Kindergarten math lessons

Unit 1: Counting to 20

Usually taught in August and September

Touch and count7 apples in a row. Touch each one once and say one number: 1, 2, 3, up to 7. Then write 7.
The last number tells how manyFixes a mistakeAsked "how many?", say the last number counted, 6. There is no need to count again.
Moved, but still the sameFixes a mistake8 stars in a row slide into a circle. None added, none taken away: still 8.
Counting a messy group9 scattered balls. Tick each one as it is counted, so none is counted twice or missed.
Counting rows to 2015 apples in 3 rows of 5. Count each row left to right, then the next row down: 15.
Count out just enough"Show 6": move counters into a ten frame one at a time, and stop at 6.
Don't skip a numberFixes a mistakeCounting out 17 as "14, 15, 17" gives only 16 counters. Every number gets its own counter.
First, second, thirdAn apple, a ball, a car, a star, and a cup in a line. From the left, the car is third and the cup is fifth.
New order, same countFixes a mistakeThe cup was fifth. Lined up another way, the cup is second, and there are still 5 things.
One more each timeCounters join a row one at a time. Each new number we say means one more counter than the number before.
How many at a glanceDots appear in a dice pattern and in a ten frame. A full row is 5, so 5 and 2 more is 7: say how many without counting each dot.

Unit 2: More, less, and counting on

Usually taught in September and October

Match them to compare6 cups and 4 straws, matched one to one. 2 cups have no straw, so 6 is greater than 4.
Equal to5 dogs and 5 bones. Every dog gets one bone and none are left: 5 is equal to 5.
Bigger things are not moreFixes a mistake4 big balls and 7 small marbles. The balls take more space, but 7 is greater than 4.
Counting by tens to 100Rows of 10 dots, counted by tens: 10, 20, 30, 40, 50, 60. Each row is ten more, and ten rows make 100.
Count on from any numberStart at 47, not at 1: 48, 49, 50, 51.
After 29 comes 30Fixes a mistake27, 28, 29, then 30, not 20 and not "twenty-ten". A new ten starts.
Counting back12 counters given away one at a time: 11, 10, 9. Each number is one less.
Which number is bigger?Two written numbers to 10, each shown as dots in a ten frame. The number with more dots is greater.

Unit 3: Sorting and counting

Usually taught in October and November

Sort, then count10 shapes sorted into circles, triangles, and rectangles. Count each group: 4, 3, and 3.
Which group has the most?Toys sorted into groups: 5 balls, 2 cars, 3 stars. Balls have the most, and cars have the fewest.
One rule at a timeFixes a mistakeBig and little circles and triangles. Sort by shape or by size, not both at once, and each one fits in just one group.
Find the part that repeatsA row of shapes: circle, square, circle, square. Ring the part that repeats, the core, then draw two more cores to keep the pattern going.
Earning money and getting giftsPay for raking leaves is earned, so it is income; a birthday dollar is a gift. Sort each one, and name a job that earns money.
Wants and needsFood, a coat, and a home are needs; a toy and a treat are wants. Sort each picture, and tell how earning money pays for them.
Sort it, then graph itA pile of 3 red blocks, 5 blue blocks, and a sock. The sock does not belong. Line each color up in its own row: blue has more, so a block picked from the pile is likely blue.

Unit 4: Putting together and taking apart

Usually taught in November and December

Put together3 apples and 2 more apples join: 3 and 2 make 5. Then write 3 + 2 = 5.
Take away7 apples, and 2 are eaten. Cross out 2, and 5 are left: 7 − 2 = 5.
One problem, many pictures4 and 2 as dots, as cubes, and as jumps on a number line. Each way makes 6.
Ways to make 55 counters, some filled and some empty: 4 and 1, 3 and 2, 2 and 3, 1 and 4, then 5 and 0.
Hidden counters7 counters, and some hide under a cup. 4 show, so 3 hide: 4 + 3 = 7.
The two parts can matchFixes a mistake8 can be 4 and 4. Two parts the same size are a way to make 8 too.
Act out an adding storyDani colored 3 pages and Ciara colored 2. Draw them, then count them all: 5.
Act out a take-away storyAshley has 10 crayons and gives 4 to Larry. Cross out 4, and 6 are left.

Unit 5: Adding and subtracting within 10

Usually taught in December and January

Count on to add5 + 3: say 5, then count 6, 7, 8. No need to count the 5 again from 1.
Start with the bigger numberFixes a mistakeFor 2 + 7, start at 7 and count 8, 9. Starting at 2 takes 7 jumps instead of 2.
Turn it around7 + 2 and 2 + 7 in cubes. Same cubes, same total: 9.
Three numbers, four facts3, 5, and 8: 5 and 3 make 8, 3 and 5 make 8, 8 take away 5 is 3, and 8 take away 3 is 5.
Count back to take away9 − 3 on a number line: 8, 7, 6. Three jumps back land on 6.
Make 106 counters in a ten frame leave 4 squares empty: 6 and 4 make 10.
Partners of 10 turn aroundFixes a mistake3 + 7 = 10, so 7 + 3 = 10 too. One pair of partners gives two facts.
How many more does he need?Eddie has 5 tokens and needs 8. Count on 6, 7, 8: he needs 3 more.
"More" does not always mean addFixes a mistakeSteve has 7 crayons, 3 more than Joane. So Joane has fewer: 7 take away 3 is 4.
Facts to 5, fastFive fingers show every way to add and take away within 5, until 3 + 2 and 5 − 1 come without counting.

Unit 6: Teen numbers and the number line

Usually taught in January and February

Ten and some more14 counters fill a ten frame with 4 left over. 14 is 10 and 4: 10 + 4 = 14.
The 1 in 16 means tenFixes a mistakeSixteen says the 6 first, but 16 is 1 ten and 6 ones. Eleven and twelve hide their ten too.
Find it on the number lineA line from 0 to 20: count the marks to 12. One more is 13, and one less is 11.
Count the marks, not the spacesFixes a mistakeNumbers sit on the marks. Number the spaces instead, and every number lands one mark too far.
Farther right is greater17 and 19 on the same line. 19 is farther right, so 19 is greater than 17.
Not every line starts at 0Fixes a mistakeA line from 8 to 15 with one number missing. Count on from 8 to find it: 11.

Unit 7: Is it true?

Usually taught in February and March

Show it is true7 = 9 − 2 with cupcakes: cross out 2 of the 9, and 7 are left. Both sides are 7.
True or false?3 + 7 = 13: draw 3 and 7, and they make 10, not 13. False. Then 7 + 6 = 13 is true.
The total can come firstFixes a mistake8 = 5 + 3 is true. The equal sign means "the same as", so the 8 can come first.

Unit 8: Shapes

Usually taught in April

Four flat shapesCircle, triangle, rectangle, and square: count the sides and corners. A circle has neither.
Turned, it is still a triangleFixes a mistakeUpside down, tall, or thin, 3 straight sides closed up make a triangle. A gap or a curve does not.
A square is a rectangle tooFixes a mistakeA rectangle has 4 sides and 4 square corners. A square has those too, and all its sides match.
Solid shapesSphere, cube, cone, and cylinder, each with a thing from home: a ball, a block, a party hat, a can.
Sort by shape, not by sizeFixes a mistakeA big circle and a small circle go together. Big or small, turned or not, the shape stays the same.
Same and differentA triangle and a rectangle both have straight sides, but 3 sides or 4. Then which is above, below, or beside.
Roll or stackSort the solids: a sphere rolls, a cube stacks, and a cylinder does both.
A cube is not a squareFixes a mistakeA square is one flat face. A cube is solid, with a square on every side. A can is a cylinder, not a circle.
Shapes all around usA window is a rectangle, a clock is a circle, a ball is a sphere, and a can is a cylinder.
Shapes make shapesTwo triangles make a rectangle. Two squares make a rectangle. A square and a triangle make a house.
Line up the sidesFixes a mistakeTwo triangles that overlap or leave a gap do not make the rectangle. Their long sides must touch all along.
Build a shapeSticks and clay balls build a triangle and a square: count the sticks for sides and the balls for corners, then draw it.

Unit 9: Measuring

Usually taught in May

What can we measure?A bucket is tall, it is heavy, and it holds sand: how long, how heavy, and how much it holds.
Line up the endsTwo pencils with their ends lined up: the blue one is longer, and the red one is shorter.
Higher is not tallerFixes a mistakeA pencil drawn higher up looks taller. Line up the bottoms, and it is the shorter one.
Bigger is not always heavierFixes a mistakeA big balloon and a small rock on a balance. The rock's side goes down, so the rock is heavier.
Taller does not always hold moreFixes a mistakeA tall thin glass and a short wide bowl. Pour the full glass into the bowl, and the bowl is not even full: the bowl holds more.
Measure with paper clipsA pencil is 6 paper clips long, clips end to end with no gaps and no overlaps.
No gaps, no overlapsFixes a mistakeClips with gaps count 4, but the pencil is 6 clips long. Clips that overlap count too many.
Bigger units, fewer of themThe same book is 10 paper clips long or 5 erasers long. The bigger the unit, the fewer it takes.
Days of the weekThe seven days written in order around a loop, so Sunday comes again after Saturday. Yesterday is the day before today, and tomorrow the day after.
Morning, afternoon, and eveningA day in three pictures: breakfast in the morning, recess in the afternoon, bedtime in the evening. Brushing teeth comes before bed. A movie takes longer than tying a shoe.
Days, months, years, and seasonsA year is 12 months and 4 seasons: spring, summer, fall, and winter, then spring again. A day is shorter than a month, and a month is shorter than a year.
Warmer or coolerA cup of cocoa and a glass of ice water: the cocoa is warmer, the water is cooler. A bucket and a cup: the bucket holds more.