First Grade - MATH
5: Math
Unit 1: Number Sense 1-20
Lesson 8
Reviewing Numbers 11-20
Students decompose numbers 11–20 by writing 10 in a number bond and finding the ones part (Activity 3), using an abacus to show 10 and the remaining ones (example: 15 → 10 and 5). Students use base-10 blocks to match ten unit blocks to a ten rod and represent numbers as 10 plus units (Activity 4). Students use coins to start at 10 and count up to 11–20, showing that numbers above 10 are composed of a ten and some ones.
Lesson 9
Ordering and Comparing
The introduction asks students to use 10 (fingers/abacus) to make numbers 11–20 and to discuss that 2 tens is 20, which highlights the role of tens. In Activity 3 (Ordering Owls) students arrange two rows so that 1 is above 11, 2 above 12, etc., and are prompted to notice that numbers in the top and bottom rows end in the same digit. Activities also have students count from numbers like 12 up to 20 and reorder number sets that include two-digit numbers.
Unit 3: Addition and Subtraction to 10
Lesson 5
Finding Differences
Students are asked to count back 10 from a two-digit number ("Start at 27. Count back 10...") and to make jumps on a large number strip (for example starting on 50 and counting up and back). The skills list includes "Count, read, and write to 120, starting at any number less than 120," and students are asked to identify when they are adding versus subtracting during those jumps. Students are also challenged to explain how successive up and back jumps result in returning to the same number.
Lesson 6
Adding and Subtracting to Solve Problems
Students count by tens using a 1–100 number strip, an abacus, and 10 dimes (Activity 3). Students are asked specific questions about 10 more and 10 less (e.g., "Which number is 10 more than 10?", "Which number is 10 less than 40?"), and they add or remove groups of ten beads to show adding or subtracting 10. Students practice moving counters and beads to show increments of 10 and recite the sequence 10, 20, 30... up to 100.
Unit 4: Data and Graphing
Lesson 3
Pictographs
The lesson explicitly reviews counting by 10s using a large number strip, asking the child to count up 10 more repeatedly (e.g., from 10 to 20, 30, 40) and to count by 10s up to 110. Activity 5 has the student build and extend number strips to 120 and asks the child to locate called-out numbers (including two-digit numbers such as 89 and 71) on the strip.
Lesson 4
Bar Graphs
Students are asked to count by 10s up to 120 while bouncing or tossing a ball, which gives practice with tens sequences and place-value increments. The lesson also has multiple activities where students read and use number scales on graphs (e.g., y-axes numbered 1–10 or 0–7), so students practice recognizing and using ten-based number intervals in context. The Guess My Number game has students compare guesses as greater than or less than target numbers, giving some experience with number relationships.
Unit 5: Addition and Subtraction to 20
Lesson 5
Addition Games and Crafts
Students practice composing and using tens in several activities: in Activity 1 they rewrite 4 + 6 + 3 as 10 + 3 to find the sum, and the materials review "5 and 10 chants." In Activity 6 (First to 10) students make tens with two or three cards and orally state addition sentences like "two plus five plus three equals ten." In Activity 5 (Coin Exchange) students exchange 10 pennies for a dime and work with totals up to 20 cents, reinforcing the ten-unit.
Lesson 6
Subtracting Within 20
Students are asked to add 10 to numbers in the egg-carton activities (Option 1: change 6 to 16 and 10 to 20; Option 2: add 10 to 4 and 7 to get 14 and 17) and then use those results in subtraction problems. The number-line activity includes operations that require adding or subtracting 10 (e.g., prompts about getting back to 20 by adding 10). The worksheets include explicit problems that involve tens changes, including a problem 20 - 10 and several two-digit subtraction problems.
Lesson 7
Problem Solving
Students solve specific subtraction problems that involve subtracting ten (for example, 18 − 10 is listed in the Getting Started problems and Activity 1 answer key shows 18 − 10 = 8). Students work with ten-dollar bills and hear a modeling statement, "Ten plus one more is 11," when making amounts with money. The zookeeper problem asks about needing to reach 10 elephants (10 − 5), giving another instance of subtracting from or comparing to ten.
Final Project
Numbers Are Missing!
Students fill in a prompt that reads "10 combines with ______ to make the missing number," so they write the ones part when a number is expressed as 10 + n (for example, writing 1 for 11). Students identify numbers that are greater than and less than the missing number (for example, stating 10 and 12 when 11 is missing). Students create addition and subtraction sentences with the two-digit missing number as the sum or as the first number in subtraction (e.g., 5 + 6 = 11 and 11 - 5 = 6).
Unit 7: Place Value
Lesson 1
What Is the Base-10 System?
Students use base-10 blocks and ten rods to build two-digit numbers (Activity 1 asks the child to show 11, 14, and to compare ten unit blocks with a ten rod). The Student Activity Pages require coloring ten-frames and rods to represent numbers from 11–19 and 20–30, and Activity 3 has the child make 19, then make 20 and observe that two ten rods show 20. The lesson has students represent numbers on the abacus (example: showing 14 by moving 10 beads on one wire and 4 on another) and identify digits in two-digit numbers (e.g., asking what digits make up 15 and 36).
Lesson 2
What Is Place Value?
Students practice skip-counting by tens when asked to count to 100 by 10s. Students use a place-value mat and base-10 blocks to build two-digit numbers, exchange ten ones for a ten rod, and write the tens and ones digits for numbers 10–19. Students compare values like 30 versus 3 cents to see that a digit in the tens place represents groups of ten and is worth more than the same digit in the ones place.
Lesson 3
Tens
Students practice grouping objects into tens and ones when they make tally marks, circle groups of ten, and report how many groups of ten and leftovers they have. Students count and represent quantities by tens using ten rods on a place-value mat and by moving groups of ten on an abacus, saying "1 ten, 2 tens..." and naming numbers like "four tens" and "forty." Students complete a "Showing Tens" activity matching two-digit multiples of ten to their tens form and base-10 block representations.
Lesson 5
Practice Time!
Students roll dice to build two-digit numbers, place place-value cards for tens and ones, say number names both as digits and as 'x tens and y ones', and draw base-10 rods and unit blocks to show the numbers. Students are asked to write a series of two-digit numbers and circle the tens digit, and to write and name a number given a specified number of tens and ones. The activities repeatedly focus on identifying and representing the tens and ones in two-digit numbers.
Lesson 8
Reaching 100!
Students create and name two-digit numbers (e.g., 57 as "5 tens and 7 ones") and compare tens and ones when forming numbers. Students model 99 on a place-value mat and trade 10 ones for a ten and 10 tens for a hundred, showing the role of tens visually. Students count by tens on the abacus and complete a number grid from 91 to 100, which highlights the pattern of tens increasing.
Lesson 9
Playing With Bigger Numbers
Students are asked to count by 10s to 100 and to count by 5s and 10s, which practices stepping by tens mentally. Students use tens and ones place-value cards to build two-digit numbers (for example, 6 tens, 5 tens and 1 one, 72, 36, 99), which reinforces the idea that tens and ones are separate units. Students are also asked to identify equivalent numbers for named groups of tens (e.g., 5 tens = 50, 9 tens = 90), linking ten as a unit of ten.
Lesson 11
Sequencing Numbers
Students cut out and sort Base-10 number cards and are asked to name numbers both in the traditional way and as numbers of tens and ones (for example, "4 tens and 2 ones"). Students use base-10 blocks and are prompted to compare numbers by counting tens (for example, comparing 30 and 70 or using ten rods to see which has more tens). Students are asked questions about which number has more tens or ones when putting randomly drawn cards in order.
Lesson 13
10 More and 10 Less
Students practice counting by tens and noticing place-value patterns (Activity 1 and Activity 2) as they move down the same column on the 1-120 number grid and observe that the tens digit increases by 1 while the ones digit stays the same. Students use base-10 blocks and an abacus to add and subtract tens (Activity 2 and Activity 3) and are asked to predict and identify numbers that are 10 more or 10 less (Activity 4). The lesson concludes by asking students to name the numbers 10 more and 10 less than given two-digit numbers (wrapping up: 55, 22, 78, 100).
Lesson 14
Working With Multiples of 10
Students are asked to point to the number 86 and name 10 more and 10 less (96 and 76) as an initial oral/visual practice. Activity 1 asks students to find 10 more than 30 on a number grid and to explain how the tens digit changes when adding 10, and models adding tens on an abacus. Activity 3 has students model subtraction by tens (e.g., 40-20) with ten-rods and beads and asks them to explain why two ten-rods/rows were removed.
Lesson 15
More Practice With 10
The lesson's Skills list explicitly names "Given a two-digit number, mentally find 10 more or 10 less than the number." The Introduction and Activity 1 ask students to generate 10 more and 10 less for drawn two-digit numbers and to try without a number grid, and provide a notecard rule: "+10: ones place stays the same; tens place goes up by 1". The Student Activity Page and Answer Key give multiple practice problems and tables where students compute 10 more and 10 less, and the wrapping-up activity has students represent tens with ten-rods.
Unit 8: Measurement
Lesson 1
Introducing Measurement
The Today's Number routine asks students to write a given two-digit number and fill in 1 more, 1 less, 10 more, and 10 less (examples given: for 26 students write 10 more = 36 and 10 less = 16; for 57 students write 10 more = 67 and 10 less = 47). The Student Activity Page includes a table specifically labeled "1 more / 1 less / 10 more / 10 less" for repeated practice with two-digit numbers. Students also break numbers into Hundreds/Tens/Ones and represent them with base-10 blocks, which makes explicit the tens and ones structure of two-digit numbers.
Lesson 2
Getting Started With Length
The "Today's Number" activities present two-digit numbers (99 on Day 1 and 15 on Day 2) and require students to represent them with ten rods and unit blocks and as hundreds/tens/ones. The materials explicitly state the results of adding or subtracting ten (for example, 99 -> 10 more is 109 and 10 less is 89; 15 -> 10 more is 25 and 10 less is 5).
Lesson 3
More Work With Length
The lesson explicitly has students represent two-digit numbers with base-ten materials and state 10 more and 10 less: for example, for 34 students are to show that 10 more is 44 and 10 less is 24, and for 41 students are to show that 10 more is 51 and 10 less is 31. Students use ten rods and unit blocks to represent tens and ones, connecting the change of 10 to the tens place when showing these examples.
Lesson 4
Working With Height
The lesson explicitly has students represent two-digit numbers with tens rods and unit blocks (e.g., "Today's number is 79…7 ten rods and 9 unit blocks" and "Today's number is 48…4 ten rods and 8 unit blocks"). For both 79 and 48 the lesson states the results for adding and subtracting 10 ("10 more is 89, and 10 less is 69"; "10 more is 58, and 10 less is 38"). The lesson also has students label numbers as hundreds, tens, and ones (e.g., "0 hundreds, 7 tens, 9 ones"), supporting place-value reasoning.
Lesson 5
Working With Weight
The introduction asks the child to identify 100 using a hundred flat and to represent it as 1 hundreds, 0 tens, 0 ones. It explicitly states that 10 more is 110 and 10 less is 90, and also models 1 more as 101 and 1 less as 99. These statements show adding and subtracting ten from a presented number.
Lesson 6
Temperature
The introduction gives a two-digit number (63) and directs the child to represent it with 6 ten rods and 3 unit blocks. The introduction then identifies 10 more as 73 and 10 less as 53 for that example. The representation with tens and ones links the two-digit number to adding or subtracting a ten.
Lesson 7
Capacity/Volume
The Introduction explicitly models the two-digit number 66 with six ten rods and six unit blocks and states that 10 more is 76 and 10 less is 56. The text asks the child to show 6 tens and 6 ones and to identify 1 more, 1 less, 10 more, and 10 less for that number. Day 2 instructs the teacher to give a child a two-digit number and ask him to name the numbers that are 1 more, 1 less, 10 more, and 10 less.
Lesson 8
Thinking More About Measurement
The introduction asks the child to represent 104 with base-ten blocks (1 hundred, 0 tens, 4 ones) and states explicitly that 10 more is 114 and 10 less is 94. Students are instructed to show 1 more (105) and 1 less (103) as well as to show the number in a way of their choosing. The materials therefore require students to work with place-value representations and identify the result of adding or subtracting ten for the given number.
Unit 9: Addition to 100
Lesson 1
Some Base-10 Review
Students practice breaking two-digit numbers into tens and ones (Activity 1 and Day 2) by counting groups of ten and unit blocks and writing numbers as 20+5 = 25. Students use ten rods to represent adding 10 (e.g., showing 2 tens and 5 ones, and modeling adding a ten rod to find 10 more). The Wrapping Up activity asks students to find 10 more and 10 less for randomly pulled numbers, and the introduction explicitly encourages students who are ready to solve problems mentally rather than with manipulatives.
Lesson 2
Working With 10 Again
Students practice counting by tens to 120 from various starting points and show two-digit multiples of 10 on an abacus (30, 80, 10, 50, 100, 40). Students add and subtract multiples of 10 using abacus and base-10 blocks (examples: 20+30, 30+30, 60+10; 60-40) and are prompted to think of these as adding or taking away tens (e.g., "2 tens and 3 tens"). The wrap-up asks students to try figuring sums and differences of multiples of 10 in their heads rather than using materials.
Lesson 3
More Practice With Multiples of 10
Students practice adding and subtracting multiples of 10 in Activity 1 and Activity 2 (examples include problems such as 70 + 10 and 100 - 10, and a grid of multiples of 10 used for sums and differences). The text prompts students to "think about numbers of tens" (for example, "3 tens plus 6 tens is 9 tens or 90") and asks them to explain strategies and say each number sentence aloud. Students are asked to use or explain use of place-value tools (base-10 blocks and abacus) to find sums and differences of multiples of 10.
Lesson 4
Adding a Multiple of 10 to Any Number
The Skills section explicitly lists "Given a two-digit number, mentally find 10 more or 10 less than the number." Activity 1 has students draw number cards (1–90) and say the number that is 10 more, encouraging them to do this mentally and without materials, and asks students to explain how they got the answer (noting that the tens digit increases by 1). The Wrapping Up task has students form two-digit numbers with dice and add 10 (and then 20 and 30), reinforcing mental work with tens-place reasoning.
Lesson 5
More Practice With Adding Multiples of 10
Students draw a two-digit card and are given a held card that is a multiple of 10 (10, 20, 30, 40, or 50) and are asked to add the two numbers (e.g., draw 56 and add 30). Activity instructions and the wrapping up explicitly encourage students to use mental math to solve these addition problems and then check answers with the abacus. Activity pages and problem-solving tasks repeatedly require students to add two-digit numbers and multiples of 10 using base-10 blocks, the abacus, or mental strategies.
Lesson 6
More Addition With Two-Digit Numbers
Students are asked to add 30 to two-digit numbers (24, 42, 67) and are reminded that adding 30 is the same as adding 3 tens, then asked to explain how they arrived at each sum. The lesson's skills list explicitly includes "adding a two-digit number and a multiple of 10." The Wrapping Up asks students to create number sentences that include decompositions such as "4 + 10," showing use of tens in forming sums.
Lesson 7
Composing 10 to Add
Students are asked to read a randomly drawn two-digit number and say the next multiple of 10 (for example, 33 → 40) in the Introduction, and the Wrapping Up prompts explicitly ask students what number is 10 more and what number is 10 less. In Activity 3 ("What's Missing?") students show two-digit numbers with base-10 blocks or an abacus and find how many ones to add to reach the next multiple of 10, then write equations like 24+6=30 and explain their thinking. Activity 4 and the skills list encourage fluency without materials by asking students to progress through timed web practice levels and to work "as high as he can without having to use materials to determine the sums."
Lesson 8
More Composing 10 to Add
The Skills section explicitly lists "Given a two-digit number, mentally find 10 more or 10 less than the number." In the Introduction students draw two-digit number cards and are asked directly, "What number is 10 more?" and "What number is 10 less?", and to explain "What do you need to add to this number to get to the next multiple of 10?" The Wrapping Up prompts students to describe their thinking for problems like 57+10 and 36+20, with an example of explaining adding tens to get 90.
Lesson 9
Adding to 100
Students practice adding multiples of 10 in problems such as 56 + 10, 40 + 30, and 28 + 20 on the "Addition to 100" pages. Students use place-value mats, base-10 blocks, and an abacus to find sums and are asked to cut and glue possible sums to corresponding number sentences. Students are prompted to explain their thinking for selected problems and asked questions such as, "What do you know about what happens to the digit in the tens place when you add 10 or a multiple of 10?"
Final Project
Addition to 100 Go Fish!
Students are asked to create addition sentences that add a multiple of 10 to reach given two-digit target numbers (the Go Fish! Numbers sheet has a column "+ a multiple of 10" and examples like "6 + 10"). The instructions tell students to use base-10 blocks and the abacus to come up with the missing target numbers and addition sentences. During play, students may use base-10 blocks and the abacus to determine sums of the cards they hold.
Unit 10: Skills Review
Lesson 3
Reviewing Large Numbers
The Skills section explicitly lists "Given a two-digit number, mentally find 10 more or 10 less than the number." Activity 2 has students roll dice to create two-digit numbers and then add 1, take away 1, add 10, and take away 10, recording the results. The Student Activity Page includes specific +10 and -10 columns for students to fill in, providing direct practice computing ten more and ten less.
Lesson 4
Reviewing Addition to 100
Students practice adding a two-digit number and a multiple of 10 in Activity 1 (for example, showing 26 + 30 with base-10 blocks and finding the sum 56). The lesson explicitly tells students that when adding multiples of 10 the tens digit changes and the ones digit stays the same. The Student Activity Page contains eight addition problems in which one addend is a multiple of 10 (e.g., 33 + 40, 56 + 30, 60 + 30), giving repeated practice with adding tens.
