1st grade math lessons

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.