“On Target”
Warm up thinking activity
List10possiblecombinationsyoucouldgetwith4darts.
Thenumbersonthetargetsare7-5-3-1.Trytoestablish
somelogicalmethodofdoingthis.
7
5
3
1
Youhave5dartsandyourtargetscoreis44.
Youareanexcellentplayerandallyourdartshitthe
board.Howmanydifferentwayscouldyouscore44?
Youcannothitthesame5numberseveninadifferent
order.Atleastonenumberhastobedifferentforeach
scoreof44.
“What’sItWorth?”
https://nrich.maths.org/1053
Eachsymbolhasanumericalvalue.Thetotalforthe
symbolsiswrittenattheendofeachrowandcolumn.
Canyoufindthemissingtotalthatshouldgowherethe
questionmarkhasbeenput?
“4DOM”
https://nrich.maths.org/179
Usethesefourdominoestomakeasquarethathasthe
samenumberofdotsoneachside.
“3Dice”
https://nrich.maths.org/1016
Threediceareplacedinarow.Findawaytoturneach
onesothatthethreenumbersontopofthedicetotal
thesameasthethreenumbersonthefrontofthedice.
Canyoufindallthewaystodothis?
(Lookatthetotalsonthebackandbottomofthethree
dice,whatdoyounotice?)
“Colourinthesquares”
Canyouputthe25colouredtilesintothe5×5square
belowsothatnocolumn,norowandnodiagonalline
havethesamecolourinthem?
5x5square
25colouredtiles
“DominoMagic
Rectangle”
“InstantInsanity”
https://nrich.maths.org/443
Thesearenetsof4differentcubes.Placetheprovided
coloureddotsonthecorrectfacesofeachcubein
ordertocreatethesecubes.
Now,buildatowersothatoneachverticalwallnocolour
isrepeated,thatisall4coloursappear.
“PrimeMagic”
https://nrich.maths.org/846
Placethenumbers1,2,3…9oneoneachsquareofa3by
3gridsothatalltherowsandcolumnsadduptoaprime
number.
Isitpossibletoplacethenumbers1,2,3…9oneoneach
squareofa3by3gridsothatthediagonals,aswellasall
therowsandcolumns,adduptoprimenumbers?
“Sandwiches”
https://nrich.maths.org/522
1?1
2??2
3???3
4????4
“BeatIt”
Sylvester measured his pulse and found that his heart beat
at a rate of 80 beats a minute at rest. At this rate, how
many days will it take his heart to beat 1,000,000 times?
Show your work and be sure you explain each step.
“Taxi!!!!”
Conrad's Taxi Service charges $1.50 for the first km and
$0.90 for each additional km. How far could Mr. Kulp go
for $20 if he gives the driver a $2 tip?
“Rodney’s Rabbit”
Regina has received a pet rabbit from her neighbour
Rodney who is about to move to an apartment that does
not allow pets. Her father is going to help her build a run
for the rabbit in their back yard, but he wants Regina to
design it.
Regina sits down to think about the possibilities. Her
father says that the run must be rectangular with whole
number dimensions. If they want to enclose 48 square
meters, how many options do they have?
Note: 1 square on your grid represents 1m"
List all the options possible.
“Hip to be square”
If you fold a square paper vertically, the new rectangle has
a perimeter of 39 cm.
1. What is the perimeter of the original square?
2. What is the area of the resulting rectangle?
“Counter Moves”
Six counters start out in the triangular shape shown in
Figure 1 below. They are to be moved into the sixsided shape as shown in Figure 2.
To move a counter, you must slide it so that it does
not disturb any other counter and so that it ends up
touching two other counters. The counters must stay
flat on the surface at all times.
Can you rearrange the counters as required, using
only four moves?
Figure 1
Figure 2
“Invert the Triangle”
A triangle of counters is made as in figure 1.
What is the smallest number of counters that have to
be moved to turn the triangle pattern upside down as
in figure 2?
Figure 1
Figure 2
“The Farmer's Sheep
Pens”
The drawing below shows how a farmer used thirteen
toothpicks to make six identical sheep pens.
Unfortunately one of the toothpicks was damaged.
Use twelve toothpicks to show how the farmer can
still make six identical pens.
“Toothpick squares”
Remove three toothpicks from the fifteen in the
arrangement shown so that only three squares are
left.
Now try removing two matches for the arrangement
shown to leave three squares. This time the squares
need not all be the same size.
“Toothpick Animal”
Show how by moving exactly one toothpick to
another position you can obtain a second animal that
is the same size and shape as the first.
“A bag of marbles”
A bag of marbles contains red, blue, green, and
yellow marbles.
How many of each are there if:
• The number of green is half the red
• There are 3 less yellow than green
• There is three times as many green as blue
• There are twelve red
“Sleepy Koala”
A sleepy koala bear wants to climb to the top of a
fruit tree that is 10 meters tall. Each day the bear
climbs up 5 meters but at night, while asleep,
slides back 4 meters. At this rate how many days
will it take the bear to reach the top of the tree?
Use the picture to help you solve the problem.
“Video Arcade”
Solve the following problem using the tables
provided. Use the whiteboard marker and clean the
sheets when you are finished.
There are four different video games at Lulu's
Arcade. Dennis, Olivia, Joey, and Grace each played
one video game. Then they each moved to another
video game one that they hadn't played yet, until each
person had played all four games.
During the second round, Dennis played Game 1, and
Olivia played Game 3.
During the third round, Joey played Game 2 and
Grace played Game 4.
During the fourth round, Olivia played Game 2 and
Grace played Game 3.
Figure out which game was played by each child for
each of the four rounds.
Name
Dennis
Olivia
Joey
Grace
Round 1
Round 2
Round 3
Round 4
“Symmetry”
What is the largest three digit number that has both
vertical and horizontal symmetry? Think of a three letter
word with horizontal symmetry.
“Going Camping”
Groups of campers were going to an island. On the
first day 10 went over and 2 came back. On the second
day, 12 went over and 3 came back. If this pattern
continues, how many would be on the island at the end
of a week? How many would have left?
“A Batty Diet”
A bat ate 1050 dragon flies on four consecutive nights.
Each night she ate 25 more than on the night before.
How many did she eat each night? Show all working
out.
“Trees”
A team of scientists found that there were 4 oak trees for
every 10 pine trees. How many oak trees were there if
they counted 36 pine?
“Cookies!”
Four friends buy 36 cookies for $12. Each person
contributes the following amount of money:
Tom $2
Jake $3
Ted $4
Sam $3
Each person gets the number of cookies proportional to
the money paid. Draw a pie chart to represent the
amount of cookies each person got.
“PYA”
Youhavefourminutestowriteasmany
equationsasyoucan,involvingP,Yand
A.
IfP=7,Y=2andA=9
Hereareafewexamples:
P+Y=9
2A–P=11
PYA=126
A+A+A=10Y+P
“RuleOfPattern”
Lookattheexampleofthetessellation
belowandseehoweachtrianglefits
ontothenextoneperfectly.
Noticetoohowtheinsidepatternshows
youwheretheapexofeachtriangleis.
Whatyouneedtodo:
Createasmanyotherregularpatterns
youcanfromyourjigsawpieces.
“EricTheSheep”
Ericthesheepislininguptobeshorn
beforethesummerahead.Thereare
50sheepinfrontofhim.Ericcan’tbe
botheredwaitinginthequeue
properly,sohedecidestosneaktowardsthe
front.
EverytimeEricpassestwosheep,onesheep
fromthefrontofthelineistakenintobeshorn.
HowmanysheepwillbeshornbeforeEric?
“Zin Obelisk”
IntheancientcityofAtlantisa
solidrectangularobjectcalleda
Zinwasbuiltinhonourofthe
goddessTina.
Thestructuretooklessthantwoweeks
tocomplete.
Thetaskofyourteamistodetermineon
whichdayoftheweektheobeliskwas
completed.
ZinObeliskInformationCard1
Note:1foot=0.3048m
https://nrich.maths.org/5992
Doesworktakeplaceon
Sunday?
WhatisZin?
Eachblockcoststwogold
fins.
Whatisacubit?
Onlyonegangisworking DayoneoftheAtlantian
ontheconstructionofthe weekiscalledAquaday.
Zin.
Workerseachlay150
DayfourintheAtlantian
blocksperschlib.
weekiscalled
Mermaidday.
ThelengthoftheZinis
Thereareeightgold
50m.
scalesinagoldfin.
Whichwayupdoesthe AnAtlantiandayis
Zinstand?
dividedintoschlibsand
ponks.
ZinObeliskInformationCard2
Note:1foot=0.3048m
https://nrich.maths.org/5992
Eachblockisonecubic
TheZinismadeofgreen
foot.
blocks.
Acubitisacube,allthe Atanytimewhenworkis
sidesofwhichmeasure takingplace,thereisa
onemegalithicyard.
gangofninepeopleon
site.
DaytwointheAtlantian Onememberofeach
weekiscalled
ganghasreligiousduties
Neptiminus.
anddoesnotlayblacks.
Therearefivedaysinan Noworktakesplaceon
Atlantianweek.
Daydoldrum.
Aworkingdaystartsat DaythreeintheAtlantian
daybreak.
weekiscalledSharkday.
ZinObeliskInformationCard3
Note:1foot=0.3048m
https://nrich.maths.org/5992
Workstartedon
Aquaday.
Thebasicmeasurement
oftimeinAtlantisisa
day.
TheheightoftheZinis
onehundredfeet.
ThewidthoftheZinis
tenfeet.
Greenhasspecial
religioussignificanceon
Mermaidday.
TheZinisbuiltofstoned
Theworkingdayhasnine
schlibs.
DayfiveintheAtlantian
weekiscalled
Daydoldrum.
Therearethreeandahalf
feetinamegalithicyard.
Eachgangincludestwo
women.
Eachworkertakesrest
periodsduringthe
workingdaytotalling
sixteenponks.
Thereareeightponksin
blocks.
aschlib.
“Pig Pen Pickle”
Materials:
27counterstorepresentpigs
4sheetsofpapertorepresentthe
pens
Task:
Howcanyouplace27pigsin4pensso
thatyouhaveanoddnumberofpigsin
eachpen?
“Blips, Blops and Bleeps”
Task:
Readthefollowinginformation
a. EveryBLIPisaBLOP
b. HalfofallBLEEPSareBLOPS
c. HalfofallBLOPSareBLIPS
d. Thereare30BLEEPSand20BLIPS
e. NoBLEEPisaBLOP
YourjobistodiscoverhowmanyBLOPS
areneitherBLIPSnorBLEEPS.
“Which One Differs?”
Task:
Four of the patterns in each row of 5 are the same.
Your job is to find the one in each row that differs.
“Pyramid Passage”
(fromCriticalThinkingPuzzles)
Task:AncientEgyptianpyramidswerebuiltas
royaltombs.Withinthesemassivestone
structureswererooms,hallsand
connectingpassageways.
Lookatthefigurebelow.Youmustdraw4
pathsthatconnectthematchingsymbols.The
pathsmaynotcross,theymaynotentera
non-matchingpyramid,normaytheygo
outsidethelargerpyramidboundary.
“Reason Teasin’”
Task: You are presented with a series of logic tests to
complete where if A changes to B then what figure does C change
to?
“Big Green Gorilla”
Task: UncleHenrywasdrivingtoCharlestown
whenhespottedabiggreengorillaonthe
sideoftheroad.Hescreechedtoastop
andjumpedoutofthecar.Hesawthe
outlineofanumberonthegorilla’schest.
Hecouldn’tquiteseethenumber,butheknew
itwasa4digitnumber.And:
i.
Herememberedseeinganumber1
ii.
Inthehundred’splaceheremembersthe
numberis3timesthenumberinthe
thousand’splace.
iii.
Hesaidthenumberintheunit’splaceis4
timesthenumberintheten’splace.
iv.
Finallyhesaidthenumber2issittingin
thethousand’splace.
FromUncleHenry’scluesyouhavetofindthe
number. “Up You
Go!”
In the old days there were elevator operators to transport
passengers. Don Downs always started his day in the
basement. He went up 20 floors to take his boss some
coffee. Then he went down 8 floors to take a Danish to his
friend. He went up 7 floors to check things out. This was
the halfway point in the building. How many floors are in
this building? Draw a diagram to show how you would
figure this out.
Solutions
1 Counter
Problems
1. Counter Moves
2. Inverted Triangle
Here's one solution:
3. Jumping Counters
Here is one solution:
•
•
•
•
•
•
•
•
9 jumps 8, remove 8
2 jumps 5, remove 5
7 jumps 4, remove 4
1 jumps 7, remove 7
2 jumps 9, remove 9
6 jumps 3, remove 3
2 jumps 1, remove 1
6 jumps 2, remove 2
[back to strand] [back to teacher notes]
2 Toothpick
Problems
1. The Farmer's Sheep Pens
2. Toothpick Squares
3. Toothpick Animal
[back to strand] [back to teacher notes]
4 A Bag of
Marbles
There are:
•
•
•
•
12 cats-eyes
6 green
2 blue
10 white
[back to strand] [back to teacher notes]
The Koala
Bear
It takes the koala bear 6 days to reach the top.
Magazine Problem Solving
You find your own problems in magazines you have to use.
Video
Arcade
Round Round Round Round
1
2
3
4
Dennis Game 1 Game 2 Game 3 Game 4
Olivia
Game 3 Game 4 Game 1 Game 2
Joey
Game 4 Game 3 Game 2 Game 1
Grace
Game 2 Game 1 Game 4 Game 3