Unit 1: Addition and subtraction facts
Usually taught in August and September
- A fact you know beats countingFixes a mistakeCounting 9 + 5 dot by dot is slow. 10 + 5 is 15, so 9 + 5 is 14.
- The total is already thereFixes a mistakeIn the bird story, 12 is the total. The answer is 7, not 12 + 5.
Unit 2: Even, odd, and equal groups
Usually taught in September
- Even or odd?Pair up 9 counters: 4 pairs and 1 left over, so 9 = 4 + 4 + 1 is odd. 8 = 4 + 4 is even.
- Even numbers end the same wayCount by 2s to 20. Even numbers end in 0, 2, 4, 6, or 8. 15 ends in 5, so it is odd.
- Doubles are always evenFixes a mistake7 + 7 = 14 is even, though 7 is odd. Every double pairs up.
- Equal groups, added again4 tables with 5 chairs each: 5 + 5 + 5 + 5 = 20.
- Rows and columnsThe 20 chairs as 4 rows of 5. Turned, they are 5 rows of 4, still 20.
- Add the rows, not the sidesFixes a mistake3 rows of 4 is 4 + 4 + 4 = 12, not 3 + 4 = 7.
- Count the inside dots tooFixes a mistakeA 3 by 4 array has 12 dots. Counting only the outside ring gives 10.
- Same pattern, new lookCircle, circle, square repeats, so its core is A A B. The same core shows as numbers, 1 1 2, and as claps. Then extend each by two more cores.
Unit 3: Adding and subtracting within 100
Usually taught in September to December
- Rounding to the nearest ten27 sits between 20 and 30. It is 3 from 30 and 7 from 20, so it rounds to 30.
- Which two tens?Fixes a mistake72 has 7 tens, so it sits between 70 and 80. It rounds to 70.
- Look at the onesFixes a mistake46 rounds to 50. The 6 ones decide, not the 4 tens.
- Halfway rounds upFixes a mistake65 is right between 60 and 70. Halfway rounds up, to 70.
- Adding by jumps41 + 23 on a number line: two jumps of ten to 61, then three ones to 64.
- Adding tens and ones38 + 45 makes 7 tens and 13 ones. 10 ones make a new ten, so 83.
- Ten ones make a tenFixes a mistake54 + 39 is 93, not 813. The 13 ones are 1 ten and 3 ones.
- Subtracting tens and ones87 − 25: 80 − 20 = 60 and 7 − 5 = 2, so 62.
- Trade a ten for ten ones73 − 48: trade 1 ten to get 6 tens and 13 ones. Take away 4 tens and 8 ones: 25.
- Not always small from bigFixes a mistake52 − 27 is 25, not 35. Taking 2 from 7 turns the problem around. Trade a ten instead.
- Count up to subtract62 − 39: from 39, jump 1 to 40, 20 to 60, and 2 to 62. That is 23.
- Two-step word problemsA bus has 27 kids. 12 get off, then 8 more get off at the next stop: 27 − 12 = 15, and 15 − 8 = 7.
- A story for an equation76 = 11 + 65 as a story: 65 kids at recess, 11 more come out, 76 in all.
- Add four numbersFour two-digit numbers in a column. Add the tens, then the ones, pairing ones that make 10.
- Why trading works10 ones bundle into 1 ten, so the total never changes. Check one sum by adding tens first, then ones first.
- Estimate, then addRound 38 and 47 to the nearest ten: 40 + 50 is about 90. Work out 85, and check it is close to the estimate.
Unit 4: True and false equations
Usually taught in December
- One less here, one more there27 + 13 = 26 + 14 is true. 26 is one less than 27, and 14 is one more than 13.
- Subtraction on both sides87 − 35 = 80 − 29 is false. One side is 52 and the other is 51.
- Find the missing number45 + □ = 23 + 46. The right side is 69, so the box is 24.
- Missing numbers in subtraction12 − □ = 5 asks 5 + □ = 12. The box is 7.
- Balance the changeFixes a mistake16 + 37 = □ + 38. 38 is one more than 37, so the box is one less than 16: 15, not 17.
Unit 5: Equal parts and time
Usually taught in January
- Halves, thirds, and fourthsA circle and a rectangle cut into 2, 3, and 4 equal parts. The whole is two halves, three thirds, or four fourths.
- Same size, different shapesA square cake cut into 4 rectangles, then into 4 triangles. Both ways make fourths.
- Equal without matchingFixes a mistakeTwo halves of a 3 by 4 grid can look different. Each has 6 squares, so both are halves.
- Time to five minutesThe minute hand on 7 means 35 minutes: count 5, 10, 15, up to 35. The time is 4:35.
- Half past and quarter afterThe clock face in halves and fourths: half past 3, quarter after 3, and quarter til 4.
- a.m. or p.m.Breakfast at 7:15 a.m. and dinner at 6:30 p.m. Noon and midnight split the day.
- Short hand, long handFixes a mistakeAt 4:10 the short hand is just past 4 and the long hand is on 2. Swapped, it reads 2:20.
- Almost the next hourFixes a mistakeAt 2:55 the hour hand is nearly on 3. The hour is still 2, so it is 2:55, not 3:55.
- Minutes, hours, days, and weeks60 minutes make an hour, 24 hours a day, 7 days a week, and 12 months a year. Then pick the unit that fits: brushing teeth takes minutes, a trip takes days.
- Halves, fourths, and eighthsA round pizza cut into 2, 4, then 8 equal slices: halves, fourths, eighths. More equal parts makes each part smaller. Eight slices of different sizes are not eighths.
- Quarter past, half past, quarter toA clock face in four quarters. At 3:15 the minute hand has gone a quarter of the way around: quarter past 3. At 3:30, half past 3. At 3:45 a quarter is left before 4: quarter to 4.
- How long did it take?Soccer practice starts at 2:00 and ends at 4:30. Jump along a timeline: 2 hours to 4:00, then a half hour to 4:30. Practice took 2 and a half hours.
Unit 6: Money
Usually taught in January and February
- Counting coinsA quarter, 2 dimes, and a nickel: 25, 35, 45, 50. That is 50¢.
- Money word problemsWhitney has 93¢. She gives away 30¢, then 25¢. 93 − 30 − 25 = 38¢ left.
- Making changeA book costs $13 and Ana pays with $20. Count up from 13 to 20: $7 change.
- Saving adds upSave $3 every week: 3, 6, 9, 12. After 4 weeks there is $12. Saving is choosing not to spend now, to have more later.
- Deposits and withdrawalsAn account holds $20. A deposit of $8 makes $28; a withdrawal of $5 leaves $23. Tell which puts money in and which takes it out.
- Borrowing, lending, and makingBorrowing $4 means paying $4 back; a lender decides if it is worth it. A producer makes lemonade: $2 of lemons and $1 of sugar cost $3 to make.
- Writing money with ¢ and $A quarter, a dime, and 2 pennies make 37¢. With a dollar sign it is $0.37: the dot sits between dollars and cents. A dollar coin and a nickel make $1.05.
Unit 7: Place value to 1,000
Usually taught in February and March
- Numbers to 1,000 three ways365 as 3 flats, 6 rods, and 5 units: 300 + 60 + 5, three hundred sixty-five.
- What is a digit worth?Fixes a mistakeThe 4 in 142 is 4 tens, worth 40. It is not 4, and not 40 tens.
- Zero holds the tens placeFixes a mistakeSeven hundred nine is 709, not 79. It has 0 tens.
- Many names for one number241 is 2 hundreds, 4 tens, and 1 one. It is also 24 tens and 1 one, or 241 ones.
- New names, same numberFixes a mistake879 as 87 tens and 9 ones is still 879. Regrouping does not change the value.
- Comparing three-digit numbers567 and 576 both have 5 hundreds. 6 tens is less than 7 tens, so 567 < 576.
- Plot and order on a number line205, 234, and 247 on a line from 200 to 250. From least to greatest: 205, 234, 247.
- Same digits, different placesFixes a mistake852 > 582. 8 hundreds is more than 5 hundreds.
- Read the line's labelsFixes a mistakeA line from 200 to 220 can be as long as one from 0 to 1,000. The labels tell the size.
- Ten more, a hundred more10 more than 428 is 438 and 10 less is 418. 100 more is 528 and 100 less is 328.
- Ten more past a hundredFixes a mistake10 more than 192 is 202. 9 tens and 1 more ten make a new hundred.
- Adding to 1,000581 + 72: 8 tens and 7 tens make 15 tens. Trade 10 tens for a hundred: 653.
- Subtracting to 1,000612 − 17 as 612 − 12 − 5. That is 600 − 5, or 595.
- Subtraction does not turn aroundFixes a mistake325 + 37 is the same as 37 + 325. But 325 − 37 starts from 325, never from 37. Only adding turns around.
- Trade only when you need toFixes a mistake325 + 37: 12 ones need a trade, but 6 tens do not. The sum is 362.
- Skip-count past a hundredCount by 5s, 10s, and 100s from any number, and say the next hundred: 380, 390, 400, 410.
- Counting by 25sQuarters in a row: 25, 50, 75, 100. After 100 the pattern starts again: 125, 150, 175, 200. Then count back by 10s from 362: 352, 342, 332.
- Which estimate makes sense?How many kids go to our school: 5, 50, or 500? One class has about 20 kids, and a school has many classes, so 500 makes sense. 5 is too few for even one class.
Unit 8: Measuring length
Usually taught in April
- Count the inches, not the marksFixes a mistakeA ruler has small marks between its numbers. A crayon from 0 to 3 is 3 inches, not one inch for every mark.
- Pick the tool and the unitA pencil in inches, a door in feet, a hallway in yards. Guess first: a paper clip is about an inch.
- Centimeters and metersA crayon in centimeters, the board in meters. A meter stick is about as long as one big step.
- Bigger unit, fewer unitsMeasure one book twice: about 30 centimeters, then about 12 inches. An inch is bigger, so fewer fit.
- How much longer?Scissors are 22 centimeters and a glue stick is 14. The scissors are 8 centimeters longer.
- No gapsFixes a mistakeWith gaps, 5 tiles cover a pencil. Packed tight, it takes 7.
- Length word problemsJeff's rope is 48 inches. Larry's is 9 inches shorter, 39. Together they have 87 inches.
- How much did it grow?Fixes a mistakeA plant grows from 24 to 37 inches. It grew 37 − 24 = 13 inches, not 24 + 37.
- Guess, then measureGuess a length from things we know, such as a paper clip is about an inch, then measure and see how close.
- Cups, pints, quarts, and gallons2 cups fill a pint, 2 pints a quart, and 4 quarts a gallon; 16 ounces make a pound. Then pick the unit that fits a glass, a bucket, or a book.
Unit 9: Shapes and perimeter
Usually taught in April and May
- Naming flat shapesTriangle, square, rectangle, pentagon, hexagon, and octagon, drawn with a ruler. Count the sides and vertices.
- Turned, still a squareFixes a mistakeA square standing on a corner is still a square. Turning does not change its sides.
- Count sides, not looksFixes a mistakeA long, thin triangle still has 3 sides. A lopsided hexagon still has 6.
- Sorting shapesSort by sides, by vertices, by open or closed, and by curved or straight edges.
- A square is a rectangle tooFixes a mistakeA square has 4 sides and 4 square corners. It belongs with the rectangles too.
- Not every half is a mirrorFixes a mistakeCut corner to corner, a long rectangle makes two equal halves. Folded, they do not match.
- More sides, not more linesFixes a mistakeA long rectangle has 4 sides but only 2 lines of symmetry. Some shapes have none.
- Perimeter: walk the edgeLay unit segments along a 5 by 3 rectangle with no gaps. The perimeter is 16 units.
- Count each unit onceFixes a mistakeTick each unit as you count around. Then no unit is counted twice.
- Perimeter by adding sidesA garden triangle has sides of 5, 7, and 8 feet. 5 + 7 + 8 = 20 feet of fence, in any order.
- Opposite sides matchA 9 by 4 foot garden shows 2 numbers but has 4 sides: 9 + 4 + 9 + 4 = 26 feet.
- Perimeter of a pentagonMeasure each side of a pentagon with a ruler: 4, 6, 5, 3, and 7 centimeters. Add all 5: 25 centimeters.
- Rows and columns of squaresSplit a rectangle into same-size squares in rows and columns, then count them row by row.
- Faces, edges, and cornersA cube and a box: each face is a flat shape, a square or a rectangle. Count the faces, the edges, and the corners, called vertices.
Unit 10: Data
Usually taught in May
- Tally marks and tablesA class votes on colors. Tally in bundles of 5, then write a table.
- Making a bar graphPets: 5 cats, 6 dogs, 4 hamsters, 2 fish. Add a title, labels, and a scale of ones.
- Name each countFixes a mistake8, 5, 7 alone says nothing. 8 red, 5 blue, 7 green does.
- Reading a pictographEach book picture stands for 5 books. 4 pictures are 20 books.
- One picture can stand for moreFixes a mistakeWhen one picture means 5, 3 pictures are 15, not 3.
- Questions from a bar graphMia read 35 minutes on Tuesday and 20 on Monday. That is 15 minutes more.
- Read the bar's heightFixes a mistakeOn a scale of fives, a bar ends on the line between 30 and 40. That line is 35. Read straight across.
- Measure, then plotMeasure six pencils to the nearest inch, then draw a line plot with one X above each length.
- What counts as data?A question: which bird visits the feeder most? Data can be photos of each bird, the songs heard, or a count in tally marks. Monday and Tuesday give different counts: data can vary.