First Grade - MATH
5: Math
Unit 1: Number Sense 1-20
Lesson 6
Numbers 11-15
Students decompose numbers 11–15 into 10 and additional ones as stated in the Skills and practice pages. Students use an abacus to show 10 beads and then add 1–5 more beads to represent 11–15, and they are asked to count all beads to verify totals. Students use concrete coin models (pennies and nickels) to make amounts such as 10 and 13 cents (e.g., 2 nickels + 3 pennies) and to count on from a nickel to find sums like 6 or 7 cents.
Lesson 8
Reviewing Numbers 11-20
Students use an abacus and coins to count up from 10 to make numbers 11–20 (e.g., dime + penny to show 11, dime + 2 pennies to show 12). Students complete number bonds with 10 in one part to find the ones needed to make numbers 11–20. Students use base-10 blocks to represent ten rods and unit blocks (e.g., one ten rod + 2 units = 12) and show that two tens make 20.
Unit 3: Addition and Subtraction to 10
Lesson 1
Getting Ready to Add and Subtract
Students use a laminated number line to point, count, and make jumps forward and backward, explicitly connecting counting on to addition and counting back to subtraction (Activity 1 and Activity 2). In Activity 2 students roll a die, start at given numbers (including 10, 11, 12, 13) and count up by the die roll and count back, then record the starting number, roll, counting up result, and counting back result on a worksheet. The teacher script explicitly tells students that counting up from a number is adding and counting back is subtracting, reinforcing the relationship between addition and subtraction.
Lesson 5
Finding Differences
Students practice basic addition facts and turn-around (commutativity) in the Introduction using counters. In Activity 2 students solve missing-addend problems like 4 + ? = 10 and 5 + ? = 8 using counters, drawings, and an abacus as concrete models. In Activity 5 students add one-digit amounts to two-digit numbers by following number-strip jumps (e.g., start at 50, count up 5 and 4) and they count by patterns (e.g., count by 5s or count back 10), which shows adding/subtracting multiples of 10 on a number line.
Lesson 6
Adding and Subtracting to Solve Problems
Students use play one-dollar bills to add item prices in the Shopping activities, writing totals on the Shopping sheets and recording amounts on a whiteboard. In Activity 2 students work with a ten-dollar bill and ten one-dollar bills to compute change, exchanging a ten for ones and counting out the remaining dollars. In Activity 3 students use an abacus, number strip, and dimes to count by 10s, to show numbers like 10, 20, 30, and to add or subtract 10 by moving groups of ten beads to represent tens.
Unit 4: Data and Graphing
Lesson 2
Tally Sticks and Tally Marks
Students use concrete materials (30 craft sticks) to show numbers and group every fifth stick diagonally to form tally groups of five, then count by 5s and add extras. Students draw tally marks on a whiteboard for given numbers (5, 11, 3, 17, 25) and record counts in a tally chart for Skittles, then write totals for each color. Students answer addition-style questions from collected data, for example combining green and purple counts to get 7 and comparing counts to find differences.
Lesson 3
Pictographs
Students count picture symbols in pictographs to determine category totals (e.g., counting ducks, bluebirds, and eagles and answering "How many birds did the birdwatcher see in all?" which yields 17). Students create and record counts from a Skittles activity and from a favorite-foods survey and then determine the total number of responses (e.g., 15). Students practice counting by tens and locating numbers up to 120 on a number strip, reinforcing number sense for two-digit numbers.
Unit 5: Addition and Subtraction to 20
Lesson 2
More About Addition
Students use counters and an abacus to build addition sentences that make 10, including splitting 10 into three addends and recording the equations (e.g., 2 + 3 + 5 = 10). Students manipulate groups to show that order does not affect the sum (associative property) and use concrete materials while matching equivalent addition sentences. Students also roll a die and add the one-digit result to 10 (e.g., 10 + 3 = 13), using the abacus to find the total.
Lesson 3
Adding to 20
Students use an abacus and counters to find sums such as 10+8, 7+8, and 10+10 and to color beads to represent those sums. Students model and practice composing a ten (for example, transforming 9+6 into 9+1+5 and then 10+5) using the abacus and counters. Students create number bonds for sums 11–20 and use manipulatives to check those bonds.
Lesson 6
Subtracting Within 20
Students use an abacus and a whiteboard to add 10 to numbers, writing the original number and the result (e.g., changing 6 to 16 and 10 to 20) and then using the abacus to work with the new two-digit numbers. Students use a number line to add and subtract, including tasks that start at two-digit numbers and add single-digit amounts (for example, "Start at 15. Add 3. Subtract 10."). Students use concrete tools (abacus, counters, number line) to find sums and differences in games and activities (e.g., domino sums and card draws) and check their work with manipulatives.
Lesson 7
Problem Solving
Students use concrete models (play dollar bills, abacus, and counters) to represent tens and ones and to form amounts such as 11 and 13 (Activity 2). The teacher models counting by tens and ones with statements like "Ten plus one more is 11" and shows alternate decompositions for ten (two fives, ten ones). Students solve addition problems that produce two-digit sums up to 19 (e.g., 5 + 8 + 6 = 19 in Activity 1) and are prompted to use the abacus or counters for computing.
Final Project
Numbers Are Missing!
Students create addition and subtraction sentences for numbers 11–18 (examples: 5+6=11, 2+5+4=11, 11−5=6) and fill a number-line activity that highlights missing two-digit numbers like 10 and 11. Students are instructed to use concrete models and drawings—abacus beads, counters, and pictures of objects—and to practice showing 11 with those tools on the whiteboard. The skills list explicitly includes "Add and subtract within 20" and "Apply properties of operations as strategies to add and subtract."
Unit 7: Place Value
Lesson 1
What Is the Base-10 System?
Students use base-10 blocks and ten rods to build and represent two-digit numbers (e.g., showing 11 as 1 ten rod + 1 unit, representing 14 as 1 ten rod + 4 units). Students align ten unit blocks to form a ten rod and then observe that 10 + 10 = 20, demonstrating composing a ten. Students move beads on the abacus to show tens and ones (e.g., moving 10 beads on the top wire and 4 on the second wire for 14) and identify the digits in two-digit numbers (e.g., asking what digits make up 15 or 36).
Lesson 2
What Is Place Value?
Students use base-10 blocks and a place-value mat to build numbers, adding unit blocks to the ones place (e.g., 9 + 1 -> 10) and exchanging ten ones for a ten rod while writing the tens and ones digits. Students match numerals to pictures of base-10 blocks in the concentration activity and use a virtual base-ten-blocks tool to show drawn numbers. Students add coins (for example, a dime and 4 pennies = 14 cents) and represent amounts in two ways using pennies, nickels, and dimes.
Lesson 8
Reaching 100!
Students represent 99 with base-10 blocks and on the abacus, then add one unit block to make 100 and trade 10 ones for a ten rod and 10 ten rods for a hundred flat. Students count by tens on the abacus and with dimes and arrange collections into groups of ten to reach 100. Students write the number 100 in place-value form (1 in hundreds, 0 in tens and ones) and point to numbers on a number grid while counting to 100.
Lesson 9
Playing With Bigger Numbers
Students repeatedly add small amounts when they roll the die and move the penny on the laminated number grid, counting forward each time and recording tally marks for each roll (Activity 1). Students use ones and tens place value cards to build and read two-digit numbers (Activity 2). In the wrap-up, students identify numbers 1 before and 1 after given numbers and translate groups of tens into their equivalent numeric values (e.g., 5 tens = 50).
Lesson 10
More Work With 100
Students use an abacus, ten rods, and base-10 blocks to build and compare groups of tens and to form number sentences such as 3+7=10 and 30+70=100; they read these as "3 tens + 7 tens = 10 tens." The Making 100 activity has students fill blanks in equations like 60 + ___ = 100 and 30 + ___ = 100, and students place ten rods on a hundred flat to show combinations of tens that make 100.
Lesson 13
10 More and 10 Less
Students use base-10 blocks and an abacus to add 10 to numbers (Activity 2: adding a ten rod to 4 to make 14 and continuing to 24, 34, etc.). Students count up and back by tens on a 1–120 number grid, identify that the tens digit changes while the ones digit stays the same, and color or circle numbers that are 10 more or 10 less (Activities 1, 3, and 4). Students explicitly find 10 more and 10 less for two-digit examples (e.g., 55 → 65 and 45; 22 → 32 and 12) demonstrating place-value thinking about tens and ones.
Lesson 14
Working With Multiples of 10
Students use base-10 blocks and an abacus to represent and add multiples of 10 (e.g., 10+30, 60+20, 30+20) and draw base-10 blocks on the activity page to find sums. Students practice counting by tens on a number grid and map increases in the tens digit when adding 10, 20, or 30. The lesson prompts students to compare 1+3=4 with 10+30=40 to connect adding tens to adding ones and to write number sentences for the sums and differences.
Lesson 15
More Practice With 10
Students draw two-digit numbers and answer questions about 1 more and 10 more/less (Getting Started and Introduction prompts). Students complete a "10 More 10 Less" worksheet and play a "Multiples of 10 Concentration" game with problems like 40+20, 90-40, and 30+40, using base-10 blocks or an abacus as needed. The lesson explicitly models place-value reasoning (3+3=6 versus 30+30=60 and 5-2=3 versus 50-20=30) to show adding/subtracting tens as adding/subtracting ones of tens.
Unit 8: Measurement
Lesson 1
Introducing Measurement
Students complete a "Today's Number" routine where they write a two-digit number (examples: 26, 57) and represent it with base-10 blocks and a Hundreds/Tens/Ones chart, showing 2 ten rods and 6 unit blocks for 26 and 5 tens and 7 ones for 57. Students fill in 1 more/1 less and 10 more/10 less for the given number, explicitly practicing adding 1 and adding 10 to a two-digit number. Students are also invited to show the number using another method, including creating an addition or subtraction sentence to represent the number.
Lesson 2
Getting Started With Length
Students write and represent anchor numbers (99 and 15) using ten rods and unit blocks and label them as hundreds/tens/ones (e.g., 9 ten rods and 9 unit blocks; 0 hundreds, 9 tens, 9 ones; 1 ten, 5 ones). Students are prompted to identify one more/one less and 10 more/10 less for these numbers (for example, 99 → one more = 100; 15 → 10 more = 25). Students are asked to create number sentences for 15, and the activities require use of concrete models (ten rods, unit blocks, coins) to show quantities.
Lesson 3
More Work With Length
Students are asked to represent two-digit numbers with base-10 ten rods and unit blocks (e.g., 34 as 3 ten rods and 4 unit blocks; 41 as 4 ten rods and 1 unit block). Students practice finding 1 more and 1 less and 10 more and 10 less for these two-digit numbers (for example, 34 → 35 and 44; 41 → 42 and 51). Students use concrete base-10 blocks when measuring and comparing lengths, reinforcing tens-and-ones representations in physical models.
Lesson 4
Working With Height
Students are asked to represent two-digit numbers (e.g., "Today's number is 79" and "Today's number is 48") using ten rods and unit blocks and to state 1 more/1 less and 10 more/10 less (e.g., 1 more is 80, 10 more is 89). The materials also mention using base-10 ten rods as measurement units in the scavenger hunt, so students handle tens and ones manipulatives. Students physically show numbers with tens/ones models and reason about adding or subtracting 1 and adding or subtracting 10.
Lesson 6
Temperature
The introduction asks students to represent 63 with 6 ten rods and 3 unit blocks and to state 1 more (64), 1 less (62), 10 more (73), and 10 less (53), which uses concrete place-value models. Students are asked to show 63 in a way of their choosing, reinforcing tens-and-ones representation. The activities repeatedly prompt comparisons of amounts that involve adding or subtracting 1 and 10 (e.g., discussing what the thermometer reading would do if moved from oven to freezer and vice versa).
Lesson 7
Capacity/Volume
Students represent the number 66 using 6 ten rods and 6 unit blocks and identify 1 more, 1 less, 10 more, and 10 less than that number. Day 2 suggests giving a child a two-digit number and asking them to name numbers that are 1 more, 1 less, 10 more, and 10 less. Students are also asked to count pours when filling containers, which involves counting repeated units of volume.
Lesson 8
Thinking More About Measurement
Students work with the number 104 by physically showing 1 hundred flat, 0 ten rods, and 4 unit blocks, and by stating 1 more is 105, 1 less is 103, 10 more is 114, and 10 less is 94. Students use concrete base-ten models (hundred flats, ten rods, unit blocks) to represent a number and to adjust it by ones and by tens. The activities ask students to show a number in a way of their choosing, which involves using concrete representations or drawings tied to place value.
Unit 9: Addition to 100
Lesson 1
Some Base-10 Review
Students use base-10 unit blocks and ten rods to make and count tens and ones (Activity 1, Making Words and Numbers, and Activity 3). Students write place-value addition sentences such as "2 tens + 5 ones" and translate them to numeric form (20 + 5 = 25). Students answer "What number is 10 more?" and add a ten rod to determine 10-more/10-less, and students practice addition facts with one-digit cards and sums/differences.
Lesson 2
Working With 10 Again
The skills list explicitly includes adding within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10. Students use concrete models (abacus and base-10 blocks) to add multiples of 10 in activities such as 20+30, 30+30, 60+10, 20+40, and 10+30. Students complete number-bond tasks with multiples of 10 and are prompted to think of sums as adding tens (e.g., "add 2 tens and 3 tens").
Lesson 3
More Practice With Multiples of 10
Students use concrete models (base-10 blocks and an abacus) to add and subtract multiples of 10 as described in the introduction. Students play a game that has them write addition and subtraction sentences with two-digit multiples of 10 and solve them (e.g., 30 + 60 = 90) and are prompted to think of numbers as tens (3 tens + 6 tens = 9 tens). Students complete worksheet problems that are all addition and subtraction problems involving two-digit multiples of 10 with answers within 100.
Lesson 4
Adding a Multiple of 10 to Any Number
Students use base-10 blocks, an abacus, and a place-value mat to add multiples of 10 (10, 20, 40, etc.) to one- and two-digit numbers. Activities ask students to show a starting number with manipulatives, add tens rods or beads, and then write the resulting number (for example, showing 26, adding two tens to get 46). Students practice with problems such as 50+9, 15+30, 13+60, 70+11 and matching tasks (e.g., 20+13, 9+20) and are prompted to explain aloud how adding 10 or 20 affects the tens digit.
Lesson 5
More Practice With Adding Multiples of 10
The lesson lists the skill 'Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10' and gives many practice problems (e.g., 56 + 30, 30 + 7, 18 + 20, 5 + 60). Students are directed to use concrete models and drawings such as an abacus, base-10 blocks, and a place-value mat to find answers and to draw base-10 blocks on the whiteboard. Problem prompts ask students reflective questions (e.g., 'How would you like to solve this problem?' and 'How do you know that your answer is correct?') which encourage use of strategies and checking answers.
Lesson 6
More Addition With Two-Digit Numbers
Students represent two-digit numbers with base-10 blocks and a place-value mat and add a multiple of 10 (e.g., add 30 to 24, 42, 67) while being reminded that adding 30 = adding 3 tens. Students draw pictures and use an abacus and base-10 blocks to add a two-digit number and a one-digit number (e.g., 13 + 6) and complete several worksheets of two-digit plus one-digit problems (examples: 27+8, 42+7, 22+7, 53+6). Students play a matching game and use manipulatives to find sums and write number sentences that show decompositions (for example, writing pairs that sum to 14, 18, 25).
Lesson 7
Composing 10 to Add
Students use base-10 blocks and an abacus to add a two-digit number and a one-digit number (for example, modeling 35 + 5, exchanging 10 ones for a ten rod, and writing 35+5=40). Students decompose numbers and relate strategies to written methods (for example, breaking 16+4 into 10+6+4 and writing number sentences). Students practice multiple two-digit-plus-one-digit problems on matching and activity sheets (e.g., 32+8, 63+7) and count on to reach the next multiple of ten (24+6=30, 46+4=50) using manipulatives.
Lesson 8
More Composing 10 to Add
Students model and solve 37+4 using a laminated place-value mat, base-10 blocks, and an abacus, physically adding 4 units to 37, exchanging 10 ones for a ten rod, and recording 41 on the whiteboard. Multiple practice problems (19+6, 25+8, 56+6) and spinner activities require students to create two-digit plus one-digit number sentences and use the same concrete materials to find sums. The Wrap Up tasks ask students to show sums on the place-value mat (e.g., 40+50, 45+5) and to explain how they add tens with tens, ones with ones, and when they compose a ten, while writing the resulting number sentences.
Lesson 9
Adding to 100
Students use concrete models (place-value mat, base-10 blocks, abacus) to find sums and practice composing ten (e.g., problems like 38 + 5). Students rewrite horizontal addition sentences vertically and place digits in tens and ones columns using grids (e.g., 15+4, 22+3, 13+5, 31+2). Students solve problems that include a two-digit number plus a one-digit number and two-digit numbers plus multiples of ten (e.g., 28+20, 56+10, 40+30) and are prompted to describe how they solved selected problems.
Final Project
Addition to 100 Go Fish!
Students are asked to create addition sentences that add a multiple of 10 to reach a two-digit target and to add a one-digit number to a two-digit number (Go Fish! Numbers sheet). Students are instructed to use base-10 blocks and an abacus as concrete models to come up with missing target numbers and addition sentences. Students write addition sentences on cards (e.g., 10+9 and 14+5 for 19) and use those written equations during game play to find matches. The activities require students to practice both two-digit + one-digit and two-digit + multiple-of-10 addition within 100.
Unit 10: Skills Review
Lesson 3
Reviewing Large Numbers
In Activity 2, students roll dice to form two-digit numbers and then write the results of adding 1, subtracting 1, adding 10, and subtracting 10 in a five-column table, so they practice adding a one-digit number (1) and a multiple of 10 (10) to two-digit numbers. The Student Activity Page explicitly prompts students to compute Number, +1, -1, +10, and -10 for several rows. In the sequencing activity, students compare two-digit numbers by referring to the tens and ones places, using place value language to decide order.
Lesson 5
Reviewing Measurement
Students are given a handful of pennies, nickels, and dimes and asked to show cent amounts 8, 10, 14, and 17 cents using coins. Students are challenged to show each amount in more than one way, which requires combining coins (for example, a dime plus pennies to make 14 or 17). The coin activity uses concrete models for composing amounts and implicitly involves combining tens (a dime) and ones (pennies).