“On Target” Warm up thinking activity

List10possiblecombinationsyoucouldgetwith4darts.Thenumbersonthetargetsare7-5-3-1.Trytoestablishsomelogicalmethodofdoingthis.

7 5 3 1

Youhave5dartsandyourtargetscoreis44.Youareanexcellentplayerandallyourdartshittheboard.Howmanydifferentwayscouldyouscore44?Youcannothitthesame5numberseveninadifferentorder.Atleastonenumberhastobedifferentforeachscoreof44.

“What’sItWorth?”https://nrich.maths.org/1053

Eachsymbolhasanumericalvalue.Thetotalforthesymbolsiswrittenattheendofeachrowandcolumn.Canyoufindthemissingtotalthatshouldgowherethequestionmarkhasbeenput?

https://nrich.maths.org/179

Usethesefourdominoestomakeasquarethathasthesamenumberofdotsoneachside.

“4DOM”

“3Dice”https://nrich.maths.org/1016

Threediceareplacedinarow.Findawaytoturneachonesothatthethreenumbersontopofthedicetotalthesameasthethreenumbersonthefrontofthedice.Canyoufindallthewaystodothis?(Lookatthetotalsonthebackandbottomofthethreedice,whatdoyounotice?)

“Colourinthesquares”

Canyouputthe25colouredtilesintothe5×5squarebelowsothatnocolumn,norowandnodiagonallinehavethesamecolourinthem?

5x5square

25colouredtiles

“DominoMagicRectangle”

“InstantInsanity”https://nrich.maths.org/443

Thesearenetsof4differentcubes.Placetheprovidedcoloureddotsonthecorrectfacesofeachcubein

ordertocreatethesecubes.Now,buildatowersothatoneachverticalwallnocolour

isrepeated,thatisall4coloursappear.

“PrimeMagic”https://nrich.maths.org/846

Placethenumbers1,2,3…9oneoneachsquareofa3by3gridsothatalltherowsandcolumnsadduptoaprimenumber.

Isitpossibletoplacethenumbers1,2,3…9oneoneachsquareofa3by3gridsothatthediagonals,aswellasalltherowsandcolumns,adduptoprimenumbers?

“Sandwiches”https://nrich.maths.org/522

1?12??23???34????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 six-sided 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 Round 1 Round 2 Round 3 Round 4

Dennis

Olivia

Joey

Grace

“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” Youhavefourminutestowriteasmanyequationsasyoucan,involvingP,YandA.

IfP=7,Y=2andA=9Hereareafewexamples:P+Y=92A–P=11PYA=126A+A+A=10Y+P

“RuleOfPattern”

Lookattheexampleofthetessellationbelowandseehoweachtrianglefitsontothenextoneperfectly.Noticetoohowtheinsidepatternshowsyouwheretheapexofeachtriangleis.

Whatyouneedtodo:Createasmanyotherregularpatterns

youcanfromyourjigsawpieces.

“EricTheSheep”Ericthesheepislininguptobeshornbeforethesummerahead.Thereare50sheepinfrontofhim.Ericcan’tbebotheredwaitinginthequeueproperly,sohedecidestosneaktowardsthefront.

EverytimeEricpassestwosheep,onesheepfromthefrontofthelineistakenintobeshorn.

HowmanysheepwillbeshornbeforeEric?

“Zin Obelisk”

IntheancientcityofAtlantisasolidrectangularobjectcalledaZinwasbuiltinhonourofthegoddessTina.Thestructuretooklessthantwoweekstocomplete.Thetaskofyourteamistodetermineonwhichdayoftheweektheobeliskwascompleted.

ZinObeliskInformationCard1Note:1foot=0.3048mhttps://nrich.maths.org/5992

DoesworktakeplaceonSunday?

Eachblockcoststwogoldfins.

WhatisZin?

Whatisacubit?

OnlyonegangisworkingontheconstructionoftheZin.

DayoneoftheAtlantianweekiscalledAquaday.

Workerseachlay150blocksperschlib.

DayfourintheAtlantianweekiscalledMermaidday.

ThelengthoftheZinis50m.

Thereareeightgoldscalesinagoldfin.

WhichwayupdoestheZinstand?

AnAtlantiandayisdividedintoschlibsand

ponks.

ZinObeliskInformationCard2

Note:1foot=0.3048mhttps://nrich.maths.org/5992

Eachblockisonecubicfoot.

TheZinismadeofgreenblocks.

Acubitisacube,allthesidesofwhichmeasureonemegalithicyard.

Atanytimewhenworkistakingplace,thereisagangofninepeopleonsite.

DaytwointheAtlantianweekiscalledNeptiminus.

Onememberofeachganghasreligiousdutiesanddoesnotlayblacks.

TherearefivedaysinanAtlantianweek.

NoworktakesplaceonDaydoldrum.

Aworkingdaystartsatdaybreak.

DaythreeintheAtlantianweekiscalledSharkday.

ZinObeliskInformationCard3Note:1foot=0.3048mhttps://nrich.maths.org/5992

WorkstartedonAquaday.

Theworkingdayhasnineschlibs.

ThebasicmeasurementoftimeinAtlantisisaday.

DayfiveintheAtlantianweekiscalledDaydoldrum.

TheheightoftheZinisonehundredfeet.

Therearethreeandahalffeetinamegalithicyard.

ThewidthoftheZinistenfeet.

Eachgangincludestwowomen.

GreenhasspecialreligioussignificanceonMermaidday.

Eachworkertakesrestperiodsduringtheworkingdaytotallingsixteenponks.

TheZinisbuiltofstoned

Thereareeightponksin

blocks. aschlib.

“Pig Pen Pickle” Materials:

27counterstorepresentpigs4sheetsofpapertorepresentthepensTask: Howcanyouplace27pigsin4pensso

thatyouhaveanoddnumberofpigsineachpen?

“Blips, Blops and Bleeps” Task: Readthefollowinginformation

a. EveryBLIPisaBLOPb. HalfofallBLEEPSareBLOPSc. HalfofallBLOPSareBLIPSd. Thereare30BLEEPSand20BLIPSe. NoBLEEPisaBLOPYourjobistodiscoverhowmanyBLOPSareneitherBLIPSnorBLEEPS.

“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:AncientEgyptianpyramidswerebuiltasroyaltombs.Withinthesemassivestonestructureswererooms,hallsand

connectingpassageways.

Lookatthefigurebelow.Youmustdraw4pathsthatconnectthematchingsymbols.Thepathsmaynotcross,theymaynotenteranon-matchingpyramid,normaytheygooutsidethelargerpyramidboundary.

“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: UncleHenrywasdrivingtoCharlestownwhenhespottedabiggreengorillaonthe

sideoftheroad.Hescreechedtoastopandjumpedoutofthecar.Hesawtheoutlineofanumberonthegorilla’schest.

Hecouldn’tquiteseethenumber,butheknewitwasa4digitnumber.And:

i. Herememberedseeinganumber1ii. Inthehundred’splaceheremembersthe

numberis3timesthenumberinthethousand’splace.

iii. Hesaidthenumberintheunit’splaceis4timesthenumberintheten’splace.

iv. Finallyhesaidthenumber2issittinginthethousand’splace.

FromUncleHenry’scluesyouhavetofindthenumber.

“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 1

Round 2

Round 3

Round 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