First Grade - MATH
5: Math
Unit 1: Number Sense 1-20
Lesson 6
Numbers 11-15
Students are asked to decompose numbers 11-20 (Skills list) and to write numbers 11-20 symbolically, numerically, and in word form. In the abacus activity, students are guided to show 11 by moving 10 beads on one wire and 1 bead on the next wire and to show 12–15 similarly, then count all beads to verify the total. Student pages for 11–15 ask students to color beads, draw pictures, and write number words to represent each number, and the coin activities have students exchange nickels for pennies and show amounts like 13 as 2 nickels + 3 pennies.
Lesson 7
Numbers 16-20
Students practice writing and representing numbers 16–20 (and 11–15 earlier) by tracing numerals and number words and by coloring beads on abacus diagrams for each teen number. Students show numbers 16–20 on a physical abacus and use the abacus to represent totals from rolled dice. The lesson explicitly has students count on a 1–20 number line and identify numbers before and after teen numbers.
Lesson 8
Reviewing Numbers 11-20
Students decompose numbers 11–20 using number bonds and the abacus by writing 10 in one small circle, drawing a card with a number 11–20, moving 10 beads and the extra ones, and writing the remaining ones in the other circle. Students use base-10 blocks to line up ten unit blocks, compare them to a ten rod, and build numbers such as a ten rod plus unit blocks to represent 11–20. Students use a dime as ten and add pennies to model and count up from 10 to make 11–20 with coin combinations.
Lesson 9
Ordering and Comparing
Students model numbers greater than ten by holding up 10 fingers and then additional fingers (for example, 10 plus 6) to make numbers such as 16. The introduction links two rows of beads on an abacus to tens (showing 2 tens is 20) and asks students to compare that to two full rows of fingers. In the Ordering Owls activity, students create two aligned rows (1–10 above 11–20) and are led to notice that 11 ends in 1, 12 ends in 2, and so on, highlighting the relationship between the teen numbers and their ones digits.
Final Project
My Math Game
Students create and play a game that uses and practices numbers 1–20 and they make 30 "Do the Math!" cards that explicitly ask about before/after, greater/less, number bonds, coin amounts, and counting by 2s and 5s. The instructions require students to sort provided cards into a group labeled "number bonds" and to fill in or create additional number-bond cards; one provided card shows a number-bond diagram. The materials also suggest choosing math-related game pieces such as a base-10 block, which could be used to represent place value.
Unit 2: Geometry
Lesson 4
Circles
Students are asked to make specific amounts that include teen values, for example making 11 cents using a dime and a penny is explicitly listed (dime + penny = 11 cents). The Skip Counting and Coins Review includes identifying amounts such as 13, 14, and 16 cents and asking students to show those amounts by drawing coins, which requires using a dime (ten) plus pennies (ones). Students are also prompted to use the abacus and number line to count and record numbers, supporting manipulation of multi-bead (ten) and single-bead (one) counts.
Unit 3: Addition and Subtraction to 10
Lesson 1
Getting Ready to Add and Subtract
Students practice counting on from 10 in Activity 2 (e.g., counting up 3 from 10 to get 13 and counting back to 7), and they work with starting numbers 11, 12, 13, 9, 8, and 7 on the "Counting Up and Back" sheet. Activity 3 has students write the numbers 11–20 and connect the strip so 10 connects to 11, and the teacher models counting from 21 to 30 while calling attention to the transition from 29 to 30. Questions in Activity 1 prompt students to identify the number between 10 and 12 (11) and to point to each number as they count on a number line.
Lesson 6
Adding and Subtracting to Solve Problems
Students work with groups of ten in multiple places: Activity 2 has students compare a ten-dollar bill to ten one-dollar bills and make change, and Activity 3 has students count by tens on a number strip and represent tens on an abacus. The lesson has students count, read, and write numbers to 100 and use one-dollar counters to add amounts (Shopping activities), which reinforces working with units and totals.
Unit 4: Data and Graphing
Lesson 2
Tally Sticks and Tally Marks
Students physically build and count numbers using craft sticks and tally marks, including specific practice for 11, 16, and 17 where they lay out sticks and group every fifth stick to make groups of five and then count by 5s and add the remaining ones. The activity instructs students to count the sticks by first counting by 5s and then adding one more after 15 (applies similarly for reaching 10 then adding ones), and to practice drawing tally marks for numbers 5, 11, 3, 17, and 25. The Rollin' Along and Tallying Skittles activities have students record totals and compare quantities, reinforcing creating and interpreting grouped counts.
Lesson 3
Pictographs
Students practice counting by tens by starting at 10 and counting up to 110 and are asked to continue counting by tens and identify numbers on a large number strip. Students cut out a small number strip beginning with 111, write in missing numbers, tape it to the larger strip, and are asked to find and point to numbers such as 89, 71, 105, 99, and 118. Students are instructed to cut out 10 one-inch squares (five colors, 10 total), indicating an action that could support grouping by tens.
Unit 5: Addition and Subtraction to 20
Lesson 2
More About Addition
Students are asked in the Wrapping Up to roll a die and add the number rolled to 10 (for example, roll a 3 and add it to 10 to make 13), and they are allowed to use the abacus to determine the new number. Multiple activities require students to model totals with counters and the abacus (e.g., move beads to show groups that add to 10 or move 10 beads then additional beads). The lesson repeatedly has students create sums that build on ten (Making 10 with Three, Order and Addition, and the web activity option to practice "10-19").
Lesson 3
Adding to 20
Students practice addition sentences that explicitly include 10 + something (for example, 10 + 8 = 18 and 10 + 10 = 20) on the abacus worksheet. Students use the abacus to trade beads and make a ten (for example, transforming 9 + 6 into 9 + 1 + 5 and then 10 + 5) and then check the sums. Students create number bonds for numbers 11–20 using number cards and represent those sums with counters or the abacus.
Lesson 4
More Adding to 20
Students use an abacus to trade beads to make a ten and then read the remaining ones (for example, trading to show 9 + 8 = 17 and noting that 17 is showing). Students group counters onto a plate labeled "10" and count the leftover counters to form numbers like 15 as 10 and 5. Multiple activities and worksheets (Making 10 to Add, What 5 Makes, Addition Concentration) require students to form sums in the 11–19 range by creating a ten and adding the remaining ones.
Lesson 5
Addition Games and Crafts
Students are shown how to regroup three addends by looking for two that make 10 and rewrite the sum as 10 + remaining ones (example: 4 + 6 + 3 is rewritten as 10 + 3 = 13). The coin-exchange and dime activities have students trade pennies for a dime and represent amounts using dimes and pennies (students show 18 cents as 1 dime, 1 nickel, and 3 pennies and exchange pennies when they reach 10). The Number Collection and paper-chain labeling tasks ask students to represent 15 with addition sentences (e.g., 5 + 5 + 5 = 15) and encourage showing numbers in multiple ways, including two- and three-addend equations that support expressing teens as a ten plus ones.
Lesson 6
Subtracting Within 20
Students practice converting ones to teens by adding 10 to single-digit numbers (Option 1 and Option 2 ask students to write original numbers and add 10 to make numbers like 14 and 17). Students represent teen numbers on an abacus by moving 10 beads on the top wire and the remaining ones on the next wire (the instructions show 17 as 10 + 7). Students show the number 18 in multiple ways including addition sentences and coins, and a pictured addition fact explicitly pairs 10 and 6, reinforcing 10 + ones compositions for teen numbers.
Lesson 7
Problem Solving
The Working with Dollars activity explicitly has students make 11 dollars by showing 1 ten and 1 one and includes the instructor model: "Ten plus one more is 11." Students are asked to show 12, 13, and other amounts in two different ways using one-dollar, five-dollar, and ten-dollar bills (e.g., 1 ten and 2 ones for 12). Several practice items and prompts require composing amounts greater than ten and describing them verbally (e.g., show ten plus ones; two fives is ten and then add one).
Final Project
Numbers Are Missing!
Students are prompted to fill in "10 combines with ______ to make the missing number" and are shown the explicit example for 11 (10 combines with 1 to make 11). Students must produce addition sentences (including 2-addend examples like 5 + 6 = 11 and opportunities to write 10 + 1 = 11) and use abacus beads, counters, and pictures to represent the number. The activity uses number cards 11–18 and asks students to create multiple representations (addition, subtraction, pictures, abacus) for each chosen missing number.
Unit 7: Place Value
Lesson 1
What Is the Base-10 System?
The Skills list explicitly states that learners will "Understand that the numbers from 11 to 19 are composed of a ten and one...nine ones." Activity 1 has students build 11 and 14 using one ten rod plus unit blocks and directs them to review making 11–19 with a video. The Student Activity Page asks students to color ten-frames for each number from 11 to 19, and the abacus task has students move 10 beads for the ten and additional beads for the ones (example: 14 as 10 beads + 4 beads). Day 2 also has students show 19 as 1 ten rod and 9 unit blocks and then represent other teen numbers similarly.
Lesson 2
What Is Place Value?
Students build 10 with unit blocks, exchange 10 unit blocks for a ten rod, and place the ten rod in the tens place while writing a 1 in the tens place and a 0 in the ones place. Students add one unit block to the ones place to make 11, erase the 0 and write 1 in the ones place, and are prompted to show and write 12 through 19 by placing 1 ten rod and 2–9 unit blocks and saying both the number name and the base-10 name (e.g., "1 ten and 3 ones"). Students also correct a set of 15 unit blocks by exchanging ten units for a ten rod and leaving 5 ones, demonstrating regrouping into tens and ones.
Lesson 3
Tens
Students count objects and then circle groups of ten and report how many tens and how many are left over (Activity 1). In the reading comprehension questions, students answer that 15 berries equals 1 group of 10 and 5 berries left over. Students use ten rods and an abacus to show and say numbers as groups of tens (e.g., showing 1 ten, 2 tens, up to 9 tens) and write tens and ones for multiples of ten on the place-value mat and worksheet.
Lesson 4
Distinguishing Tens and Ones
Students are asked to represent 18 using the abacus, place value cards, and base-10 blocks, explicitly showing it as 10 + 8 (10 beads on the top wire and 8 beads on the second wire; the 10 card and the 8 card; 1 ten rod and 8 unit blocks). The materials and instructions show students placing a ones card over the zero of a ten card (e.g., placing the 5 over the 0 in 20 to make 25) and state that 10 can be thought of as a bundle of ten ones called a "ten." Students encounter other teen examples (16 and 15) in the wrapping up and activities where they identify the tens and ones digits.
Lesson 5
Practice Time!
Students create two-digit numbers by choosing a tens card and a ones card (Activity 1) and say both forms of the number (for example, "42" or "4 tens and 2 ones"). Students draw base-10 rods and unit blocks to show numbers and are prompted to write several two-digit numbers (36, 23, 19, 52, 41) and circle the tens-digit (Wrapping Up). The skills list explicitly includes understanding that the two digits of a two-digit number represent amounts of tens and ones.
Lesson 6
More Work With Tens and Ones
Students sort and represent two-digit numbers using gumball-machine activity pages that label quantities in the tens or ones place (e.g., boxes labeled "5 in ones place" and "3 in tens place") and fill squares to show those counts. Students color squares in a Place Value Quilt based on digits in the ones or tens place and encounter teen numbers such as 13, 15, and 19 in that activity. Students write given two-digit numbers, circle the ones digits (e.g., 13 -> circle 3), and are asked to write and name a number specified by its tens and ones (write and name 68).
Lesson 7
Building Numbers Using Tens and Ones
Students use ones and tens place value cards and base-10 blocks to create and show two-digit numbers (e.g., they place cards to make 23 and draw base-10 blocks for 23). Students cut and combine a 10 card with smaller one-digit cards to make numbers (the activity explicitly gives 10 and the ones 2,4,7,9 and prompts the smallest number 12). Students represent numbers as tens and ones using dominos (writing how many tens and ones a domino shows and drawing base-10 blocks) and use dimes and pennies to show tens and ones (e.g., showing 43 and rolling to create numbers like 52).
Lesson 8
Reaching 100!
Students draw two single-digit cards to create two-digit numbers and then say them as tens and ones (for example, saying "57" as "5 tens and 7 ones") and show those numbers with base-10 drawings. In Activity 1 students trade 10 unit blocks for a ten rod and trade 10 ten rods for a hundred flat, showing that 10 ones make a ten and 10 tens make 100. In Activities 2 and 3 students complete number sequences up to 100 and count or group objects by tens to reach 100, reinforcing tens-and-ones structure and counting by tens.
Lesson 9
Playing With Bigger Numbers
Students count across the transition from 10 to 11 during the rolling activity, being prompted to "count correctly as he moves from one row to the next" (e.g., moving from 10 to 11). Students use ones and tens place value cards to build two-digit numbers in Activity 2, placing the ones digit over the 0 on the tens card for examples such as "5 tens and 1 one," 72, and 36. In Wrapping Up, students say the equivalent number for given groups of tens (e.g., "1 ten (10)", "5 tens (50)", "9 tens (90)"), reinforcing the tens-place concept.
Lesson 10
More Work With 100
Students fill sequential number boxes that include the range 9–16, requiring them to write the numbers 11–16. Students use an abacus, ten rods, and number bonds to model groups of ten and to make larger numbers (for example, showing 30 as 3 tens, using ten rods to make 100, and representing numbers such as 109, 115, and 113 with hundreds/tens/ones). Students complete a Place Value to 120 activity that has them color or show the number of hundreds, tens, and ones for numbers up to 120.
Lesson 11
Sequencing Numbers
Students cut out and use Base-10 Number cards and base-10 block pictures that show rods (tens) and unit cubes (ones). In Activity 1 they compare pairs such as 8 and 18 and are prompted to "count ten rods" and to say numbers as tens and ones (for example, "4 tens and 2 ones"). Activity 3 asks students to decide which numbers have more tens or more ones, reinforcing tens/ones decomposition for two-digit numbers including 18 and 19.
Lesson 12
Comparing Numbers
Students are asked to pay attention to how many tens and ones are in numbers when comparing them (Activity 2) and are shown explicit examples comparing the tens place (e.g., 33 vs 24) and ones place (e.g., 37 vs 39) on Day 2. The Comparing Two Numbers flowchart guides students to compare number of digits, then digits in the tens place, then digits in the ones place. The Domino Place Value game has students form two-digit numbers from domino ends and discusses that placing 0 in the tens place yields a one-digit number, reinforcing the role of the tens and ones places.
Lesson 13
10 More and 10 Less
Students use base-10 blocks to show a one-digit number (e.g., 4) and then add a ten rod to make 14, and they are asked what number was made by adding 10. The teacher asks the child to pick a one-digit start (for example 3) and use the abacus to add 10, producing 13. Activities ask students to notice that when counting by tens the ones digit stays the same and that adding one ten increases the tens place by one.
Lesson 15
More Practice With 10
Students work with tens and ones using base-10 blocks and ten rods (Wrapping Up and Activity 2) and hear language equating tens to groups of ten (e.g., "3 tens plus 3 tens equals 6 tens" and comparing 5 ones to 5 tens). Students form two-digit numbers from drawn digits 1–9 in the introduction and complete problems that include two-digit values such as 13 and 16 on the activity pages. Students practice adding and subtracting multiples of ten (10 more/10 less and Multiples of 10 Concentration), reinforcing the role of the tens digit.
Final Project
Place Value BINGO!
Students are asked to show numbers in four ways: base-10 blocks, abacus beads, tens + ones, and digit form, which explicitly includes written tens-and-ones representations. Option 2 Step 3 directs students to model the number 15 on the whiteboard in all four ways before placing it on Bingo cards. The "BINGO Card Spaces" and other activity pages include squares labeled with tens-and-ones descriptions (for example, "1 ten + 5 ones").
Unit 8: Measurement
Lesson 1
Introducing Measurement
Students are asked to complete a "Today's Number" sheet where they show a given number with base-10 blocks (e.g., "2 ten rods and 6 unit blocks") and record the number in a Hundreds/Tens/Ones chart. The activity pages repeatedly prompt students to represent numbers using tens and ones, draw base-10 block representations, and find 1 more/1 less/10 more/10 less for given numbers.
Lesson 2
Getting Started With Length
On Day 2 students write the number 15 and are asked to show it as 1 ten rod and 5 unit blocks and as 0 hundreds, 1 ten, 5 ones. Students are asked to produce two number sentences that show 15. On Day 1 students represent 99 as 9 ten rods and 9 unit blocks, reinforcing tens-and-ones representation of two-digit numbers.
Lesson 3
More Work With Length
Students are asked to represent specific two-digit numbers with base-ten materials (e.g., show 34 as 3 ten rods and 4 unit blocks and 41 as 4 ten rods and 1 unit block). Students practice using ten rods and unit blocks to measure objects and write the number of units (choosing between tens or ones and recording the measurement). Students are also asked to show coin amounts including 15 cents, which can be represented as a ten (dime) and five ones (pennies).
Lesson 4
Working With Height
Students are asked to represent two-digit numbers with ten rods and unit blocks, for example showing 79 as 7 ten rods and 9 unit blocks and 48 as 4 ten rods and 8 unit blocks. The student directions explicitly list '0 hundreds, 7 tens, 9 ones' and '0 hundreds, 4 tens, 8 ones' as expected representations. The Measurement Scavenger Hunt and activities use base-10 ten rods as measurement units, reinforcing tens-and-ones manipulatives.
Lesson 7
Capacity/Volume
Students are asked to represent "Today's number is 66" by showing 6 ten rods and 6 unit blocks and to say "6 tens and 6 ones." Students practice finding 1 more/1 less and 10 more/10 less for two-digit numbers (example given for 66). The materials suggest optionally giving a child a two-digit number and asking for 1 more, 1 less, 10 more, and 10 less.
Unit 9: Addition to 100
Lesson 1
Some Base-10 Review
Students group unit blocks into groups of ten and count leftover ones (Activity 1), then name the resulting two-digit number (for example, 3 tens and 4 ones = 34). Students model and write place-value equations such as "2 tens + 5 ones = 25" and write expanded form for several two-digit numbers (Activity 3). The "Writing Place Value" answer key explicitly decomposes 19 as 1 ten and 9 ones, and the "Tens and Ones Practice" page has six visuals where students count tens and ones and write the total.
Lesson 4
Adding a Multiple of 10 to Any Number
Students read place-value clues such as "This number has a 1 in the tens place and an 8 in the ones place (18)," and they use the place-value mat and base-10 blocks to show numbers with 1 ten and several ones. Students practice adding 10 to single-digit numbers (example given: draw 8 and say 18) and are prompted to show that result with a ten rod plus ones. Activities ask students to model numbers on the mat/abacus and add tens (e.g., demonstrating that adding 10 increases the tens digit by 1).
Lesson 5
More Practice With Adding Multiples of 10
Students are asked to add two-digit and one-digit numbers and to add two-digit numbers and multiples of 10 (Skills). Activities instruct students to use base-10 blocks, an abacus, and a place-value mat to solve addition problems (Activity 1 and Activity 2). Several problems include teen numbers (e.g., 15, 12, 17, 18) in equations such as 15 + 30 and 12 + 20, and students are prompted to model and compute these sums using base-10 representations.
Lesson 6
More Addition With Two-Digit Numbers
Students represent 13 on the abacus and on a laminated place-value mat by placing 1 ten rod in the tens place and 3 unit blocks in the ones place (Activity 1). Students model and add numbers that fall in the teens (for example 16, 13, 19) using base-10 blocks and the abacus in multiple problems and concentration/matching activities. In the Wrapping Up, students write number sentences for 14 and are prompted to write decompositions such as 4+10 and 13+1, explicitly expressing a teen number as ten plus some ones.
Lesson 7
Composing 10 to Add
Students represent two-digit numbers with base-10 blocks and abacus (e.g., showing 35 with 3 ten rods and 5 unit blocks and exchanging 10 unit blocks for a ten rod to make 40). Students break a teen number into ten and ones explicitly (the text models breaking 16 into 10 + 6 and then adding 4 to make another ten). Students solve and write equations involving teen numbers (examples include 16+4, 17+3, 18+2) and count unit blocks to find how many ones are needed to reach the next ten.
Lesson 8
More Composing 10 to Add
Students are asked to show two-digit numbers on a laminated place-value mat, base-10 blocks, and an abacus (e.g., show 37 in two ways). Activity 1 has students add to numbers such as 19+6 and uses base-10 blocks to add unit blocks, count 11 ones, and exchange 10 unit blocks for a ten rod. Multiple activities (spinner addition, web practice, and wrapping up) require students to model sums with tens rods and unit blocks and to compose a ten when ones exceed ten.
Lesson 9
Adding to 100
Students rewrite addition sentences (e.g., 15 + 4) vertically and align digits so that the 5, 4, and resulting 9 are in the ones column and the 1 is placed in the tens column. Students use a place-value mat, base-10 blocks, and an abacus to find sums and are prompted to add ones first and then tens, sometimes composing a ten. Students complete grid exercises that explicitly show decompositions such as 1 (ten) + 8 (ones) and work with numbers like 13, 15, 17, 18, and 19 in tens-and-ones columns.
Final Project
Addition to 100 Go Fish!
Students are asked to write addition sentences of the form "+ a multiple of 10" and "+ a single-digit number" for each target number, and the provided table includes examples such as 19 with "10 + 9" and 16 with spaces for similar decompositions. The instructions tell students to use base-10 blocks and an abacus to come up with the missing target numbers and addition sentences, supporting hands-on composition of numbers into tens and ones. Students must write two cards for each target number, one showing a multiple-of-10 addition (e.g., 10 + ones) and one showing adding a one-digit number to a two-digit number.
Unit 10: Skills Review
Lesson 2
Reviewing Place Value
Students are asked to use place-value cards (1–9 and 10–90) and an abacus to create specific numbers, including 19, which requires combining a ten and nine ones. In the Bags of Blocks activity, students draw ten rods and unit blocks, write the resulting two-digit number (example given 5 tens and 7 ones → 57), and answer questions about the tens and ones digits. The matching activity presents and asks students to connect representations written as "__ tens + __ ones," numeric expressions like "90+9," and base-ten visuals, reinforcing tens-and-ones decompositions.
Lesson 3
Reviewing Large Numbers
Students are asked to compare two-digit numbers and explicitly prompted to use what they know about the tens place and the ones place to decide order in the sequencing activity. Students create two-digit numbers from dice rolls (e.g., 56 or 65) and record results when they add or subtract 10 on the 'Review: Adding and Subtracting 10' sheet. The wrap-up has students read pairs of numbers and identify which is greater, encouraging attention to tens and ones digits when comparing numbers.
Lesson 5
Reviewing Measurement
Students are asked to use a handful of pennies, nickels, and dimes to show cent amounts including 8, 10, 14, and 17 cents. They are challenged to show each amount in more than one way, which could lead them to represent 14 and 17 as a dime plus additional pennies. The lesson explicitly models decomposition of an amount into coin combinations with the 8-cent example (8 pennies or 1 nickel and 3 pennies).