Unit 1: Adding and subtracting within 20
Usually taught in August to October
- Ways to make 10Ten counters in two colors: 9 + 1, 8 + 2, 7 + 3, every pair that makes 10.
- Facts that go together4, 3, and 7 make four facts: 4 + 3, 3 + 4, 7 − 3, and 7 − 4.
- Read the story firstFixes a mistakeA story with 5 and 3 can take away. What happens decides: 5 − 3, not 8.
- Make a ten to add8 + 5: move 2 into the ten frame, then 10 + 3 = 13.
- Doubles and near doubles6 + 6 = 12, so 6 + 7 is one more: 13.
- Subtract back to ten15 − 7: take 5 to reach 10, then 2 more, 8. Quicker than counting back by ones.
- Don’t flip the onesFixes a mistake12 − 5 takes 5 from 12. Taking 2 from 5 gives 3, the wrong answer. Open the ten: 7.
- Subtraction is a missing part12 − 7 = ? becomes 7 + ? = 12. 7 and 5 make 12.
- Which addition helps?Fixes a mistakeFor 11 − 4, 4 + ? = 11 helps. 11 + ? = 4 does not.
- Act out the storyGavin has 8 cars and his brother takes 3. Draw what happens, then write 8 − 3 = 5.
- How many were added?Trevor had 16 cars and now has 20: 16 + ? = 20.
- How many at the start?Some birds sat on a fence. 5 more came, and now there are 12: ? + 5 = 12.
- How many more?9 shells and 14 shells in two rows. The extra shells are the difference: 5.
- “More” can mean subtractFixes a mistakeSam has 4 more than Ana, and Sam has 12. Ana has 12 − 4, not 12 + 4.
- Count on to add, back to subtractStart at 8 on a number path and count on 3 to add 3. Start at 11 and count back 3 to take away 3.
- Five and some moreA ten frame shows 8 as a full row of 5 and 3 more, and 13 as a full frame and 3 more. See the parts and say the total without counting each dot.
Unit 2: Equations and three numbers
Usually taught in October and November
- What the equal sign meansA balance: 8 = 3 + 5 stays level, and 8 = 2 + 4 tips.
- The total can come firstFixes a mistake9 = 8 + 1 is true. The equal sign means “the same as”, not “the answer comes next”.
- True or false?4 + 3 = 6 + 1 is true: both sides make 7. 9 − 1 = 7 is false.
- The missing number anywhere9 + □ = 12, 17 = □ + 5, and □ − 4 = 8, each turned into a fact you know.
- A missing start□ − 7 = 9: a bar for the whole, split into 9 and 7. The whole is 16.
- Both sides must matchFixes a mistake5 + 6 = □ + 4 is not 11. The right side must make 11 too: 7.
- Check by putting it backFixes a mistake18 − □ = 14: is it 8 or 4? Put each back in. Only 18 − 4 makes 14.
- Any order, same total3 + 9 + 4 and 9 + 4 + 3 in cubes. Same numbers, same total: 16.
- Find the ten first8 + 7 + 2: add 8 + 2 to make 10, then 7 more is 17.
- Three numbers in a storyA story adds three groups. Find two that make 10, add them first, then add the third.
Unit 3: Tally marks and pictographs
Usually taught in November and December
- Tally marks in fivesShirt colors as tallies: the fifth mark crosses the four, and bundles count by 5s.
- The fifth mark crossesFixes a mistakeFive standing marks are hard to count. The fifth lies across, and the sixth starts a new bundle.
- Making a pictographFavorite milk: one picture for each kid, lined up in a row for each flavor.
- Reading a pictographFavorite sports: how many chose soccer, and how many in all, 4 + 3 + 5 = 12.
- How many more, how many fewerBaseball has 6 and soccer has 3: 6 − 3 = 3 more. Fewer asks the same subtraction.
- Count every rowFixes a mistake“How many in all” adds every row, not only the longest one.
- Ask a question, count the answersA question for the class, like which fruit each kid likes best. Tally each answer in fives, count each choice, and say which got the most.
- Sort two ways with a Venn diagramTwo circles that overlap: red things in one, thick things in the other. A red, thick block goes in the middle, where both are true; a thin blue one goes outside both. A yes-no chart asks one question: is it red?
- Graphs help us predictA picture graph of the fruit a class picked: 8 apples, 3 bananas, 5 grapes. Most kids picked apples, so a new kid will most likely pick apples too.
Unit 4: Counting and place value to 120
Usually taught in December to February
- Counting on and back to 120On a 120 chart, count on from 96 to 104 and back from 54 to 47.
- The end of a rowFixes a mistakeAfter 39 comes 40, the next ten, not 30. Move to the start of the next row.
- Skip counting by 2s and 5sShade by 2s to 20 and by 5s to 100. The 5s always end in 5 or 0.
- Tens and ones76 as 7 rods and 6 cubes: 70 + 6, seventy-six.
- Fifteen is not 51Fixes a mistakeFifteen says the ones first, but writes the ten first: 1 ten, 5 ones, 15.
- Expanded form counts tensFixes a mistake83 is 80 + 3, not 8 + 3. The 8 stands for 8 tens.
- Many ways to make a number37 as 3 tens and 7 ones, 2 tens and 17 ones, or 37 ones. Open a rod each time.
- Extra ones make a tenFixes a mistake6 tens and 13 ones is 73, not 63. Ten of the ones make another ten.
- One more, ten more47 on a hundred chart: one more is 48, one less 46, ten more 57, ten less 37.
- Ten more changes the tensFixes a mistakeTen more than 23 is 33, not 24. The tens digit moves, the ones stay.
- Greater than, less than63 and 36: compare the tens first. Read 63 > 36 as “63 is greater than 36”.
- Numbers on a number lineA line from 0 to 100: place 50, then 25 and 75, then 79, 89, and 99 in order.
- The tens decide firstFixes a mistake59 has more ones than 61, but fewer tens. 59 < 61.
- Growing patternsTowers of cubes grow by 2 each step: 2, 4, 6. Find the rule, then build the next tower and say its number.
- About, nearly, and benchmarksA line from 0 to 100 with 10, 50, and 100 marked. 48 sits just before 50: it is nearly 50. 52 is about 50 too, and 90 is nearly 100.
- About how many?A jar of marbles: count one group of 10, see that the jar holds about 5 groups like it, and estimate 50. Counting finds 47, close to the estimate.
Unit 5: Adding and subtracting with tens
Usually taught in February and March
- Adding ones to a two-digit number36 + 5 in blocks: 11 ones make a new ten and 1 one. 41.
- Get to the next ten68 + 7 on a number line: 2 to reach 70, then 5 more. 75.
- Twelve ones is a new tenFixes a mistake56 + 6 makes 5 tens and 12 ones. That is 62, not 512.
- Count back to the ten33 − 6 on a number line: back 3 to 30, then 3 more. 27.
- Open a ten32 − 8 in blocks: 2 ones are not enough, so trade a rod for 10 ones. 24.
- The ten you opened is goneFixes a mistakeAfter opening a ten in 32 − 8, 2 tens are left, not 3. 24, not 34.
- Take away tens70 − 30 drawn as ten-sticks: 7 tens take away 3 tens leaves 4 tens, which is 40.
Unit 6: Length
Usually taught in March
- Longer, shorter, longestThree towers side by side, ends lined up, put in order.
- Compare with a third thingThe rope is longer than the bench. The bench is longer than the table. So the rope is longer than the table.
- Inches and centimeters don’t mixFixes a mistakeA 6-inch pencil is longer than a 10-centimeter crayon. The bigger number is not always longer.
- Measuring with a rulerLine the end up at 0 and count the inches: 3 inches. In centimeters the count is bigger.
- Start at zeroFixes a mistakeA crayon from 2 to 6 on the ruler is 4 inches long, not 6.
- Estimating in inchesA paper clip is about 1 inch, so a crayon about 4 clips long is about 4 inches.
- Which holds more, which is heavierTwo jars filled with scoops: the one that takes more scoops holds more. A balance tips down on the heavier side, and cubes on the other side show how heavy.
Unit 7: Money and time
Usually taught in April
- Pennies, nickels, dimes, quartersBoth sides of each coin, its value in cents, and how many make a dollar: 100, 20, 10, and 4.
- Bigger coin, not bigger valueFixes a mistakeA dime is smaller than a nickel and a penny, but worth 10¢.
- Counting coinsDimes by 10s, then nickels by 5s, then pennies by 1s: 3 dimes and 7 pennies is 37¢.
- Count each coin’s valueFixes a mistake4 coins are not 4¢. 2 dimes, a nickel, and a penny are 26¢.
- Counting dollar bills$10, $10, $5, $1, $1: count 10, 20, 25, 26, 27. $27.
- Time to the hourThe short hand points to 3 and the long hand to 12: 3:00 on both clocks.
- Time to the half hourHalf the clock is half an hour. The long hand on 6 is 30 minutes: 11:30.
- The short hand tells the hourFixes a mistakeAt 4:30 the short hand sits between 4 and 5. The long hand is the minutes.
- The 6 means 30 minutesFixes a mistakeThe long hand on 6 reads :30, not :06. Count by 5s to it.
- Reading a calendarA month's page: 7 columns for the days, a row for each week. Find a date, count the Fridays, and name the date before and after.
- Every coin, every valuePenny 1¢, nickel 5¢, dime 10¢, quarter 25¢, half-dollar 50¢, and dollar coin 100¢. Order them by what they are worth, not how big they are.
- Earning and spendingMoney earned is income. A kid with $10 picks between a book she wants and shoes she needs: the money buys goods and services, but not everything.
- Spend it or save it$5 now: spend it on a snack today, or save it, and after 2 more weeks have $15 for a ball. Tell spending from saving.
Unit 8: Shapes, halves, and fourths
Usually taught in April and May
- Sides and cornersTriangle, square, rectangle, hexagon, circle, and semicircle by sides, vertices, and straight or curved edges.
- Turned is still a triangleFixes a mistakeUpside down or long and thin, 3 sides and 3 vertices make a triangle.
- Solid shapesSphere, cube, rectangular prism, cone, and cylinder by faces, edges, and vertices.
- Not every box is a cubeFixes a mistakeA cube’s faces are all squares. A cereal box is a rectangular prism.
- Draw a shape from cluesSix sides and six vertices: draw a hexagon. Four equal sides: a square.
- Four sides fits two shapesFixes a mistake“Four sides and four vertices” fits a square and a rectangle. Both are right.
- Shapes from shapesSix triangles make a hexagon, two trapezoids make a hexagon, two squares make a rectangle.
- Shapes in the real worldA castle tower is a cylinder and a cone. An ice cream cone is a triangle and a semicircle.
- Halves and fourthsFold a rectangle and a circle into 2 equal parts, then 4: halves, then fourths.
- Equal parts onlyFixes a mistakeTwo pieces of different sizes are not halves.
- Many ways to make halvesCut a rectangle down, across, or corner to corner. Each way gives two halves.
- Sharing fairly12 counters shared one at a time into 3 groups, until each has 4. Check every group has the same, so each share is fair.