Learn by doing.

Count to five, see small groups at a glance, and find out that the last number is how many.

1. 1One, Two, ThreeTouch each one as you say it.6 min
2. 2Four and FiveTwo more numbers to know.6 min
3. 3See It Without CountingSome little groups you just know.6 min
4. 4How Many AltogetherThe last number you say.7 min
5. 5Which Has MoreLine them up and look.7 min

Count all the way to ten, add one more, meet zero, and count things that are not in a line.

1. 1Six, Seven, EightCounting past five.6 min
2. 2Nine and TenAll the way to ten.7 min
3. 3One MoreAdding just one.7 min
4. 4Zero Means NoneA number for nothing at all.6 min
5. 5Counting a JumbleWhen things are not in a line.7 min

Circles, squares, triangles and rectangles, and a shape hunt around the room.

1. 1Circles and SquaresRound ones and boxy ones.6 min
2. 2TrianglesThree sides, three corners.6 min
3. 3RectanglesLike a square, but stretched.6 min
4. 4Shape HuntFinding shapes in real things.7 min

Sort things by colour, shape and size, then compare the piles.

1. 1Sorting by ColourPutting the same ones together.6 min
2. 2Sorting by Shape and SizeMore ways to make groups.6 min
3. 3Which Group Has MoreComparing your piles.7 min

Spot what comes next in a repeating pattern, then make one of your own.

1. 1What Comes NextRed, blue, red, blue...6 min
2. 2Making Your Own PatternYou decide the rule.7 min

Compare big and small, put three things in order, and say where things are.

1. 1Big and SmallComparing two things.6 min
2. 2Putting Things in OrderSmallest to biggest.7 min
3. 3Where Is It?On, under, next to, behind.6 min

Count to twenty, meet the teen names, and match written numerals to amounts.

1. 1Counting to Ten AgainWarming up the numbers you know.8 min
2. 2Eleven to FifteenPast ten, into the teens.8 min
3. 3Sixteen to TwentyAll the way to twenty.8 min
4. 4Writing NumbersThe squiggle that means how many.8 min

Match one to one to compare groups, compare written numbers, and find each number’s neighbours.

1. 1More, Fewer, the SameMatching one to one.8 min
2. 2Comparing Written NumbersDeciding without counting things.8 min
3. 3One More, One LessStepping up and stepping down.8 min

Add by putting groups together, learn to count on, and discover that either order works.

1. 1Putting Two Groups TogetherAdding is joining.9 min
2. 2Counting OnA faster way to add.9 min
3. 3Adding in Any OrderTwo plus five is the same as five plus two.9 min

Take away and count what is left, break a number into two parts, and find a missing part.

1. 1Taking AwaySome go, some stay.9 min
2. 2Breaking a Number ApartFive can be four and one, or three and two.9 min
3. 3The Missing PartYou know the whole and one part. Find the other.9 min

Find the pairs that make ten, see every number as five and some more, and write the ten sums.

1. 1Pairs That Make TenThe most useful pairs there are.9 min
2. 2Five and Some MoreA shortcut hiding in the top row.9 min
3. 3Sums That Make TenWriting the ten pairs down.9 min

Discover that every teen number is a full ten and some more, then build and compare them.

1. 1Ten and Some MoreWhat a teen number really is.9 min
2. 2Building Teen NumbersMaking any teen number you like.9 min
3. 3Comparing Teen NumbersThe extras decide.8 min

Count to a hundred by ones, jump by tens, and use the chart to find ten more and ten less.

1. 1Counting by Ones to a HundredThe pattern that keeps repeating.9 min
2. 2Counting by TensTen, twenty, thirty, jumping along.8 min
3. 3Ten More on the ChartStraight down is a jump of ten.9 min

Name flat and solid shapes, build big shapes from small ones, and say where things are.

1. 1Naming Flat ShapesSquares, circles, triangles, rectangles.8 min
2. 2Solid ShapesShapes you can hold.9 min
3. 3Building Bigger ShapesSmall shapes make big ones.9 min
4. 4Where Things AreAbove, below, beside, behind.8 min

Learn to see numbers up to 10 without counting one by one, and to see them as two parts that make a whole.

• 1.OA.A.1
• 1.OA.B.3
• 1.OA.C.5
• 1.OA.C.6

1. 1See It FastLook at dots and know how many, without counting.9 min
2. 2Five and Some MoreSee a big group as a full five, plus a little more.11 min
3. 3Number BondsShow two parts that make one whole.11 min
4. 4All the Ways to Make 6 and 7Find every pair of parts that makes 6 or 7.13 min
5. 5All the Ways to Make 8 and 9Find every pair of parts that makes 8 or 9.13 min
6. 6Partners to TenKnow fast how many more you need to make ten.13 min
7. 7One More, One LessFind one more or one less without recounting.10 min
8. 8How Many Do You See?Put it all together with picture and story problems.13 min

Join two groups and write what happened, then learn to count on, swap the parts, and use facts you already know.

• 1.OA.A.1
• 1.OA.B.3
• 1.OA.C.5
• 1.OA.C.6
• 1.OA.D.7
• 1.OA.D.8

1. 1Putting Groups TogetherJoin two groups and write what happened.11 min
2. 2Counting OnStart at one number instead of going back to one.11 min
3. 3Counting On With PicturesUse a number and a dot card together.10 min
4. 4Adding in Any OrderSwap the parts and the total stays the same.12 min
5. 5What Does Equals Mean?The two sides must be worth the same.12 min
6. 6Finding the Missing PartWork out the number that is hiding.12 min
7. 7DoublesTwo groups the same size.10 min
8. 8Doubles and One MoreUse a double you know to work out one you do not.12 min
9. 9Facts to TenPut every strategy together and spot the patterns.13 min

Find missing parts and take away, and see that adding and subtracting are one relationship.

• 1.OA.A.1
• 1.OA.B.4
• 1.OA.C.5
• 1.OA.C.6
• 1.OA.D.8

1. 1How Many More To Make It?Find the part that is missing.11 min
2. 2Counting Up To SubtractHop from the part to the whole and count the hops.11 min
3. 3Taking AwaySome go away, and you count what is left.11 min
4. 4The Hidden PartYou can see one part. Work out the other.11 min
5. 5What Changed?You know the start and the end. What happened in between?12 min
6. 6Fact FamiliesThree numbers make four sentences.12 min
7. 7Taking Nothing and Taking AllSome subtractions you can answer without working.10 min
8. 8Subtracting From TenYour partners to ten work backwards too.11 min
9. 9Adding and Subtracting to TenMix them up and pick your own way.13 min

Bundle ten ones into one ten, then build, name, and write every number from 11 to 20.

• 1.NBT.B.2
• 1.NBT.B.2.a
• 1.NBT.B.2.b
• 1.NBT.A.1
• 1.OA.C.6

1. 1Ten Ones Make One TenBundle ten little ones into one big ten.11 min
2. 2Ten and Some MoreEvery teen number is a ten with a few left over.11 min
3. 3Saying It the Ten WayThirteen is really "ten three".10 min
4. 4Writing Teen NumbersThe tens digit always comes first.11 min
5. 5Breaking Teen Numbers ApartSplit a teen number into ten and the rest.11 min
6. 6One More, One Less to TwentyKeep going past ten, including the tricky bit at 19.11 min
7. 7Counting to Twenty and BackStart anywhere and keep going, forwards or backwards.11 min

Make a ten to add past ten, and take from the ten to subtract from a teen number.

• 1.OA.A.1
• 1.OA.A.2
• 1.OA.B.3
• 1.OA.C.6
• 1.OA.D.7

1. 1Adding Three NumbersLook for two that make ten first.12 min
2. 2Making Ten From NineMove one across and the hard sum turns easy.13 min
3. 3Making Ten From EightNow move two across.13 min
4. 4Start With the Bigger OneSwap first, then make your ten.12 min
5. 5Counting On or Making Ten?Two good ways. Which is quicker here?12 min
6. 6Taking From TenBreak the teen number apart and take from the ten.14 min
7. 7Take From Ten in StoriesUse the same move on real problems.13 min
8. 8Missing Numbers to TwentyThe box can be anywhere in the sentence.13 min
9. 9True or False to TwentyNow both sides can have sums in them.13 min

Compare and measure length with same-size units, then sort things and read a graph.

• 1.MD.A.1
• 1.MD.A.2
• 1.MD.C.4
• 1.OA.A.1

1. 1Longer Than, Shorter ThanLine them up at the same end first.10 min
2. 2Using a Third ThingCompare two things that cannot be moved.11 min
3. 3Putting Three in OrderShortest, middle, longest.10 min
4. 4Measuring With CubesNo gaps and no overlaps.12 min
5. 5Why Same-Size Units?Bigger units give a smaller number.11 min
6. 6How Much Longer?Find the difference between two lengths.12 min
7. 7Sorting and Showing DataPut things into groups and build a graph.12 min
8. 8Asking Questions About DataRead a graph and answer questions from it.12 min

Count to 40, build any number from tens and ones, compare two numbers, and move by ten.

• 1.NBT.A.1
• 1.NBT.B.2
• 1.NBT.B.2.c
• 1.NBT.B.3
• 1.NBT.C.5

1. 1Counting Beyond 20Count to 40 and find the pattern that repeats.9 min
2. 2Tens and Ones on a MatShow any number to 40 as tens and ones.12 min
3. 3Multiples of TenSee that 10, 20, 30, and 40 have no ones at all.9 min
4. 4Many Ways to Show a NumberThe same number can be built in more than one way.12 min
5. 5Which Is More?Compare two numbers by looking at the tens first.11 min
6. 6Greater Than, Less Than, Equal ToWrite your comparison using a symbol.11 min
7. 7Ten More, Ten LessAdd or take ten without counting one by one.12 min
8. 8One More, One Less, Ten More, Ten LessMove in all four directions and say where you will land.12 min

Add and subtract whole tens, add ones to two-digit numbers, and make a new ten when the ones fill up.

• 1.NBT.C.4
• 1.NBT.C.6
• 1.NBT.C.5
• 1.OA.A.1

1. 1Adding Tens to TensAdd whole tens the same way you add ones.10 min
2. 2Subtracting Tens From TensTake whole tens away and count what is left.10 min
3. 3Adding Tens to Any NumberAdd whole tens and watch the ones stay put.11 min
4. 4Adding Ones Without Making a New TenAdd a small number when the ones still fit.11 min
5. 5Making the Next TenUse the make-ten move on bigger numbers.13 min
6. 6Tape Diagrams for StoriesDraw a story as two bars and the whole they make.13 min
7. 7Word Problems Within 40Find the missing part as well as the whole.14 min
8. 8Adding Two-Digit NumbersAdd tens to tens, then ones to ones.13 min
9. 9When the Ones Make a TenSometimes the ones fill up and you need a new ten.14 min

Name flat and solid shapes, build shapes from other shapes, split a whole into equal shares, and tell the time.

• 1.G.A.1
• 1.G.A.2
• 1.G.A.3
• 1.MD.B.3

1. 1What Makes a Shape a Shape?Some things about a shape matter. Some do not.11 min
2. 2Naming Flat ShapesLearn the names of the flat shapes you see everywhere.12 min
3. 3Naming Solid ShapesMeet the shapes you can pick up and hold.12 min
4. 4Making New ShapesPut small shapes together to build a bigger one.13 min
5. 5Shapes Inside ShapesA shape you built can become a piece of something bigger.12 min
6. 6HalvesCut a whole into two equal shares.13 min
7. 7Fourths and QuartersCut a whole into four equal shares.13 min
8. 8Telling Time to the HourRead a clock when the long hand points straight up.13 min
9. 9Telling Time to the Half HourHalf past is exactly half of the way round.14 min

Compare two amounts, count and write numbers to 120, and add two-digit numbers within 100.

• 1.NBT.A.1
• 1.NBT.B.2
• 1.NBT.B.3
• 1.NBT.C.4
• 1.NBT.C.5
• 1.OA.A.1

1. 1How Many More? How Many Fewer?Match two groups up and see what is left over.12 min
2. 2Two-Bar Tape DiagramsDraw a comparison as two bars from the same starting line.13 min
3. 3Numbers to 100Tens and ones work the same all the way to 100.12 min
4. 4Counting to 120Keep counting past 100.12 min
5. 5Comparing Numbers to 100Compare bigger numbers the same way as before.12 min
6. 6Ten More, Ten Less to 100Move by ten anywhere on the chart.12 min
7. 7Adding to 100 With Place ValueAdd bigger numbers by adding tens to tens.13 min
8. 8When You Need a New TenMake a new ten with bigger numbers too.14 min
9. 9Tricky Comparison ProblemsSome problems try to lead you the wrong way.14 min
10. 10Year-End Fluency FestivalLook back at everything you learned this year.14 min

Turn the strategies from Grade 1 into facts you simply know: doubles, near doubles, making ten, and taking from ten.

• 2.OA.A.1
• 2.OA.B.2

1. 1DoublesTwo equal groups make a double.11 min
2. 2Near DoublesIf you know a double, you know its neighbours.12 min
3. 3Make Ten to AddGet to ten first, then add what is left.12 min
4. 4Take From Ten to SubtractBreak the teen number apart and subtract from the ten.12 min
5. 5Addition and Subtraction TogetherOne fact family, four number sentences.12 min
6. 6Find the Missing NumberThe unknown can sit anywhere in the sentence.13 min
7. 7Choosing a StrategyLook at the numbers before you start.13 min
8. 8Two-Step Word ProblemsSome problems need two answers before the real one.14 min

Measure with rulers in centimetres and inches, estimate, compare lengths, and turn the ruler into a number line.

• 2.MD.A.1
• 2.MD.A.2
• 2.MD.A.3
• 2.MD.A.4
• 2.MD.B.5
• 2.MD.B.6

1. 1Measuring in CentimetresA ruler has the units printed on already.12 min
2. 2Centimetres and MetresBig things need a bigger unit.11 min
3. 3Inches and FeetAnother pair of units, used the same way.11 min
4. 4The Same Object, Two UnitsA smaller unit always gives a bigger number.13 min
5. 5Estimating LengthA good guess uses something you already know.12 min
6. 6How Much Longer?Compare two lengths and find the difference.12 min
7. 7Length Word ProblemsStories about how long things are.13 min
8. 8From Ruler to Number LineTake the object away and the ruler becomes a number line.12 min
9. 9Adding and Subtracting on a Number LineA jump forward adds. A jump back takes away.14 min

Meet the hundred, build and read every number to 1,000, write them three ways, and compare them.

• 2.NBT.A.1
• 2.NBT.A.2
• 2.NBT.A.3
• 2.NBT.A.4
• 2.NBT.B.8

1. 1A New Unit: The HundredTen tens bundle into one hundred.11 min
2. 2Building Numbers to 1,000Every three-digit number is hundreds, tens, and ones.12 min
3. 3Skip-Counting by 5s, 10s, and 100sCount in jumps instead of one at a time.12 min
4. 4Counting to 1,000Crossing each hundred is the only tricky bit.12 min
5. 5Three Ways to Write a NumberDigits, words, and expanded form.13 min
6. 6What Zero MeansA 0 holds a place open. It does not mean nothing is there.12 min
7. 7Comparing Three-Digit NumbersHundreds first, then tens, then ones.12 min
8. 8Using Greater Than and Less ThanWrite your comparison with a symbol.12 min
9. 9Ten More, Ten LessAdd or take a ten without counting.12 min
10. 10A Hundred More, A Hundred LessThe same trick, one place further left.12 min

Add and subtract two-digit numbers, making a new ten and breaking one open, and explain why it works.

• 2.NBT.B.5
• 2.NBT.B.7
• 2.NBT.B.9
• 2.OA.A.1

1. 1Adding With Place ValueTens with tens, ones with ones.11 min
2. 2Making a New TenWhen the ones fill up, bundle them.13 min
3. 3Adding Past 100Ten tens make a hundred, in the middle of a sum too.13 min
4. 4Explaining Why It WorksSay what you did and why it was allowed.12 min
5. 5Subtracting Tens and OnesTake the tens away, then the ones.11 min
6. 6Breaking a Ten ApartNot enough ones? Open a ten.13 min
7. 7Subtracting With a Broken TenOpen a ten, then take away as usual.14 min
8. 8Checking by AddingAdd your answer back and see if you return.12 min
9. 9Word Problems Within 100Draw the bars, then choose what to do.13 min
10. 10Two-Step Word Problems Within 100Find the hidden question first.15 min

Add and subtract three-digit numbers, making a new hundred and breaking one open, including across a zero.

• 2.NBT.B.6
• 2.NBT.B.7
• 2.NBT.B.9
• 2.OA.A.1

1. 1Adding and Subtracting HundredsWhole hundreds behave like single digits.11 min
2. 2Adding Within 1,000Three columns now, same rule.12 min
3. 3Making a New HundredWhen the tens fill up, bundle them.13 min
4. 4Subtracting Within 1,000Take away each kind of block in turn.12 min
5. 5Breaking a Hundred ApartNot enough tens? Open a hundred.14 min
6. 6Subtracting Across a ZeroThe hardest case, taken slowly.15 min
7. 7Adding Up to Four NumbersLook for pairs that make a friendly number.13 min
8. 8Word Problems Within 1,000Bigger numbers, same thinking.15 min

Pair numbers to find odd and even, then build arrays of equal groups and write the sentences they spell.

• 2.OA.C.3
• 2.OA.C.4
• 2.G.A.2

1. 1Odd or EvenPair them up and see if one is left over.11 min
2. 2Two Equal AddendsEvery even number splits into two equal halves.11 min
3. 3Equal GroupsGroups that all hold the same number.12 min
4. 4Rows and ColumnsAn array is equal groups lined up neatly.12 min
5. 5Writing the EquationTurn an array into a number sentence.12 min
6. 6Filling a Rectangle With SquaresRows and columns again, this time in shapes.12 min
7. 7Equal Groups in StoriesSpot the equal groups hiding in a word problem.13 min

Know the coins by value, count mixed collections, work out change, and read picture graphs, bar graphs, and line plots.

• 2.MD.C.8
• 2.MD.D.9
• 2.MD.D.10
• 2.OA.A.1

1. 1Meet the CoinsSize does not tell you what a coin is worth.11 min
2. 2Counting Coins of One KindSkip count by the coin you are holding.11 min
3. 3Counting Mixed CoinsStart with the biggest and work down.13 min
4. 4Dollars and CentsA hundred cents make a dollar.12 min
5. 5Money ProblemsBuying, paying, and working out the change.14 min
6. 6Picture GraphsOne picture stands for one thing.11 min
7. 7Bar GraphsA bar instead of a row of pictures.12 min
8. 8Line PlotsMarks stacked over a number scale.13 min

Tell time to five minutes with a.m. and p.m., name shapes by their sides, and split wholes into halves, thirds, and fourths.

• 2.MD.C.7
• 2.G.A.1
• 2.G.A.3

1. 1Time to Five MinutesThe long hand counts in fives.13 min
2. 2A.M. and P.M.Two threes in every day.11 min
3. 3Shapes by Their SidesTriangles, quadrilaterals, pentagons, and hexagons.12 min
4. 4Cubes and Solid ShapesFaces, edges, and corners.11 min
5. 5HalvesTwo equal shares of one whole.11 min
6. 6ThirdsThree equal shares.12 min
7. 7FourthsFour equal shares, also called quarters.12 min
8. 8Equal Shares, Different ShapesTwo halves of a shape need not look the same.13 min

Meet multiplication as equal groups and division as the missing factor, then build the 2, 3, 4, 5, and 10 times tables.

• 3.OA.A.1
• 3.OA.A.2
• 3.OA.A.3
• 3.OA.A.4
• 3.OA.B.5
• 3.OA.B.6
• 3.OA.C.7

1. 1Equal Groups and MultiplicationA short way to write repeated addition.12 min
2. 2Arrays and the Commutative PropertyTurn the array and the product stays the same.12 min
3. 3Division as SharingSplitting a total into equal shares.12 min
4. 4Division as an Unknown FactorEvery division is a multiplication with a gap in it.13 min
5. 5Multiplication and Division Fact FamiliesFour facts from one array.12 min
6. 6Multiplying by 2, 5, and 10The three easiest tables, and why they are easy.12 min
7. 7Dividing by 2, 5, and 10The same three tables, read backwards.12 min
8. 8Multiplying and Dividing by 3 and 4Two more tables, built from ones you know.13 min
9. 9Multiplying by 0 and 1Two special cases that trip people up.11 min
10. 10Multiplication and Division Word ProblemsDeciding which operation the story needs.14 min

Round on a number line, add and subtract within 1,000 fluently, tell time to the minute, and measure mass and volume.

• 3.NBT.A.1
• 3.NBT.A.2
• 3.MD.A.1
• 3.MD.A.2

1. 1Rounding to the Nearest TenWhich ten is it closer to?13 min
2. 2Rounding to the Nearest HundredThe same rule, one place bigger.12 min
3. 3Estimating Sums and DifferencesA quick answer that tells you if the real one is sensible.12 min
4. 4Adding Within 1,000 FluentlyFaster now, with the blocks in your head.13 min
5. 5Subtracting Within 1,000 FluentlyBreak a unit open when you need to.14 min
6. 6Telling Time to the MinuteEvery little mark is one minute.12 min
7. 7Time IntervalsHow long did that take?14 min
8. 8Grams and KilogramsReading a scale to find a mass.12 min
9. 9Litres and MillilitresMeasuring how much a container holds.12 min

Build the harder times tables by cutting arrays apart, then multiply by multiples of ten and solve two-step problems.

• 3.OA.B.5
• 3.OA.C.7
• 3.OA.D.8
• 3.OA.D.9
• 3.NBT.A.3
• 3.OA.A.4

1. 1Breaking an Array ApartA hard fact is two easy facts in disguise.14 min
2. 2Multiplying by 6Double the threes.12 min
3. 3Multiplying by 7Fives plus twos.13 min
4. 4Multiplying by 8 and 9Doubling again, and a pattern worth spotting.14 min
5. 5The Associative PropertyMultiply three numbers in any order you like.13 min
6. 6Multiplying by Multiples of TenMultiply the digits, then count the tens.13 min
7. 7Missing Factors and DivisorsFinding the gap in any position.13 min
8. 8Patterns in the Times TablesThe tables are full of patterns, and each one has a reason.13 min
9. 9Multiplication and Division FluencyKnowing them, not working them out.13 min
10. 10Two-Step Problems With a LetterNaming the number you do not know yet.15 min

Measure area by covering and by multiplying, find perimeter, and learn to tell the two apart.

• 3.MD.C.5
• 3.MD.C.6
• 3.MD.C.7
• 3.MD.D.8

1. 1What Area IsHow much space a shape covers.12 min
2. 2Area by MultiplyingRows and columns again, so you can multiply.12 min
3. 3Finding a Missing SideWorking backwards from the area.12 min
4. 4Breaking a Big Area ApartThe distributive property, in shapes.13 min
5. 5PerimeterThe distance all the way round.12 min
6. 6Telling Area and Perimeter ApartTwo different questions about the same shape.14 min
7. 7Same Area, Different ShapeRectangles can share an area and look nothing alike.13 min
8. 8Area of Joined ShapesSplit an odd shape into rectangles.13 min

Meet fractions as numbers with a place on the line: unit fractions, equivalence, comparing, and fractions past one.

• 3.NF.A.1
• 3.NF.A.2
• 3.NF.A.3
• 3.G.A.2

1. 1Equal Parts of a WholeCutting fairly is where fractions start.12 min
2. 2Unit FractionsOne piece out of the whole.12 min
3. 3Fractions as Copies of a UnitThree quarters is three one-quarters.12 min
4. 4Fractions on the Number LineA fraction is a number, so it has a place.14 min
5. 5Fractions Equal to OneWhen the top and bottom match.12 min
6. 6Comparing Fractions With the Same BottomSame size pieces, so just count them.12 min
7. 7Comparing Fractions With the Same TopSame number of pieces, so the piece size decides.13 min
8. 8Equivalent FractionsDifferent names for the same place on the line.14 min
9. 9Fractions Greater Than OnePast the 1, and still counting.13 min
10. 10Fractions of Different WholesHalf of what?13 min

Read graphs where one symbol stands for several, and plot measurements that land between whole numbers.

• 3.MD.B.3
• 3.MD.B.4
• 3.OA.D.8

1. 1Scaled Picture GraphsWhen one picture means more than one.13 min
2. 2Scaled Bar GraphsWhen the scale counts in twos, fives, or tens.13 min
3. 3Two-Step Graph ProblemsQuestions that need two readings.13 min
4. 4Measuring to Halves and FourthsA ruler has marks between the numbers.13 min
5. 5Line Plots With FractionsPlotting measurements that land between numbers.13 min

Sort quadrilaterals into families, split shapes into equal areas, and solve two-step problems with all four operations.

• 3.G.A.1
• 3.G.A.2
• 3.OA.D.8
• 3.OA.D.9

1. 1The Quadrilateral FamilyA square is a rectangle, and both are quadrilaterals.13 min
2. 2Equal Areas of a ShapeEach part is a unit fraction of the whole.12 min
3. 3Two-Step Problems With All Four OperationsWorking out which operations, and in what order.15 min
4. 4Patterns and Explaining ThemSpotting a pattern is half. Saying why is the other half.13 min

Read, compare and round large numbers, and add and subtract them using the standard algorithms.

• 4.NBT.A.1
• 4.NBT.A.2
• 4.NBT.A.3
• 4.NBT.B.4

1. 1Ten Times BiggerEach place is worth ten times the one to its right.14 min
2. 2Reading and Writing Large NumbersThousands, ten thousands, hundred thousands.14 min
3. 3Comparing Large NumbersStart at the left and find the first difference.13 min
4. 4Rounding to Any PlaceSame rule, whichever place you are asked for.14 min
5. 5Adding Multi-Digit NumbersThe standard algorithm, and why it works.14 min
6. 6Subtracting Multi-Digit NumbersUnbundling across several places.15 min

Read multiplication as a comparison, then multiply multi-digit numbers with area models and partial products.

• 4.OA.A.1
• 4.OA.A.2
• 4.NBT.B.5

1. 1Multiplication as Comparison"Times as many" is a different question from "more than".14 min
2. 2Multiplying by 10, 100, and 1,000Counting in bigger units.13 min
3. 3The Area Model and Partial ProductsOne rectangle, split by place value.15 min
4. 4Two-Digit by Two-DigitFour pieces instead of two.16 min
5. 5Estimating ProductsRound first, so a wrong answer stands out.13 min

Divide by one digit, find remainders, and work out what a remainder means in a real situation.

• 4.NBT.B.6
• 4.OA.A.3

1. 1Dividing by One DigitShare the biggest units first.15 min
2. 2RemaindersWhat is left when it will not share evenly.14 min
3. 3What the Remainder MeansOne division, three different right answers.15 min
4. 4Multistep Word ProblemsSeveral operations, in the right order.16 min

Find every factor pair, tell primes from composites, list multiples, and follow a rule to build a pattern.

• 4.OA.B.4
• 4.OA.C.5

1. 1Factor PairsEvery rectangle you can build from a number.14 min
2. 2Prime and CompositeNumbers that make only one rectangle.14 min
3. 3MultiplesCounting on from a number.13 min
4. 4Number PatternsFollow the rule, then notice what it did not say.15 min

Read a fraction as a count of named units, find equivalents, compare, add, subtract, and multiply by a whole number.

• 4.NF.A.1
• 4.NF.A.2
• 4.NF.B.3
• 4.NF.B.4
• 4.MD.B.4

1. 1A Fraction Counts UnitsThe bottom number names what you are counting.14 min
2. 2Equivalent FractionsSame amount, cut a different way.15 min
3. 3Comparing Unlike FractionsMake the pieces the same, then count.16 min
4. 4Adding Fractions with the Same UnitCount the units. The name does not change.14 min
5. 5Why 1/2 + 1/3 Is Not 2/5You cannot count two different things together.15 min
6. 6Mixed NumbersWhole ones and some pieces left over.15 min
7. 7Multiplying a Fraction by a Whole NumberRepeated copies of the same unit.16 min
8. 8Line Plots with FractionsMeasurements that land between the whole numbers.14 min

Meet tenths and hundredths as fractions written another way, then compare, add, and read money.

• 4.NF.C.5
• 4.NF.C.6
• 4.NF.C.7
• 4.MD.A.2

1. 1TenthsA fraction written a different way.14 min
2. 2HundredthsCut each tenth into ten again.14 min
3. 3Why 0.7 and 0.70 Are EqualMore digits does not mean more.15 min
4. 4Comparing DecimalsSame unit first, then compare.14 min
5. 5Adding Tenths and HundredthsChange the tenths into hundredths, then count.15 min
6. 6Decimals and MoneyA cent is one hundredth of a dollar.14 min

Measure angles as turns, add them, sort shapes by their properties, find symmetry, and convert units.

• 4.MD.C.5
• 4.MD.C.6
• 4.MD.C.7
• 4.G.A.1
• 4.G.A.2
• 4.G.A.3
• 4.MD.A.1
• 4.MD.A.3

1. 1An Angle Is a TurnLonger arms do not make a bigger angle.14 min
2. 2Naming and Measuring AnglesAcute, right, obtuse, straight.15 min
3. 3Angles Add TogetherTwo turns side by side make one bigger turn.15 min
4. 4Lines, Rays, and SegmentsThree things that all look like a straight line.14 min
5. 5Sorting Shapes by Their AnglesWhat a shape has decides what it is called.15 min
6. 6Lines of SymmetryA fold that makes both halves match.14 min
7. 7Units of MeasurementBigger units, smaller numbers.15 min
8. 8Area and Perimeter FormulasTwo different questions about the same rectangle.16 min

Ten times and one tenth, powers of ten, and reading, comparing and rounding decimals to thousandths.

• 5.NBT.A.1
• 5.NBT.A.2
• 5.NBT.A.3
• 5.NBT.A.4

1. 1Ten Times and One TenthEvery place is worth ten of the one to its right.15 min
2. 2Powers of TenA short way to write a long number.15 min
3. 3ThousandthsOne more place to the right.15 min
4. 4Comparing Decimals to ThousandthsBiggest place first, every time.15 min
5. 5Rounding DecimalsWhich mark is it closer to?15 min

Multiply multi-digit numbers, divide by two digits, read a fraction as a division, and use brackets.

• 5.NBT.B.5
• 5.NBT.B.6
• 5.NF.B.3
• 5.OA.A.1
• 5.OA.A.2

1. 1Multiplying Large NumbersThe same four pieces, with bigger numbers.16 min
2. 2Dividing by Two DigitsGuess how many fit, then check.17 min
3. 3A Fraction Is a DivisionThe leftover has a name after all.16 min
4. 4Brackets and OrderBrackets say what to do first.15 min

Add and subtract decimals by lining up the places, and estimate to catch an answer of the wrong size.

• 5.NBT.B.7
• 5.NBT.A.4

1. 1Lining Up the PlacesTenths go with tenths.15 min
2. 2Subtracting DecimalsUnbundle across the point.15 min
3. 3Estimating with DecimalsRound to the nearest whole one first.14 min

Multiply and divide decimals, and find out why multiplying can shrink a number and dividing can grow one.

• 5.NBT.A.2
• 5.NBT.B.7
• 5.NF.B.5

1. 1Multiplying by Powers of TenEvery digit shifts one place.15 min
2. 2Multiplying a Decimal by a Whole NumberCount in tenths, then say what you counted.15 min
3. 3When Multiplying Makes Things SmallerA rule that has finally run out.16 min
4. 4Dividing DecimalsHow many of these fit into that?16 min

Find a common denominator, add and subtract unlike fractions and mixed numbers, judge answers with benchmarks, and read fraction data.

• 5.NF.A.1
• 5.NF.A.2
• 5.MD.B.2

1. 1Finding a Common DenominatorCut both into the same size pieces.15 min
2. 2Adding Unlike FractionsMatch, then count.15 min
3. 3Mixed Numbers with RegroupingBorrow a whole one and cut it up.16 min
4. 4Judging an Answer with BenchmarksIs it near 0, near a half, or near 1?14 min
5. 5Line Plots and Fraction DataAdd up measurements that are not whole numbers.15 min

Multiply a fraction by a fraction, find areas with fractional sides, judge a product against its factor, and multiply mixed numbers.

• 5.NF.B.4
• 5.NF.B.5
• 5.NF.B.6

1. 1A Fraction of a FractionCut it, then cut the piece again.16 min
2. 2Multiplying as ScalingDecide the size before you multiply.16 min
3. 3Area with Fractional SidesA rectangle that is part of a unit wide.15 min
4. 4Multiplying Mixed NumbersTurn them into pieces first.16 min

Divide a whole number by a unit fraction and a unit fraction by a whole number, and say which way the answer goes.

• 5.NF.B.7

1. 1Dividing a Whole Number by a Unit FractionHow many small pieces fit?16 min
2. 2Dividing a Unit Fraction by a Whole NumberShare a small piece among several.15 min

Count cubes and find volume, plot ordered pairs, sort shapes into a hierarchy, and convert units in problems.

• 5.MD.C.3
• 5.MD.C.4
• 5.MD.C.5
• 5.MD.A.1
• 5.G.A.1
• 5.G.A.2
• 5.G.B.3
• 5.G.B.4
• 5.OA.B.3

1. 1Measuring Volume by Counting CubesHow many unit cubes fit inside?15 min
2. 2The Volume FormulaA shortcut for the count you can already do.15 min
3. 3The Coordinate PlaneAcross first, then up.15 min
4. 4Patterns as PairsTwo rules, plotted together.16 min
5. 5The Shape HierarchyA property of a group belongs to everything in it.15 min
6. 6Converting Units in ProblemsGet everything into one unit first.15 min

Read and write ratios, scale them up and down, and find out why scaling multiplies rather than adds.

• 6.RP.A.1
• 6.RP.A.3

1. 1What a Ratio SaysA comparison between two amounts.16 min
2. 2Equivalent RatiosScaling up keeps the comparison the same.17 min
3. 3Why You Multiply and Not AddThe most common mistake in all of middle school.18 min
4. 4Tape Diagrams and Ratio ProblemsDrawing the parts before you count them.18 min
5. 5Double Number LinesTwo rulers that move together.17 min
6. 6Comparing Two RatiosWhich mix is stronger?18 min

Find unit rates, compare deals, and meet percent as a rate per hundred.

• 6.RP.A.2
• 6.RP.A.3

1. 1Unit RatesHow much for exactly one.17 min
2. 2Percent as a Rate per HundredA ratio with the second number fixed at 100.17 min
3. 3Finding a Percent of a NumberTen percent first, then build.18 min
4. 4Comparing with Unit RatesWhich one is the better buy?18 min
5. 5Finding the Whole from a PercentWorking backwards to the total.18 min
6. 6Converting Units with RatesChanging the unit without changing the amount.18 min

Divide a fraction by a fraction, multiply and divide decimals, and use common factors and multiples.

• 6.NS.A.1
• 6.NS.B.2
• 6.NS.B.3
• 6.NS.B.4

1. 1Dividing a Fraction by a FractionHow many of these fit into that.18 min
2. 2Multiplying and Dividing DecimalsCount the places, and check the size.17 min
3. 3Common Factors and Common MultiplesWhat two numbers share.17 min
4. 4Dividing Multi-Digit NumbersLong division, one place at a time.18 min
5. 5Adding and Subtracting DecimalsLine up the point, not the digits.17 min
6. 6Pulling Out a Common FactorThe distributive property, read backwards.18 min

Meet numbers below zero, absolute value as distance, and points in all four quadrants.

• 6.NS.C.5
• 6.NS.C.6
• 6.NS.C.7
• 6.NS.C.8

1. 1Numbers Below ZeroZero is a starting point, not the end of the line.17 min
2. 2Absolute ValueDistance from zero, with no direction.16 min
3. 3All Four QuadrantsThe grid carries on in every direction.17 min
4. 4OppositesSame distance from zero, other side.16 min
5. 5Ordering Negative NumbersFurther left is always smaller.17 min
6. 6Distance on the Coordinate PlaneCounting the gap between two points.18 min

Use exponents and the order of operations, write expressions with letters, and simplify them.

• 6.EE.A.1
• 6.EE.A.2
• 6.EE.A.3
• 6.EE.A.4

1. 1Exponents and Order of OperationsWhich part of an expression happens first.17 min
2. 2Letters for NumbersA variable stands for a number you do not know yet.17 min
3. 3Equivalent ExpressionsTwo recipes that always give the same number.18 min
4. 4Writing Expressions from WordsTurning a sentence into algebra.17 min
5. 5Combining Like TermsTidying an expression without changing it.18 min
6. 6Expanding BracketsThe distributive property, forwards.18 min

Find out what solving means, solve one-step equations, and meet inequalities and linked variables.

• 6.EE.B.5
• 6.EE.B.6
• 6.EE.B.7
• 6.EE.B.8
• 6.EE.C.9

1. 1What Solving MeansFinding the values that make it true.16 min
2. 2Solving One-Step EquationsDo the same to both sides.17 min
3. 3Inequalities and Two VariablesWhen many numbers work, not just one.18 min
4. 4Writing Equations from StoriesFrom a situation to a solvable sentence.18 min
5. 5Inequalities on a Number LineWhen the answer is a stretch, not a point.17 min
6. 6Two Variables That Move TogetherOne depends on the other.19 min

Find the area of triangles by relating them to rectangles, and surface area from nets.

• 6.G.A.1
• 6.G.A.3
• 6.G.A.4

1. 1Area of TrianglesHalf of the rectangle around it.17 min
2. 2Surface Area from NetsUnfold the solid and add up the faces.18 min
3. 3Area of a ParallelogramCut a piece off one end and slide it to the other.18 min
4. 4Area of a TrapezoidTwo copies make a parallelogram.18 min
5. 5Breaking a Shape ApartAn awkward outline is a few easy ones.19 min

Find the volume of a prism whose edges are fractions, using the same formula as always.

• 6.G.A.2

1. 1Volume When the Edges Are FractionsThe formula does not change.18 min
2. 2Packing with Fraction CubesCounting the little cubes that fit.18 min
3. 3Finding a Missing EdgeWorking backwards from the volume.17 min

Tell a statistical question from an ordinary one, then summarise a set with centre and spread.

• 6.SP.A.1
• 6.SP.A.2
• 6.SP.A.3
• 6.SP.B.4
• 6.SP.B.5

1. 1What Makes a Question StatisticalA question that expects different answers.16 min
2. 2Centre and SpreadOne number for the middle, one for the scatter.18 min
3. 3Dot Plots and HistogramsTwo ways to show the same data.18 min
4. 4Mean, Median, and Which to TrustOne outlier can drag an average anywhere.19 min

Make and read scale copies, use a map scale, and find out why area scales by the square of the factor.

• 7.G.A.1

1. 1Scale CopiesThe same shape, a different size.17 min
2. 2Scale Drawings and AreaDoubling the sides does not double the area.18 min
3. 3Reading a ScaleOne centimetre on the map, half a kilometre on the ground.18 min
4. 4Redrawing at a New ScaleThe same object, a different size of picture.18 min

Meet the constant of proportionality in tables, graphs and equations, and tell proportional from merely linear.

• 7.RP.A.1
• 7.RP.A.2

1. 1The Constant of ProportionalityThe number you have been multiplying by all along.18 min
2. 2Telling Proportional from NotStraight through the origin, or it is not proportional.18 min
3. 3The Graph of a Proportional RelationshipA straight line through the origin.18 min
4. 4Unit Rates with FractionsRates when neither quantity is whole.19 min

Work out percent increase and decrease, tax, tips and discounts, using the multiplier method.

• 7.RP.A.3

1. 1Percent Increase and DecreaseChange measured against where you started.18 min
2. 2Tax, Tips, and MarkupAdding a percent on top.18 min
3. 3Discounts and Sale PricesTaking a percent off.18 min
4. 4Simple InterestWhat money earns for sitting still.18 min
5. 5Finding the Original PriceUndoing a percent change.19 min

Add and subtract signed numbers as movement and distance on a number line, with no sign rules to memorise.

• 7.NS.A.1

1. 1Adding Signed NumbersA walk along the line.17 min
2. 2Subtraction as DistanceHow far, and in which direction.18 min
3. 3The Additive InverseSubtracting is adding the opposite.18 min
4. 4Signed Fractions and DecimalsThe same rules, with messier numbers.19 min

Multiply and divide signed numbers, and find out why a negative times a negative has to be positive.

• 7.NS.A.2
• 7.NS.A.3
• 7.EE.B.3

1. 1Why a Negative Times a Negative Is PositiveA pattern that has to keep going.19 min
2. 2Rational Numbers in ProblemsAll four operations, with signs.18 min
3. 3Why Two Negatives Make a PositiveNot a rule to memorise — a pattern that has to continue.19 min
4. 4Terminating and Repeating DecimalsEvery fraction becomes one or the other.18 min

Solve two-step equations by undoing the operations in reverse order.

• 7.EE.A.1
• 7.EE.A.2
• 7.EE.B.4

1. 1Two-Step EquationsUndo the operations in reverse order.18 min
2. 2Solving px + q = rUndoing two operations in the right order.19 min
3. 3Solving p(x + q) = rTwo routes to the same answer.19 min
4. 4Solving InequalitiesOne step where the rules change.19 min

Measure a circle to discover pi for yourself, then find circumference and area and tell them apart.

• 7.G.B.4

1. 1Measuring a CircleWhere π actually comes from.18 min
2. 2Area of a CircleA different question, with different units.18 min
3. 3Area of a CircleWhy the radius is squared.19 min
4. 4Telling Area from CircumferenceWhich question is being asked.18 min

Use angle pairs to find unknown angles, and find the volume and surface area of prisms.

• 7.G.A.2
• 7.G.A.3
• 7.G.B.5
• 7.G.B.6

1. 1Angle PairsAngles that always add to the same total.17 min
2. 2Volume and Surface Area of PrismsBase area times height, whatever the base.18 min
3. 3Angle PairsAngles that add to 90 or to 180.18 min
4. 4When Three Measurements Fix a TriangleOne triangle, many, or none at all.19 min

Express probability as a number from 0 to 1, and use a fair sample to say something about a population.

• 7.SP.A.1
• 7.SP.A.2
• 7.SP.C.5
• 7.SP.C.7

1. 1Probability as a NumberFrom impossible to certain, on a scale of 0 to 1.17 min
2. 2Samples and What They Tell YouAsking some to learn about all.18 min
3. 3Probability as a NumberNought means never, one means always.18 min
4. 4What Actually HappenedExperimental probability against theoretical.19 min

Slide, flip and turn a figure without changing it, and define congruence by the moves that carry one onto another.

• 8.G.A.1
• 8.G.A.2

1. 1Moving a Shape Without Changing ItSlides, flips, and turns.18 min
2. 2CongruenceSame shape, same size, wherever it sits.18 min
3. 3What a Transformation Does to CoordinatesThe rule behind the movement.19 min
4. 4Sequences of MovesSeveral transformations, one journey.19 min

Meet the move that does change size, and use similarity to find missing lengths.

• 8.G.A.3
• 8.G.A.4
• 8.G.A.5

1. 1DilationsThe move that does change size.18 min
2. 2Similar FiguresSame shape, different size.19 min
3. 3Dilations on the Coordinate PlaneMultiply both coordinates by the scale factor.19 min
4. 4Angle-Angle SimilarityTwo angles are enough.19 min

Find out why slope is the same everywhere on a line, then read any line from y = mx + b.

• 8.EE.B.5
• 8.EE.B.6
• 8.F.A.3

1. 1Why Slope Is the Same EverywhereThe similar triangles you just built.19 min
2. 2y = mx + bThe slope and where it starts.19 min
3. 3Slope from Two PointsRise over run, from any pair.19 min
4. 4Unit Rate as SlopeThe rate is the steepness.18 min
5. 5Comparing Lines in Different FormsA table, a graph, and an equation, side by side.19 min

Solve equations with variables on both sides, and meet the ones with no solution or infinitely many.

• 8.EE.C.7

1. 1Variables on Both SidesGather them up first.19 min
2. 2None, One, or Infinitely ManyNot every equation has exactly one answer.18 min
3. 3Equations with Brackets and FractionsClear the clutter first.19 min
4. 4Writing Equations from SituationsTurning a story into something solvable.19 min

Find the point that satisfies two equations at once, graphically and by substitution.

• 8.EE.C.8

1. 1Where Two Lines MeetA solution that satisfies both at once.19 min
2. 2Solving a System by SubstitutionReplace one letter and one equation is left.20 min
3. 3Solving a System by EliminationAdd the equations and one letter disappears.20 min

Meet a function as a rule with exactly one output per input, before any notation for one.

• 8.F.A.1
• 8.F.A.2
• 8.F.B.4
• 8.F.B.5

1. 1What a Function IsOne output for every input.18 min
2. 2Linear and Nonlinear FunctionsStraight, or something else.19 min
3. 3Rate of Change and Starting ValueBuilding a function from a situation.19 min
4. 4Reading a Graph as a StoryRising, falling, flat.18 min

Derive the laws of exponents by counting factors, and write very large and very small numbers compactly.

• 8.EE.A.1
• 8.EE.A.3
• 8.EE.A.4

1. 1Laws of ExponentsCount the factors and the rules explain themselves.19 min
2. 2Scientific NotationVery big and very small, written compactly.18 min
3. 3Zero and Negative ExponentsContinuing the pattern downwards.19 min
4. 4Calculating in Scientific NotationMultiplying and dividing very large and very small numbers.20 min

Evaluate square and cube roots, and meet numbers whose decimals never end or repeat.

• 8.NS.A.1
• 8.NS.A.2
• 8.EE.A.2

1. 1Square Roots and Irrational NumbersNumbers that never settle down.19 min
2. 2Cube RootsThe side length of a cube.18 min
3. 3Placing an Irrational NumberTrapping √2 between two numbers you know.19 min

Use the Pythagorean theorem to find a missing side of a right triangle and a distance on a grid.

• 8.G.B.6
• 8.G.B.7
• 8.G.B.8
• 8.G.C.9

1. 1The Pythagorean TheoremThe two smaller squares add to the biggest.19 min
2. 2Distance Between Two PointsPythagoras on a coordinate grid.19 min
3. 3Volume of Cones, Cylinders, and SpheresThree solids, three formulas, one radius.20 min

Read a scatter plot, describe the association, and fit a line to predict from.

• 8.SP.A.1
• 8.SP.A.2
• 8.SP.A.3
• 8.SP.A.4

1. 1Scatter Plots and AssociationTwo measurements from the same thing.19 min
2. 2The Line of Best FitA straight line through a cloud of points.19 min
3. 3Two-Way TablesTwo categories at once.19 min