful in mathematics is becoming increasingly important for all children. It is true that
children can learn more than we thought possible in years past but only if they are allowed the
time and experiences they need to understand the mathematics they are learning. When the
pressure is on, there is a temptation to get the kids to “do it.” Too often we end up creating “illusions of learning” rather than building the solid foundation that helps the children continue to
move forward after they leave us. We must find ways to meet children where they are in their
learning and not demand they perform beyond what they can do with understanding and competence. No matter what external pressures we feel, we must stay focused on providing children
with the experiences that will be most appropriate for them.
The following are quotes I have gathered from various places that help me remember how important our job is and to whom we are most accountable.
The mathematical experiences of a child before the age of eleven, and the responses he
has been encouraged to make to them, largely determine his potential mathematical
development. . . . The learning of mathematics in the widest sense, begins before the
child goes to school and continues throughout the primary (elementary) school and
beyond. (Notes on Mathematics in Primary Schools, p. 1)
Virtually all young children like mathematics. They do mathematics naturally, discovering patterns and making conjectures based on observation. Natural curiosity is a powerful teacher, especially for mathematics. Unfortunately, as children become socialized
by school and society, they begin to view mathematics as a rigid system of externally
dictated rules governed by standards of accuracy, speed, and memory. Their view of
mathematics shifts gradually from enthusiasm to apprehension, from confidence to
fear. Eventually, most students leave mathematics under duress, convinced that only
geniuses can learn it. (National Research Council, Everybody Counts, p. 44)
More than any other subject, mathematics filters students out of programs leading to
scientific and professional careers. . . . Mathematics is the worst curricular villain in driving students to failure in school. When mathematics acts as a filter, it not only filters
students out of careers, but frequently out of school itself. (National Research Council,
Everybody Counts, p. 7)
No matter what the age or ability of the students, their experiences with mathematics
teach them something about themselves and their place in the world. (K. Richardson,
Calif. State Dept. of Ed., Math Model Curriculum Guide K–8, p. 11)
© Kathy Richardson, Math Perspectives, Bellingham, WA. 1999.
From Helping
with Math
at Home:
IdeasIdeas
for Parents.
2006.Portsmouth,
Portsmouth,NH:
NH:Heinemann.
Heinemann.
© 2006 by Mathematics Education Collaborative
from Helping
with Math
at Home:
for Parents.
HANDOUT 12
Helping with Math at Home: Ideas for Parents
Handout 13
Research Brief
National Research Council. (2001). Adding It Up: Helping Children Learn
Mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics
Learning Study Committee, Center for Education, Division of Behavioral and
Social Sciences and Education, Washington DC: National Academy Press.
www.nap.edu
Excerpts: This report was “approved by the Governing Board of the National
Research Council, whose members are drawn from the Councils of the National
Academy of Sciences, the National Academy of Engineering, and the Institute of
Medicine. The members of the committee responsible for the report were chosen
for their special competences with regard for appropriate balance.” They were
given the following charges:
• to synthesize the rich and diverse research on prekindergarten through
eighth-grade mathematics learning
• to provide research-based recommendations for teaching, teacher education,
and curriculum for improving student learning and to identify areas where
research is needed
• to give advice and guidance to educators, researchers, publishers, policy makers, and parents
Adding It Up addresses many questions: What exactly do we know from research
about the teaching and learning of mathematics? And what does this research
really tell us? Should children learn computation methods before they understand
the concepts? What is the role of concrete manipulatives? Do teachers and student
expectations make a difference? The conclusions and recommendations drawn
from this report of the research provide us with information about improving the
teaching and learning of mathematics.
Selected Quotes:
Knowledge that has been learned with understanding provides the basis for
generating new knowledge and for solving new and unfamiliar problems.
When students have acquired conceptual understanding in an area of mathematics, they see the connections among concepts and procedures and can
give arguments to explain why some facts are consequences of others. They
gain confidence, which then provides a base from which they can move to
another level of understanding. (p. 119)
A significant indicator of conceptual understanding is being able to represent
mathematical situations in different ways and knowing how different representations can be useful for different purposes. (p. 119)
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 13
Connections are most useful when they link related concepts and methods
in appropriate ways. Mnemonic techniques learned by rote may provide
connections among ideas that make it easier to perform mathematical
operations, but they also may not lead to understanding. These are not the
kinds of connections that best promote the acquisition of mathematical
proficiency. (p. 119)
Washington State Office of the Superintendent of Public Instruction. (2000).
Teaching and Learning Mathematics: Using Research to Shift From the “Yesterday” Mind to the “Tomorrow” Mind. J. Johnson (Ed.).
Excerpts: This book provides an overview of the potential and challenges of teaching quality mathematics (K–12). A good portion of it summarizes some of the
research results, in a very concise format, related to each of the essential learning
academic requirements in mathematics. It is a resource text designed to serve as a
catalyst for promoting reflection, discussion, and problem solving within the education community, and to help educators become knowledgeable about available
research results and ways they can be integrated into the classroom. It is available
at www.k12.wa.us.
Summary: Students learning the processes of addition and subtraction need a ‘rich
problem solving and problem-posing environment’ that should include:
1. Experiences with addition and subtraction in both in-school and out-ofschool situations to gain a broad meaning of the symbols +/–.
2. Experiences both posing and solving a broad range of problems.
3. Experiences using their contextual meaning of +/– to solve and interpret
arithmetic problems without a context.
4. Experiences using solution procedures that they conceptually understand and
can explain.
Summary:
Meaningful instruction and drill go together as part of a successful learning
experience, but meaningful instruction must precede drill or practice (Dessert). A balanced approach to both is needed in mathematics classrooms, as
students who can access both memorized and meaningful ideas in mathematics achieve at a higher level than those who rely on either one without
the other. (Askew and William, p. 47)
Summary:
Teachers need to choose instructional activities that integrate everyday uses
of mathematics into the classroom learning process as they improve students’ interest and performance in mathematics. (Fong, Krantz, and Nisbett,
p. 38)
References
Askey, M. and William, D. Recent Research in Mathmatics Education 5–16. London.
Her Majesty’s Stationary Office, 1995.
Fong, G., Krantz, D., and Nisbett, R.“The Effects of Statistical Training on Thinking
About Everyday Problems.”Cognitive Psychology, 1986, 18: 253–292.
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
HANDOUT 13 (continued)
Helping with Math at Home: Ideas for Parents
Handout 14
Feedback Form
Session Title:
Location:
Date:
1. What new ideas do you have as a result of this session?
2. What ideas from this session will you use with your child(ren)?
3. Overall, how would you rate this session?
Not
Informative
Extremely
Informative
4. Is there anything else you would like us to know?
5. Would you like to be informed about any upcoming sessions? If
so, please provide the following:
Name:
Address:
E-mail:
© 2006 by Mathematics Education Collaborative from Helping with Math at Home: Ideas for Parents. Portsmouth, NH: Heinemann.
Helping with Math at Home: Ideas for Parents
HANDOUT 14