‘GROWING LEARNERS’
Family Literacy and
Math Night 2016
Math Review and
Enrichment
in Number Sense,
Problem Solving,
Measurement, &
Geometry
Building Number Sense with Card
Games
Compare: For Basic Number Sense (very similar to the traditional game of
“War”.
Materials: Deck of cards (you can choose to leave the face cards in to use as a
“Wild” card if you choose. *If you’re playing with “Wild” cards-a wild card can be
played as any number between 0 and 10. ).
Instructions:
● Deal all cards face down (players do not look at their cards)
● Players will turn over the first card from the top of their face down stack
● The player with the highest card “wins” and takes their card and their
opponents cards. They will add them face down to the bottom of their
deck.
● Play continues until someone runs out of cards.
Variations-play that the lowest card “wins” the flip.
Double Compare: For building single digit addition and subtraction
skills/fluency
●
For addition: Follow all directions above except each player flips two cards
from the top of their stack and adds them together. The player with the
highest sum wins and takes all cards to add to the bottom of their stack.
Play continues until someone runs out of cards.
●
For subtraction: Follow above directions for addition except students will
subtract their two numbers and the player with the largest difference is
the winner and takes all cards to add to the bottom of their stack. Play
continues until someone runs out of cards.
Variations-play that the lowest sum or difference “wins” the flip.
*If needed, encourage your child to utilize the images on the card to help with
their addition and subtraction.
Building Number Sense with Card
Games
Place Value Compare: For building place value concepts
Materials:
● Deck of cards (you can choose to leave the face cards in to use as a “Wild”
card if you choose. *If you’re playing with “Wild” cards-a wild card can be
played as any number between 0 and 10. ).
● You could use a place value chart or create one on a white board or sheet
of paper. This could be used as a guide for students when creating their
number.
Tens
Ones
Instructions:
● Deal all cards face down (players do not look at their cards)
● Players will turn over the first two cards from the top of their face down
stack
● Players will then decide how to arrange their cards in order to create the
largest number. (Example, if a player turns over a 2 and a 6 they would
want to create the number 62 by putting the 6 in the tens place and the 2
in the ones place instead of creating 26). Encourage your child to use the
terms tens place and ones place in order to further develop their
understanding of place value.
● The player who creates the highest number “wins” and takes their cards
and their opponents cards. They will add them face down to the bottom of
their deck.
● Play continues until someone runs out of cards.
Variations● Play that the player who creates the lowest number “wins” the flip.
● Flip 3 cards instead of 2 and incorporate the hundreds place. (Example: if
a player flips 2, 8, and 5 they could create 852). This will force them to think
about the placement of which number to select for the hundreds place
and also which number would be best in the tens place in order to make
the largest number possible.
Building Number Sense with Cards
Double Digit Addition/Subtraction Practice:
Materials:
● Deck of cards (you can choose to leave the face cards in to use as a “Wild”
card if you choose. *If you’re playing with “Wild” cards-a wild card can be
played as any number between 0 and 10. ).
● White board or scrap paper for working out problems
Instructions:
● Deal all cards face down (players do not look at their cards)
● Players will turn over the first two cards from the top of their face down
stack
● Players will then decide how to arrange their cards in order to create a
number. (Example, if a player turns over a 2 and a 6 they could make 62 or
26). Encourage your child to use the terms tens place and ones place in
order to further develop their understanding of place value.
● Once both players have created their number, both players will set the
numbers up into a horizontal addition number sentence. Both players will
then begin solving the problem. Some problems will require regrouping,
others will not.
Example:
42
+28
●
●
●
Both players will then share and check to see if they came up with the
same answer. If their answers are the same, they will continue by flipping
a new set of numbers. If their answers are different, they will discuss the
problem and share their thinking to find a correct answer agreed upon
by both players.
There isn’t a specific winner for this activity-it’s just a way to implement
practice in a different way. You could keep track of correctly solved
problems as a means for generating a way to keep score and establish a
winner.
Play can continue for as long as desired.
Variations● Play by subtracting instead of adding the two numbers. This will add in
additional mathematical thinking because students will have to ensure
they write the larger number on the top for the number sentence.
Building Number Sense
Race to 40 (or higher): For practice with addition and
regrouping (ideally, it would be great practice for students to build up to 120)
Materials:
● Materials to represent ones and tens (goldfish crackers (for ones) and
pretzel sticks (for tens), pennies (for ones) and dimes (for tens). You
could also use a similar material but different colors (red beads are ones,
blue beads are tens).You will need about 15-20 of each.
○ If you choose to work into the 100’s you’ll need another material to
represent hundreds (i.e. 1 dollar bill, different bead color)
● dice
● 1 Place value chart-these can be made on a piece of paper
Hundreds
Tens
Ones
Instructions: (for collaborative play)
● Player 1 rolls the die to get a number. Put this number of ones on your
place value chart in the ones column.
● Player 2 rolls the die to get a number. Player 2 adds that number of ones
to the ones place in the same board.
● Based on the numbers rolled, players will have to decide whether they
need to regroup their ones. If there are more than 9 ones, students will
trade the 9 ones for a ten. The 10 ones will be removed from the ones
place and a ten will be added to the tens place. (Example: if you have 13
ones, you will take 10 ones out (leaving the additional 3 remaining in the
ones place) and trade it in for a ten that will be added to the tens place.
● Play will continue until you reach 40. Once you reach 40 you can restart
the game or work beyond 40.
Additional Notes:
● For competitive play, you could use 2 place value boards and double the
amount of place value materials you are using. Each player would add to
their own board to see which player can reach 40 first.
● If you are playing to a higher number (such as 120), you could have
players start with 60 and then build on in order to get to 120.
Building Number Sense
Race to 0: For practice with subtraction and regrouping
Materials:
● Materials to represent ones and tens (goldfish crackers (for ones) and
pretzel sticks (for tens), pennies (for ones) and dimes (for tens). You
could also use a similar material but different colors (red beads are ones,
blue beads are tens).You will need about 15-20 of each.
● dice
● 1 Place value chart-these can be made on a piece of paper
Tens
Ones
Step 1
Instructions: (for collaborative play)
●
●
●
●
Tens
Ones
Step 2
Tens
Ones
Start with 4 tens (40) on your chart (See step 1).
Exchange 1 ten for 10 ones and move those ones into the ones place (see
step 2). Then roll the die.
Subtract the number you roll on the die from your ten ones. Continue
subtracting from your ones until you don’t have enough ones. Once you
don’t have enough ones left to subtract (example: you have 2 ones left
and you roll a 6), you will exchange another one of your tens for 10 ones.
Play will continue until you reach 0.
Additional Notes:
● For competitive play, use 2 place value boards and have each player start
with 4 of their own tens on their own board.
● You could also choose to play with more than 4 tens in order to extend
your length of play.
Websites for Math
●
www.learnzillion.com
●
www.mathplayground.com
●
www.calculationnation.nctm.org
●
www.xtramath.org
●
www.frontrowed.com
Hundreds Chart Activities
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Count forward and backward from any number
Count a vertical column (down) or a horizontal row (across)
Skip count by 2’s, 5’s, and 10’s (Challenge: Count by 3’s,4’s, etc.)
Pick a number- tell what is above, below, before, and after the number
Pick a number - add 1, 5, 10 to it, subtract 1, 5, 10 from it
Pick a number and tell what is 1 more, 1 less, 10 more, 10 less
(challenge - 100 more, 200 more, etc.)
●
●
Find an odd or even number in a row, in a column (Do you notice any pattern?)
Cross out or place a counter such as a bean or penny on even numbers
or odd numbers (for example: place a bean on the even numbers from 62 and 72 or
on the odd numbers from 30-40)
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●
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Tell how many tens and ones a number has
Play Guess My Number. Cover random numbers and have a partner guess your
number given clues such as: I’m thinking of a number that is even and is between 25
and 28 or I’m thinking of a number with a 5 in the tens place and a 2 in the ones place.
I’m thinking of a number that comes after 42, before 46 and is odd.
Find a pattern on the hundreds chart. Examples: Mark off or shade the
numbers 2,4,6,8 and ask the pattern (The pattern is counting by 2’s). Mark
or shade the numbers 14, 24, 34, 44, 54 (The pattern is counting by 10’s).
Ask which number is closer to 100 - 53 or 35, 74 or 47, etc.
Cover the number or numbers with a chip or bean. Have the partner figure
out what the is by seeing what number is before , after and between.
Roll to 100. Roll 2 dice. Add the numbers and place a counter on the number you get.
Continue to roll 2 dice and add on each time until you get to 100. Variations: You can
play this with a partner to see who gets to 100 first (race to 100) Try rolling the dice
starting at 100 and subtract the number each time until you make it back to zero.
Easier: Roll 1 dice each time and play to 50. Challenge: Roll more than 2 dice. Add a zero
in the ones place and play roll to 1000 as you count by 10’s each time you roll.
Use tens families partners to get to a multiple of 10. Example: Pick the number
57 - ask what they need to add to get to 60. Since 7 + 3 = 10, then 57 + 3 = 60.
Use for an addition or subtraction strategy - When adding 15 + 3, count up 3
more to get to 18. When subtracting 9 - 5, start on 9 and count backward 3 to get to 6.
Challenge: Use to add double digits such as 35 + 14. Start at 35 and break 14 into
expanded form 10 + 4 and go 10 down and then add on 4 more to get to 49. Use to add
number strings such as 9 + 6 + 2 or 16 + 12+ 17.
Count money using the hundred chart - Choose 2 coins and add them together
on the 100’s chart, keep adding coins to get to 50 cents or $1.00.
Variation: Start at $1.00 and use coins to subtract until you are all the way
back to zero cents.
‘GROWING LEARNERS’
MEASUREMENT
Review and
Enrichment
Family Literacy & Math Night
Measurement
Cotton Ball Throw
1.
Stand behind a designated line (certain tile on your floor, carpet line, sidewalk line, etc).
2.
Throw one cotton ball* as far as you can. Think about strategies that might help the
cotton ball go further. Find the distance your cotton ball traveled by counting the
number of footsteps it takes you to walk there. (Discuss with your family how your
different sized feet will change the results.)
Results: 1st Try - _____________________
2nd Try - _____________________
3rd Try - _____________________
4th Try - _____________________
Straw Throw
1.
Throw a straw as far as you can.
2.
Have a family member watch for and mark the place where your straw first hits the
ground.
3.
Find the distance using toilet paper squares between the throwing line and this point.
4.
For a greater challenge, measure using inches.
5.
Compare your results.
Results: 1st Try - _____________________
2nd Try - _____________________
3rd Try - _____________________
4th Try - _____________________
Family Literacy & Math Night
Measurement
Giant Step
1.
2.
3.
4.
Put both feet on the starting line on the floor.
Take one giant step forward.
Mark the back of your forward heel.
Find the length of your giant step by measuring with inches.
Results: 1st Try - _____________________
2nd Try - _____________________
3rd Try - _____________________
4th Try - _____________________
Side Step
1.
2.
3.
4.
5.
6.
Stand with both feet together with one foot on a designated line.
Take a giant step with one foot to the side.
Mark the inside spot where your stepping foot lands.
Measure the width of your step in spoons.
For a greater challenge, measure using inches.
Compare your results.
Results: 1st Try - _____________________
2nd Try - _____________________
3rd Try - _____________________
4th Try - _____________________
‘GROWING LEARNERS’
PROBLEM SOLVING
Review and
Enrichment
Math as Problem Solving
Why Problem Solve?
Problem solving is more than a vehicle for teaching and reinforcing mathematical knowledge and
helping to meet everyday challenges. It is also a skill which can enhance logical reasoning. Individuals
can no longer function optimally in society by just knowing the rules to follow to obtain a correct answer.
Problem solving allows the student to experience and cope with a range of emotions associated with
various stages in the solution process. Mathematicians who successfully solve problems say that the
experience of having done so contributes to an appreciation of the 'power and beauty of mathematics'
(NCTM, 1989, p.77). They also speak of the willingness or even desire to engage with a task for a length
of time which causes the task to cease being a 'puzzle' and allows it to become a problem.
One of the aims of teaching through problem solving is to encourage students to refine and build onto
their own processes over a period of time as their experiences allow them to discard some ideas and
become aware of further possibilities (Carpenter, 1989). As well as developing knowledge, the students
are also developing an understanding of when it is appropriate to use particular strategies.
Students need to develop their own theories, test them, test the theories of others, discard them if they
are not consistent, and try something else (NCTM, 1989).
It is of particular importance to note that [students] are encouraged to discuss the processes which they
are undertaking, in order to improve understanding, gain new insights into the problem and
communicate their ideas (Thompson, 1985, Stacey and Groves, 1985).
Carpenter, T. P. (1989). 'Teaching as problem solving'. In R.I.Charles and E.A. Silver (Eds), The Teaching and Assessing of Mathematical Problem
Solving, (pp.187-202). USA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and Evaluation Standards for School Mathematics, Reston, Virginia:
NCTM.
Stacey, K. and Groves, S. (1985). Strategies for Problem Solving, Melbourne, Victoria: VICTRACC.
Thompson, P. W. (1985). 'Experience, problem solving, and learning mathematics: considerations in developing mathematics curricula'. In E.A. Silver
(Ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, (pp.189-236). Hillsdale, N.J: Lawrence Erlbaum.
These Math Practices are underlying skills students from K to 12 work on building as math
problem solvers!
Math Practice 1 Toughen up!
This is problem solving where our students develop grit and resiliency in the face of perplexing
thorny problems. It is the most sought after skill for our students.
Math Practice 3 Work together!
This is collaborative problem solving in which students discuss their strategies to solve a
problem and identify missteps in a failed solution. Solving challenging math problems in
partners or teams adds brain power, communication and resilience.
Math Practice 6 Be precise!
This is where our students learn to communicate using precise terminology. We need to
encourage students not only to use the precise terms of others, but to invent and rigorously
define their own terms.
Math Practice 7 Be observant!
One of the things that the human brain does very well is identify pattern. We sometimes do this
too well and identify patterns that don't really exist.
Math as Problem Solving
Problem Solving Tactics:
Re-state the problem in your own words
Act the problem out
Make an organized list
Use a math model (bar model, number bond, numberline)
Make a sketch or visualization of the problem
Look for a pattern
Use simpler numbers to solve
Guess and check; retry with new information
Make a table, chart or graph
Work backwards
Reason logically (If….then…)
Consult a friend about how they might solve and compare efficiency
LAST: Check your solution in the problem!
Websites that explore mathematical problem solving and games:
www.figurethis.nctm.org
www.tenmarks.com
www.mathwire.com
www.openmiddle.com
www.mathpickle.com (Canadian)
www.nrich.maths.org (British)
www.mathplayground.com
(Many number models similar to our math curriculum, especially “thinking blocks” and number bonds. )
www.kidsmathgamesonline.com
www.sheppardsoftware.com
www.aaaknow.com (formerly www.aaamath.com)
www.ipracticemath.com
www.mathgametime.com
www.mathschallenge.net
www.mathinaction.org (Choose any school--it’s free!)
Cool Math Apps:
Sudoku
2048
Math Blaster
Lunch Date
Three women each have two daughters.
They are having lunch at a restaurant .
There are only seven chairs in the restaurant.
All the women are seated.
Question: How is this possible?
Promises, Promises
A father promises to pay his son $5.00 for each correct
answer on his math homework. For each incorrect
answer, the son must pay the father $8.00. The boy
answered twenty-six math problems. At the end there
was no money exchanged.
Question: How many correct and incorrect answers did the boy have?
Can you write problems similar to these (using different numbers) for
someone else to solve?
---from pedagonet.com
Lunch Date Answer
Three women each have two daughters.
They are having lunch at a restaurant .
There are only seven chairs in the restaurant.
All the women are seated.
Question: How is this possible?
A mother and her two daughters, who bring their daughters makes 7
people. The oldest two daughters are also the other two mothers.
Promises, Promises
A father promises to pay his son $5.00 for each correct
answer on his math homework. For each incorrect
answer, the son must pay the father $8.00. The boy
answered twenty-six math problems. At the end there
was no money exchanged.
Question: How many correct and incorrect answers did the boy have?
16 correct (16 x $5 = $80), 10 incorrect (10 x $8 = $80)
Can you write similar problems (using different numbers) for someone
else to solve?
---from pedagonet.com
Cheap Jewelry
Your mother has four separate pieces of gold chain, each with three links,
that she wants to have made into a bracelet. The jeweler charges $10 to
open and solder closed one link.
What is the minimum amount it will cost to have the bracelet made?
Can you put the chain back together for $30 or less??
Hint: Use 12 links to model the problem.
from www.aimsedu.org
Cheap Jewelry
Your mother has four separate pieces of gold chain, each with three links,
that she wants to have made into a bracelet. The jeweler charges $10 to
open and solder closed one link.
What is the minimum amount it will cost to have the bracelet made?
Can you put the chain back together for $30 or less??
Hint: Use 12 links to model the problem.
from www.aimsedu.org
Answer: Open all three links from one section. Use these links to connect the
other three sections.
The 8 Digit Puzzle
Write the one number on 8 post-it notes from one to eight.
The challenge in this puzzle is to place the number cards in the rectangles below so
that no two consecutive numbers are next to each other horizontally, vertically, or
diagonally. For example, if the 5 is placed in the far left box, then the 4 or 6 can’t be
placed in the box directly to the right of the 5 or the two boxes that are diagonally
above and below the 5.
Think about how you tried to solve this problem so that you can discuss it afterwards.
How many times did you check a possible solution to find it did not meet all the criteria?
What strategies did you use? Which were most helpful? Are there other solutions? How
do you know? What hint could you give a friend to solve this puzzle that might help
them?
from www.aimsedu.org
Number Icicles
Use skip counting and number patterns to solve number icicles.
Use the information shown in the icicles to complete the missing numbers in the icicles.
The numbers in the diamonds beside each icicle indicate the change that occurs from
circle to circle on the icicle. Some icicle designs might use different rates of change within
one design. Look to the diamonds to guide you.
Where icicles overlap, the number must be the same for both icicles.
Some number icicles are purposefully impossible as students learn a lot from working an
impossible problem--reasoning, questioning, strategy and persevering. Not all problems
are solvable.
There’s a great opportunity for students to create their own number icicles to develop
number sense for larger numbers.
7
8
9
1
2
4
6
1
6
5
5
1
1
5
8
from www.mathpickle.com
Magic Hats
(A math puzzle first explored by Issai Schur, 1916)
Students need to add rabbits into Magic Hats sequentially beginning with one. Students
continue to add “numbered rabbits” to the hats but must make sure that the number added is
not the sum of the numbers (two, three or more) already in the Magic Hat. If they add “3” to a
hat with a “1” and “2”, the hat will explode! Elementary students should be able to solve the
Magic Hat problem using the numbers 1 to 8 with some time. More challenges can go in other
directions:
1) Add a Magic Hat. Now the students must try to get as high as possible with three bubbling
cauldrons. After a first attempt, students should be encouraged to try to get at least 20 rabbits
in the three hats. (Don’t tell...but the highest possible is twenty-three.)
2) The first rabbit escapes! Still working with two hats show that you can fit the numbers 2-12
in the hats. After they solve this, say the first two rabbits escape… then the first three…
from www.mathpickle.com
Magic Hats
(A math puzzle first explored by Issai Schur, 1916)
Students need to add rabbits into Magic Hats sequentially beginning with one. Students
continue to add “numbered rabbits” to the hats but must make sure that the number added is
not the sum of the numbers (two, three or more) already in the Magic Hat. If they add “3” to a
hat with a “1” and “2”, the hat will explode! Elementary students should be able to solve the
Magic Hat problem using the numbers 1 to 8 with some time. More challenges can go in other
directions:
1) Add a Magic Hat. Now the students must try to get as high as possible with three bubbling
cauldrons. After a first attempt, students should be encouraged to try to get at least 20 rabbits
in the three hats. (Don’t tell...but the highest possible is twenty-three.)
2) The first rabbit escapes! Still working with two hats show that you can fit the numbers 2-12
in the hats. After they solve this, say the first two rabbits escape… then the first three…
Answer: 1,2,4, and 8 go into one hat. 3,5,6,and 7 go into the 2nd hat.
from www.mathpickle.com
The Envelope Enigma
Can you connect six points (labeled A-F) with line segments to form the outline of
an envelope. To make this a challenge, you must do this without lifting your
pencils once you start. In addition, you may not cross any lines already drawn or
retrace any line segment. You may cross back over a point.
After finding a solution (there are several) make a record of it. To do this, circle
your starting point. Then add numbers and arrows to each line segment showing
the order and direction in which they were drawn.
from www.aimsedu.org
The Envelope Enigma
Can you connect six points (labeled A-F) with line segments to form the outline of
an envelope. To make this a challenge, you must do this without lifting your
pencils once you start. In addition, you may not cross any lines already drawn or
retrace any line segment. You may cross back over a point.
After finding a solution (there are several) make a record of it. To do this, circle
your starting point. Then add numbers and arrows to each line segment showing
the order and direction in which they were drawn.
One Answer:
E to D, D to B,
B to E, E to F,
F to C, C to A,
A to B, B to C,
C to D, D to F
from www.aimsedu.org
‘GROWING LEARNERS’
GEOMETRY
Review and
Enrichment
Ask your child questions about the plan they
developed to create the shape, the shapes
name, number of sides and vertices (corners),
and compare several different shapes or
different ways to create the same shape.
THANK YOU FOR
HELPING US GROW!