First Grade - MATH
5: Math
Unit 1: Number Sense 1-20
Lesson 6
Numbers 11-15
Students use an abacus to show 10 beads moved to the right and then add 1 more bead to represent 11, and they are asked to color or count beads to show numbers 11–15. The skills list and activities ask students to decompose numbers 11–20 to show they are made up of 10 and other ones. Students use coins and the abacus to show 10 cents (exchanging two nickels for 10 pennies) and to reason that two groups of five make ten.
Lesson 7
Numbers 16-20
Students model 20 on an abacus and are told explicitly that "two tens makes 20" when they show 20 as two complete rows of beads. Students color beads on number-specific activity pages (16–20), including a 20 page where they color all beads to represent 20. Students count up from 10 on the number line and place/recognize number cards up to 20, reinforcing the ten-to-twenty range.
Lesson 8
Reviewing Numbers 11-20
Students use the abacus to model that two tens make 20 and to represent 20 with two dimes. Students use base-10 blocks to match ten unit blocks to a ten rod and to build numbers like 12 as one ten rod plus two unit blocks. Students use number bonds with 10 in one small circle to decompose numbers 11–20 as 10 plus the remaining ones and use the abacus to find the ones.
Lesson 9
Ordering and Comparing
Students use fingers and an abacus to combine tens (for example, holding up two full rows of fingers and noting that 2 tens is 20). Students build two rows of owl puppets (1–10 above 11–20) and are led to observe that numbers in the top and bottom rows end in the same ones digit (e.g., 1 and 11). Students also order and compare numbers up to 20 using number lines, counters, and printed decade numbers such as 10 and 20 in activity pages.
Final Project
My Math Game
Students practice with the numbers 1 through 20 (Count to 20, counting by 2s and 5s to 20) and create and answer cards that explicitly include 10 and 20 (e.g., number bonds with 10, a card showing coins 10¢ + 1¢ + 1¢, and counting by 5s including 10 and 20). The activities ask students to identify numbers before and after numbers like 15 and to complete number-bond tasks that reference 10 and 20. Students also work with dimes (10¢) when counting money, which provides repeated exposure to the value ten.
Unit 3: Addition and Subtraction to 10
Lesson 3
Getting on Board with Addition
Students use an abacus to count beads and are asked to note that each abacus wire has 10 beads and to show pairs that add to 10 (e.g., 1+9, 2+8). Students color beads on a 'Showing 10 on the Abacus' page and create physical groups of 10 (wristbands, snacks) to represent ten as a unit. Students write and lay out number strips for 31–50 and 51–60 and count by 5s, noting numbers that end in 0 and placing counters at 5, 10, 15, …, 50.
Lesson 6
Adding and Subtracting to Solve Problems
Students count and represent 10, 20, 30, ... 100 using an abacus and a 1–100 number strip, placing counters above 10, 20, 30, etc., and sliding groups of 10 beads to show each ten. Students use a ten-dollar bill as worth 10 one-dollar bills and practice giving change using ten one-dollar bills, showing a ten as ten ones. Students use 10 dimes to count by tens and compare counting 100 pennies vs. 10 dimes to reinforce grouping by tens.
Unit 4: Data and Graphing
Lesson 1
What Is Data?
Students practice counting by 10s to 100 using a large number strip and are asked to identify and outline the boxes around the tens (noting those boxes are used to count by 5s and 10s). Students are prompted to count groups of 10 with concrete examples (fingers, 10 pennies in a dime, bowling pins) and to practice counting by 2s starting from 20. Students use an abacus to collect and record counts, moving one bead per item as they observe.
Lesson 3
Pictographs
Students are prompted to review counting by 10s by laying out a large number strip, starting at 10 and counting up by tens up to 110, and are challenged to count to 110 by 10s. Activity 5 has students extend their number strip and practice writing and locating numbers up to 120, reinforcing the sequence of multiples of ten within a larger counting context. The introduction and activities repeatedly call attention to the sequence 10, 20, 30, etc., through oral counting and number-strip work.
Lesson 4
Bar Graphs
Students are asked to count by 10s up to 120 during the Wrapping Up activity, practicing skip-counting by tens. Students also encounter the number 20 in the optional Skittles activity (pick 20 Skittles) and work with graphs whose vertical axes go to 10, giving repeated exposure to multiples of ten in counting and data contexts.
Unit 5: Addition and Subtraction to 20
Lesson 3
Adding to 20
Students use the abacus to represent numbers by showing 10 beads on the top wire and remaining beads on the second wire (for example, the abacus should show 10 on the top wire and 7 on the second wire for 17). Students complete problems that include 10+8=18 and 10+10=20 on the "Adding to 20 on the Abacus" sheet. Students create number bonds for cards 11–20 and are asked to identify the sum (the large circle) and addends (the smaller circles).
Lesson 4
More Adding to 20
Students use an abacus to trade beads to make 10 (e.g., moving a bead to the top wire to form 10 and then reading 17), and they place counters on a paper plate labeled "10" to form a ten as a unit. Students practice making 10 with problems like 9+8, 8+5, and 9+6 and use the 5+5 = 10 strategy and chants that emphasize 10 as a group.
Lesson 5
Addition Games and Crafts
Students practice making tens in multiple activities (for example, the "First to 10" card game where students form sums equal to 10 and the dice/path and number-toss activities that encourage "making 10"). In Activity 5 (Coin Exchange Game) students trade 10 pennies for a dime and are instructed to trade 10 cents for a dime and continue play until reaching 20 cents, giving students experience grouping 10s as a unit. The Party Paper Chains activity and several problems explicitly use the count 10 (e.g., "There are 10 green links"), reinforcing the quantity ten as a countable group.
Lesson 6
Subtracting Within 20
Students add 10 to single-digit and teen numbers in the egg-carton activity (e.g., 6 becomes 16; 10 becomes 20) and write the new numbers on a whiteboard. Students use an abacus to represent numbers by moving 10 beads on the top wire and ones on the second wire (example given for representing 17 as 10 + 7). The worksheet and activities include the number 20 explicitly (flashcards, number-line tasks, and the problem 20 − 10).
Lesson 7
Problem Solving
Students use play dollar bills to represent amounts and are asked explicitly, "How many tens?" and to show ten dollars in multiple ways (1 ten, 2 fives, 10 ones, etc.). The activity has students make 11 by saying "Ten plus one more is 11," and asks students to show 20 dollars using 2 tens (and other combinations). Students practice forming and counting amounts using ten-dollar bills and ones.
Final Project
Numbers Are Missing!
Students are asked to fill in a prompt "10 combines with ______ to make the missing number," and an explicit example shows 11 written as 10 + 1. Students create addition sentences (two 2-addend and two 3-addend) and subtraction sentences with the missing number as the first number, and they use abacus beads and counters to represent the number. The set of missing-number activities includes the number 10 and has students show numbers using pictures, counters, and abacus beads.
Unit 6: Time
Final Project
How to Spend the Perfect Day
Students set analog clocks to specific times (e.g., 3:30, 1:00, 6:00) and write the matching digital times (for example, writing "7" before the colon and "00" after it). Students record times on scheduling sheets that list hours and half hours (e.g., 7:00, 7:30, 10:30) and place sticky notes with start times above activities. Students practice identifying what time it will be a half hour or an hour after a given time.
Unit 7: Place Value
Lesson 1
What Is the Base-10 System?
Students use base-10 blocks and abacus to represent tens and ones: they show 10 as a ten rod and 10 unit blocks, show 11 as 1 ten rod + 1 unit, and complete 11–19 activities with a ten and ones. In Activity 3 students make 20 by combining unit blocks into a second ten rod and are guided to see that two groups of 10 make 20 (2 tens). Students are asked to show 30 using only ten rods (3 ten rods) and to model tens on the abacus by moving groups of 10 beads.
Lesson 2
What Is Place Value?
Students exchange ten unit blocks for a ten rod on the place-value mat and write 1 in the tens place and 0 in the ones place while saying, "We have 1 ten and 0 ones," to make 10. Students place 2 ten rods and are asked to name the number (20) and write 2 in the tens place and 0 in the ones place; they also place 3 ten rods to name 30. Students are asked to count to 100 by 10s, providing practice with the sequence of tens (10, 20, 30, ...).
Lesson 3
Tens
The lesson's Skills list explicitly states the target: "Understand that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one... nine tens (and 0 ones)." During Day 2 Activity 2, students place ten rods (e.g., 4 ten rods), are asked "What number is 4 tens?", count by tens to 90, and are prompted to say phrases like "4 tens or forty." Activity 3 and the Student Activity Page require students to match numbers (10–90) with their "__ tens" forms and with base-10 block representations, and the Wrapping Up section asks students to name numbers both as "four tens" and "forty."
Lesson 4
Distinguishing Tens and Ones
Students are asked to write and label numbers such as 60, 4 tens (child writes 40), 70, 2 tens (child writes 20), 10, and 50 and then identify the digit in the ones place as 0. Activity 1 explicitly prompts students to point to cards (including 10 through 90) and states that 20 can be called "twenty" or "2 tens," and shows combining a 20 card with a 5 card to make 25. The Matching Numbers and Day 2 activities require students to match and represent multiples of ten (for example, 40) with the verbal form "4 tens" and to show tens with ten-rods and 0 ones using place value cards and the mat.
Lesson 5
Practice Time!
Students roll one die to choose the tens digit and find a place-value card showing that many tens, then roll a second die to choose the ones digit and find the corresponding ones card. Students say both forms of the number (for example, "42" and "4 tens and 2 ones") and draw base-10 blocks, including ten rods and unit blocks, to represent the numbers they create. Introductory clues ask students to identify a number described as "made up of 2 tens and 3 ones (23)," and the wrap-up asks students to write and name a number that has 4 tens and 5 ones (45).
Lesson 7
Building Numbers Using Tens and Ones
Students are asked to use ones and tens place value cards to build two-digit numbers and to place the ones digit over the 0 on the tens card, showing the tens/ones structure. Activity 1 has students write how many tens and ones a domino shows (example: 4 tens and 3 ones) and draw base-10 blocks to represent that. Activity 4 explicitly links a dime to a ten-rod and instructs students to place 4 ten rods (and 4 dimes) in the tens place to show 40, and to repeat the process for 60 and 70. Activity 3 has students cut out boxes showing 10 abacus beads and the numbers 10, 20, 30, 40 to create two-digit numbers using tens and ones representations.
Lesson 8
Reaching 100!
Students create and say two-digit numbers and explicitly state them as '5 tens and 7 ones' and '7 tens and 5 ones' when forming numbers from digit cards. Students represent 99 on a place-value mat and abacus, identify 9 tens and 9 ones, add one unit to make 10 ones, trade 10 ones for a ten rod, and then trade 10 ten rods for a hundred flat, showing 10 tens = 100. Students count by tens on the abacus and use 10 dimes and grouped baggies to count to 100, repeatedly working with groups of ten.
Lesson 9
Playing With Bigger Numbers
The Skills section explicitly lists understanding that the numbers 10, 20, …, 90 refer to one through nine tens (and 0 ones). In Activity 2, students use ones and tens place value cards to create prompts such as "6 tens," "8 tens and 4 ones," and are instructed to place the ones digit over the 0 on the tens card. The Wrapping Up section asks students to say the equivalent number for named groups of ten, listing 1 ten (10), 2 tens (20), …, 9 tens (90).
Lesson 10
More Work With 100
The Skills section explicitly states students should understand that 10, 20, …, 90 refer to one through nine tens (and 0 ones). In Activity 2 students model 30 on the abacus, identify the remaining 7 sets of ten, and read 30+70=100 as "3 tens + 7 tens = 10 tens." Activity 3 has students identify 2 ten rods as "2 tens or 20," and the Making 100 worksheet and Wrap-up prompt students to name and combine multiples of ten (e.g., 40+60, 50 then add 5 more tens). Activity 4 has students place ten rods on a place-value mat to show numbers like 120 (1 hundreds, 2 tens, 0 ones) and explicitly discusses zeros in the tens/ones places.
Lesson 11
Sequencing Numbers
Students cut out and use base-10 block cards that show groups of ten and single units, and they are prompted to read numbers both in the traditional way and as numbers of tens and ones (for example, "4 tens and 2 ones"). Activity prompts ask students to compare numbers that are multiples of ten (e.g., 30 and 70) and to "count ten rods" to see which number has more tens. Activity 3 asks students to decide which number "has more tens," reinforcing tens-place reasoning.
Lesson 12
Comparing Numbers
Students are asked in Activity 1 to think of numbers 'more than 50 (5 tens)' and asked 'What does it mean for a number to be equal to 50/5 tens?', directly invoking the idea of 50 as five tens. In Day 2 Activity 3 students compare 24 and 33 and are prompted to note that '33 has 3 tens while 24 has only 2 tens,' using tens as the deciding place-value. The Domino Place Value game has students decide between numbers like 3 and 30 and explicitly explains that putting a 0 in the tens place means there are no tens, leading students to choose 30 to make a larger number.
Lesson 13
10 More and 10 Less
Students count by tens to 100 and point to numbers on a 1-120 number grid while the lesson asks, "What digit is in the ones place in all of these numbers? (0)" and, "What do you see happening with the digits in the tens place as you count up by 10s?" The introduction prompts students to explain comparisons by talking about the digits in the tens and ones places (for example, "30 is greater than 20 because it has more tens"). Activity 4 explicitly tells students that "counting up by 10 is the same as adding 1 ten to a number," and Activity 2 has students use base-10 blocks to add a ten rod to 4 to make 14, showing the ten rod as a unit of ten.
Lesson 14
Working With Multiples of 10
Students are given an explicit definition of multiples of 10 stating these numbers have 0 in the ones place and a nonzero digit in the tens place, with examples 10, 20, …, 90. Students use base-10 blocks and the abacus to show 30 as 3 ten rods, 20 as 2 tens, and are asked to reason that 1 ten plus 3 tens is 4 tens (40). Students roll dice to create multiples (e.g., roll a 4 → 40 or 4 tens), write those multiples, and match/add/subtract them on activity sheets, reinforcing the tens interpretation for 10–90.
Lesson 15
More Practice With 10
Activity 2 explicitly models tens-language (e.g., teacher says, "We can say 3 tens plus 3 tens equals 6 tens") and contrasts ones- vs tens-operations (5 ones vs 5 tens). The wrapping-up task has students use ten rods and state that 5 ten rods equal 5 tens or 50. The concentration activity and worksheet require students to add and subtract multiples of 10 (e.g., 40+20, 90-40) and match those results to card values like 50, 70, 60, etc.
Final Project
Place Value BINGO!
Students are asked to show numbers in four ways including "tens + ones," base-10 blocks, and digit form (e.g., Option 2 has students show 15 as "1 ten + 5 ones"). The BINGO Numbers and Card Spaces include multiples of ten (30, 50, 70, 90) and at least one space explicitly labeled "9 tens." Students cut out and place representations (base-ten drawings and written tens + ones) onto BINGO cards, practicing matching numerals to tens-and-ones descriptions.
Unit 8: Measurement
Lesson 1
Introducing Measurement
Students are asked each day to show a given number by drawing base-10 blocks and by identifying the number using hundreds, tens, and ones (e.g., the materials model 26 as 2 ten rods and 6 unit blocks and 0 hundreds, 2 tens, 6 ones). The student activity page includes a Hundreds/Tens/Ones chart and a box for base-10 blocks so students practice decomposing numbers into tens and ones and representing them physically. The "Today's Number" routine also asks students to find 10 more and 10 less, reinforcing use of tens in operations.
Lesson 2
Getting Started With Length
Students represent two-digit numbers with ten rods and unit blocks (99 is shown as 9 ten rods and 9 unit blocks; 15 is shown as 1 ten rod and 5 unit blocks). Students write numbers in place-value form (99 shown as 0 hundreds, 9 tens, 9 ones; 15 shown as 0 hundreds, 1 ten, 5 ones). Students also use base-10 blocks as a measurement unit in a recording table, connecting physical ten-units to quantities.
Lesson 3
More Work With Length
Students are asked to represent two-digit numbers with base-10 materials: for example, for 34 they should show "3 ten rods and 4 unit blocks" and state "0 hundreds, 3 tens, 4 ones." Day 2 repeats this with 41: "4 ten rods and 1 unit block; 0 hundreds, 4 tens, 1 one." Activity 2 has students choose ten rods as a unit of measure and count how many ten rods long an object is, and the wrap-up asks students to compare quantities like "2 ten rods or 5 paper clips."
Lesson 4
Working With Height
Students are asked to represent two-digit numbers using base-ten materials: for 79 they show 7 ten rods and 9 unit blocks and state "0 hundreds, 7 tens, 9 ones." Students do the same for 48, showing 4 ten rods and 8 unit blocks and stating "0 hundreds, 4 tens, 8 ones." Students also use base-10 ten rods as measurement units in activities (e.g., finding the width of 4 base-10 ten rods on the scavenger hunt), practicing counting and grouping by tens.
Lesson 6
Temperature
The lesson has students represent the number 63 by showing 6 ten rods and 3 unit blocks and stating it as 0 hundreds, 6 tens, 3 ones. The lesson also has students use 10 more and 10 less (e.g., 63 → 73 and 63 → 53), which practices adding and subtracting tens.
Lesson 7
Capacity/Volume
Students are asked to represent the "Today's number" 66 with 6 ten rods and 6 unit blocks, explicitly showing tens and ones. Students practice finding 1 more/1 less and 10 more/10 less for two-digit numbers (e.g., 10 more is 76, 10 less is 56). A suggested extension asks the child to name numbers that are 1 more, 1 less, 10 more, and 10 less than a given two-digit number.
Unit 9: Addition to 100
Lesson 1
Some Base-10 Review
Students group unit blocks into sets of ten and are asked how many groups of ten they have and how many unit blocks remain, connecting grouped tens to two-digit numbers (Activity 1). The lesson asks what a ten rod represents (10 unit blocks) and models examples such as writing '2 tens' and showing that '2 tens' is the same as 20, and writes expanded forms like 20+5=25 and 50+6=56 (Activity 3). Students complete Tens and Ones Practice and Writing Place Value pages where they count tens and ones and write numbers and expanded forms (answer keys show examples with 2–9 tens).
Lesson 2
Working With 10 Again
The Facts and Definitions section names 10, 20, 30, …, 90 as multiples of 10 and states they have 0 in the ones place. In Activities, students show numbers like 30, 80, 10, 50, and 40 on an abacus by moving groups of ten and use base-10 blocks/ten rods to represent those amounts (e.g., five ten rods for 50). Students also reason explicitly with tens in problems: they are asked to think of 20+30 as 2 tens + 3 tens and 60-40 as 6 tens take away 4 tens, and they complete number bonds using multiples of 10 (e.g., 60 as 20 and 40).
Lesson 3
More Practice With Multiples of 10
Students use base-10 blocks, ten rods, and the abacus to model multiples of ten and to count and combine groups of ten when finding sums and differences. The text explicitly directs students to "think of multiples of 10 as numbers of tens" and gives the example "3 tens plus 6 tens is 9 tens or 90." Students are given explicit examples and practice problems (e.g., "50 is 5 tens," 50 + 50 = 100, 30 + 40 = 70) that require interpreting 10, 20, …, 90 as one, two, …, nine tens.
Lesson 4
Adding a Multiple of 10 to Any Number
Students practice adding 10 and are asked to note that the digit in the tens place goes up by 1 when 10 is added. During adding 20 activities, students are instructed to "add 2 ten rods to the tens place because 2 tens is the same as 20" and to observe that the tens digit goes up by 2. Activity 3 asks "How many tens make 40?" and has students add 4 ten rods to represent adding 40; several matching activities require students to match number sentences with base-ten block representations.
Lesson 5
More Practice With Adding Multiples of 10
Students are instructed to use base-10 blocks, an abacus, and a laminated place-value mat to add multiples of 10 (e.g., adding 56 + 30 and other problems with 10, 20, 30, 40, 50). Students complete cut-and-glue activities and problem-solving sheets that repeatedly require adding numbers that are multiples of ten (10, 20, 30, 40, 50, etc.). Students practice mental math with drawing number cards that include 10, 20, 30, 40, and 50 and then check answers with manipulatives.
Lesson 6
More Addition With Two-Digit Numbers
Students represent two-digit numbers (24, 42, 67, 13) with base-10 blocks and a laminated place-value mat, placing ten-rods in the tens place and unit cubes in the ones place. Students are told that adding 30 is the same as adding 3 tens and are asked to add 30 to given numbers using materials. Students solve problems that add multiples of ten (for example, 30+7) and are allowed to use base-10 blocks and the abacus to model tens and ones.
Lesson 7
Composing 10 to Add
Students use base-10 blocks and a place-value mat to represent numbers (for example, placing 3 ten rods and 5 unit blocks and writing 3 in the tens place and 5 in the ones place). They exchange 10 unit blocks for a ten rod and rewrite the digits (for example changing 35+5 into 4 tens and 0 ones and writing 40). Students draw number cards 10–90, identify the next multiple of ten, and answer questions about 10 more/10 less and what to add to reach the next multiple of ten.
Lesson 8
More Composing 10 to Add
Students draw number cards 10–90 and answer questions about 10 more/10 less and next multiple of 10, prompting attention to multiples of ten. In Activity 1 students use base-10 blocks and a place-value mat to exchange 10 unit blocks for a ten rod and identify quantities as tens and ones (e.g., 4 ten rods and 1 unit = 41). In Wrapping Up students show problems like 40+50=90 on the mat and are prompted to say they add 4 tens and 5 tens to get 9 tens (90).
Lesson 9
Adding to 100
Students use a place-value mat, base-10 blocks, and an abacus to find sums that include multiples of ten (e.g., 40 + 30, 56 + 10, 28 + 20). Students place digits into labeled tens and ones columns on grids (examples show "1 (ten) + 8 (ones)" and vertical alignment of tens and ones) and are asked to consider what happens to the tens digit when adding 10 or a multiple of 10. Worksheets and the answer key show students producing and matching sums that are multiples of ten (e.g., 40 + 30 = 70).
Final Project
Addition to 100 Go Fish!
Students create addition sentences in a column labeled "+ a multiple of 10" (examples include 10 + 9 and 21 + 30) and work with target numbers that include 20 and 60. Students are instructed to use base-10 blocks and an abacus to come up with missing target numbers and addition sentences. The listed skills state that students add tens and tens and ones and ones, and sometimes compose a ten.
Unit 10: Skills Review
Lesson 1
Reviewing Addition and Subtraction
Students practice counting by 10s to 100 during the Wrapping Up activity, explicitly encountering the sequence 10, 20, 30, …, 100. Students also work with problems and sorting boxes that include the number 10 and equations like 10-0, 10-2, and columns headed with 10 in the Sorting Number Sentences activity. Materials provided (abacus, counters) are available for students to model numbers and sums, which could be used to represent groups of ten.
Lesson 2
Reviewing Place Value
The Skills list explicitly states the target about 10, 20, ... 90 referring to tens and 0 ones. In the Introduction, students use place-value cards 1–9 and 10–90 and place numbers on an abacus, showing tens and ones. In Activity 1, students draw ten rods and unit blocks, write the resulting two-digit number (e.g., 5 ten rods + 7 ones -> 57), and identify the digit in the tens and ones places. The Matching activity has students match representations written as "X tens + Y ones" and base-ten visuals to numeric forms.
Lesson 3
Reviewing Large Numbers
Students are asked to use what they know about the tens place and the ones place to decide the order of two-digit numbers during the sequencing activity, prompting attention to tens and ones. Students roll dice to create two-digit numbers and then compute +10 and -10 on the provided worksheet, practicing how adding or subtracting ten changes the number. The wrap-up has students compare pairs of numbers using the number cards 1–100, reinforcing comparison by tens and ones.
Lesson 4
Reviewing Addition to 100
Students model 26 + 30 with a place-value mat and base-10 blocks by placing 2 ten rods and 6 unit blocks, then adding 3 more ten rods to the tens place; the text explicitly states, "she has added 3 tens to 26." The lesson reminds students that when adding multiples of 10 the digit in the tens place changes but the digit in the ones place does not. In the wrap-up students use number cards 10, 20, 30, …, 90 and 100 and name complements to 100 (for example, flipping 60 and saying "Forty"), reinforcing understanding of tens values.
Lesson 5
Reviewing Measurement
Students are given pennies, nickels, and dimes and asked to show specific cent amounts including 10 cents. They are challenged to show each amount in more than one way, which allows representation of 10 cents either as ten pennies or as one dime. The activity explicitly models value-building with coins and asks students to construct given amounts.