Second Grade - MATH
5: Math
Unit 1: Number Sense
Lesson 3
Missing Numbers
Students are asked to count by 10s to 100 and to practice counting by 5s and 10s. Students fill in missing numbers on a 10x10 number grid that displays numbers 1–100 and complete number-cluster puzzles that include sequences showing tens (for example 50, 60, 70, 80 and clusters with 88, 89, 90, 91). Students create and extend patterns that include counting by tens and place numbers in order on the 1–100 grid.
Unit 2: Addition and Subtraction/Fact Power!
Lesson 2
So Many More Ways to Add
Students use an abacus flipped to the side labeled 1000, 100, 10, and 1 and practice moving beads on the ones and tens wires. Students model 8 + 7 by counting out beads from the ones wires to make ten and then moving those ten beads while placing one bead on the tens wire, showing 10 + 5 = 15. Students also practice making 5, 10, and demonstrating 5 + 5 = 10 on the abacus, reinforcing grouping into tens.
Unit 4: Place Value I
Lesson 2
Adding to 100
Students play "Race to 100" using Cheerios as ones, pretzel sticks as tens, and a cookie to represent 100; they count pretzel sticks and determine how many tens (pretzel sticks) are needed to reach 100 (10 pretzel sticks). Students use base-10 blocks and an abacus to show and add tens (for example, showing 45 then adding two ten rods to make 65 and counting by tens on the abacus). The place value mat used in activities explicitly labels Hundreds, Tens, and Ones, and students compose tens from ones during play and exchanges.
Lesson 5
Place Value to 1000
Students are asked in Activity 1 to count 10 individual cans to make a 10-bag and 10 bags to make a 100-bag, explicitly modeling bundling 10s to make 100. In Activity 2 students are asked, "How many ten rods does it take to equal one hundred?" and are instructed to place ten ten-rods on a hundreds flat to prove it. Students also place one hundreds flat on a place-value mat, write 1 in the hundreds place and 0 in the tens and ones places, and repeat this for 200, 300, etc., reinforcing that 100 equals ten tens.
Lesson 6
More Practice With Numbers to 1000
Students use base-10 blocks to show three-digit numbers, with examples written as "6 hundred flats, 3 ten rods, 1 unit block" and representations for numbers like 999, 540, and 308. Students match images of flats, rods, and units to three-digit numbers and glue the hundreds place on the left, tens in the middle, and ones on the right. Students also use hundreds, tens, and ones place-value cards to build numbers called aloud and answer questions identifying digit values (e.g., 2 is 200, 8 is 80).
Lesson 8
Skip Counting by 10 Within 1000
In Activity 2 students use base-10 blocks to show 180, add ten rods to make 190, then add another ten rod until there are 10 ten rods in the tens place. The teacher asks "What is 10 tens equal to?" and directs students to trade 10 ten rods for 1 hundred flat, place the hundred flat in the hundreds place, and change the digits to reflect the trade. Wrapping Up also has students handle hundred flats and counts by hundreds, reinforcing the hundred as a unit built from tens.
Lesson 9
Fun With Big Numbers
Students practice skip-counting by 10s using cards (e.g., draw 60 and count up by 10s) and are reminded that the tens place increases and resets when moving beyond 100. In Activity 1 and the wrapping up task, students create and discuss three-digit numbers and state the value of each digit (for example, in 416 they identify 4 as 400 and 1 as 10). The skills list also explicitly includes understanding hundreds, tens, and ones and skip-counting by 10s and 100s.
Final Project
Place Value Think-Tac-Toe
Students represent three-digit numbers in hundreds/tens/ones form and with base-ten blocks (Three-Digit Concentration and several student pages). Students create and compare three-digit numbers using hundreds, tens, and ones (Make the Greatest!, Place Value Yahtzee, Hunting and Sequencing). Students use manipulatives like base-10 blocks and are prompted to write numbers as e.g. "3 hundreds 2 tens 4 ones," demonstrating attention to the hundreds and tens places.
Unit 5: Measurement: Length
Lesson 1
Why Do We Use Standard Measurement Units?
Students are asked to create a "Numbers to 1000 Collection" by filling blank number grids, and are told that each number grid shows 100 numbers and that 10 such grids make 1000. The Student Activity Page depicts a 10-by-10 grid of 100 squares that students use to write numbers 1–100, arranging numbers into 10 rows of 10. Students also practice counting by 100s to 1000 and counting by 10s and identifying numbers 10 more/less during the wrap-up.
Lesson 2
Inches
Students complete a 1–100 number grid and then a 101–200 grid and are asked to count up by tens from a chosen start to 200, practicing grouping by tens. Students are asked to identify the hundreds, tens, and ones digits and the value of each digit for a number between 150 and 170 and to add 20 to see the effect on the tens place. The skills list also includes "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones."
Lesson 3
Inches and Feet
Students fill 10x10 number grids to 100 (and continue to 300), and the wrap-up asks them to lay three completed 100-grids side by side and to reason that those are "3 hundreds" and how many more such grids are needed to reach 1000. The Skills list explicitly states that students should "Read and write numbers to 1000" and "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." The Introduction has students continue number grids (201–300), reinforcing counting by ones across hundreds.
Lesson 4
The Metric System, Too
Students are asked to complete a 10x10 number grid (301–400) and to stop periodically to name the hundreds, tens, and ones digits of the number they are writing. The Skills list explicitly says students will "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." The wrapping-up activity asks students to pick numbers and provide the digits and the values of those digits, which requires identifying hundreds, tens, and ones. The student activity page description also includes a 10x10 grid of 100 squares that could visually represent a group of 100.
Lesson 5
More Work With Measurement Units
The lesson includes the skill statement that students should "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." Students complete a 10-by-10 number grid (100 squares) for numbers 401–500, and the wrapping-up activity has students lay out number grids and count by 100s from 100 to 500. The wrapping-up questions also have students identify numbers that are 10 more or 10 less, which engages them with changes in the tens place.
Lesson 6
Creating With Measurement
Students write and order numbers up to 600 using number grids (writing numbers 1 through 600 and completing a grid starting at 501). Students practice counting by 10s and are prompted to count by 100s, with explicit questions about which digit changes when counting by 10s (the tens place) and which digit changes when counting by 100s (the hundreds place). Students are asked to predict successive numbers when adding 100 (e.g., identifying that 126 → 226 → 326), reinforcing the role of the hundreds digit.
Lesson 7
The Right Tools for the Job
The Skills list explicitly states students will "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." The materials include a 10x10 (100-square) number grid and ask students to lay out seven completed number grids from 1 to 700 and to count aloud from 585 to 615 while pointing to numbers. The Wrap-Up prompts students to answer place-value yes/no questions such as "Does this number have a 4 in the hundreds place?" and "Does this number have an 8 in the tens place?".
Lesson 9
Gummy Worms and Measurement Data
Students complete and lay out 10x10 number grids (each grid = 100 squares) and are asked to begin one grid at 801 and recognize it ends at 900. Students are prompted to count by 100s from 100 to 900 and to consider how many 100-grids remain to reach 1000. The wrap-up secret-number game has students ask and answer questions about the hundreds place (e.g., "Does this number have a 4 in the hundreds place?").
Lesson 10
Measurement Practice and Problem Solving
Students complete 10x10 number grids (100 squares) and count up to 1000, and they are asked to count by 10s and by 100s (examples: count by 10s from 350 to 460; count by 100s from 100 to 1000). The skills list explicitly states students should "Read and write numbers to 1000" and "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." Students lay out all 10 of their number grids and are told this shows they have written 1000 numbers.
Unit 6: Place Value II
Lesson 1
Adding Multi-Digit Numbers
Students model additions like 60 + 40 on Side 2 of the abacus, combine 6 ten-beads and 4 ten-beads to make 10 ten-beads, and are prompted to exchange those 10 ten-beads for 1 hundred bead. The text explicitly allows students to prove the exchange using base-10 blocks by exchanging 10 ten rods for 1 hundreds flat. Multiple guided examples (40+70, 80+40, 50+90, 42+80 yielding 122) and the 'Adding Over 100' practice sheet require students to perform and check these exchanges.
Lesson 3
Three-Digit Place Value Review
Students manipulate base-10 blocks and place-value cards to show three-digit numbers (e.g., 352, 781, 864) and are asked how many hundreds, tens, and ones each number has. Students write and match expanded form expressions that include hundreds (e.g., 400+80+1, 900+30+6) and use the abacus to show numbers by placing a hundred bead plus ten and one beads (e.g., showing 49 then adding a hundred bead to make 149). Students also complete activities that require reading, building, and comparing numbers based on the hundreds digit.
Lesson 4
Adding and Subtracting 10 and 100
Students use hundreds, tens, and ones place value cards and an interactive abacus to show numbers and to add and subtract by tens and hundreds. While adding 10 repeatedly, students are prompted that when the tens place goes from 9 to 10 "we go to the next hundred," and they check this by continuing to add tens until a hundred boundary is crossed. Students press "+" under the hundreds place to add 100 (counting 0, 100, 200, ... to 1000) and are asked which place changes when 100 is added or subtracted (the hundreds place).
Lesson 5
Adding Within 1000
Students model and add hundreds using base-10 blocks (e.g., showing 4 hundred flats and then adding 3 more hundred flats to make 7 hundred flats). Students solve problems like 572 + 300 while being asked which place changes and how many hundreds are being added, reinforcing that hundreds are distinct place-value bundles. Students also perform abacus exchanges explicitly (exchanging 10 ten-beads for 1 hundred-bead) when regrouping, showing the conversion between tens and hundreds.
Lesson 6
Subtracting Within 1000
Students use base-10 blocks to represent three-digit numbers (e.g., showing "5 hundred flats, 6 ten rods, and 8 unit blocks") and physically remove or add hundred flats when subtracting or adding multiples of 100 (e.g., taking away 2 hundred flats from 568 to get 368). Students complete counting-by-10s and counting-by-100s practice and are asked to attend to how the hundreds place changes when adding or subtracting multiples of 100. The Close Call game and other activities prompt students to consider the hundreds place and to use ten-rods and hundred-flats as manipulatives while making and comparing three-digit numbers.
Lesson 7
More Addition and Subtraction Practice
Students draw ones, tens, and hundreds place-value cards to create three-digit numbers and answer questions such as "How many hundreds does it have?" and "What is the value of the digit in the tens place?" Students are asked to find "100 more" and "100 less," and they may use base-10 blocks, an abacus, and a place-value mat to find sums and differences. Students play addition and subtraction games with three-digit numbers and are allowed to use manipulatives (base-10 blocks) while teachers model carrying between places.
Final Project
Traveling Adventure!
Students are asked to consider place value (the Getting Started question "How does place value work?") and to read and write numbers to 1000. Students are allowed to use base-10 blocks and a laminated place value mat as tools while they write number sentences and compute sums and differences. Students are prompted to check regrouping/borrowing ("Did you regroup (or borrow) correctly?"), which involves working across hundreds, tens, and ones.
Unit 8: Money
Lesson 1
Penny, Nickel, and Dime Review
Students are asked to count by 10s to 200 and answer questions about how the tens and ones digits change when counting by 10s (e.g., "What happens to the digit in the tens place when you count by 10 from any number?"). Students practice grouping ones into higher-value units through coin exchanges (for example, answering "How many pennies can we exchange for 1 dime?" with 10). Students count coin groups by tens and fives (counting dimes by 10s) when computing totals for mixed coins.
Lesson 2
Introducing Quarters!
Students use base-10 blocks and an abacus to represent the values of groups of quarters and to check their work (Activity 2 and Activity 3). Students determine that 1, 2, 3, and 4 quarters equal 25¢, 50¢, 75¢, and 100¢ respectively, and they are told that 100 cents is the same as one dollar. Students practice counting coin totals that sum to 100¢ (e.g., four quarters) and record those values on an activity page.
Lesson 5
Making a Dollar
Students cut out and glue coin pictures to show that 10 dimes, 20 nickels, 4 quarters, or 100 pennies make one dollar. Students are instructed to count the dimes by 10s and the nickels by 5s to prove they total 100 cents. Students also represent $1.00 on the whiteboard and show $1.25 and $1.45 using a dollar bill plus coins.
Lesson 6
Work With a Dollar and More
In Day 2 Activity 2 students are shown a one-dollar bill and a hundred flat (base-10 block) and are asked to note that both represent 100 (the dollar is 100 cents and the hundred flat is 100 unit blocks). The activity has students view two hundred flats to see that 2 dollar bills equal 200 cents and uses base-10 materials to represent 100 and 200. Students also trade coins up to a dollar and exchange coins for dollar bills, reinforcing the idea that groups of smaller units make larger amounts.
Lesson 9
Some More Practice With Money
Students count and combine coins, including half-dollars, and are asked to recognize that "two half dollars is one dollar or 100 cents." Students practice exchanging coins and bills to have as few coins as possible and create amounts using dollars and cents (for example, $3.64). Activities include dimes and other coins and instruct students to use $ and ¢ symbols appropriately, linking cents to dollar units.
Unit 10: Skills Review
Lesson 1
Reviewing Numbers to 1000
Students practice writing three-digit numbers in expanded form (e.g., 257 → 200 + 50 + 7; 431 → 400 + 30 + 1) and complete a worksheet that breaks numbers into hundreds, tens, and ones. Students mentally add and subtract 100 (e.g., identify 193 as 100 more than 93) and play ordering/comparing games that use expanded-form representations (e.g., compare 278 to 200 + 60 + 8). Students also create three-digit numbers from digit rolls, which requires placing a digit in the hundreds, tens, and ones positions.
Lesson 2
Reviewing Addition and Subtraction
Students practice skip-counting by tens and hundreds in the Introduction (e.g., count up by 10 from 30 to 120 and by 100 from 300 to 1000). Students add and subtract multiples of 10 and 100 (problems such as 300+400, 456+300, and worksheet items like 378+400) and are asked to explain which place value digit changes and why. Students are reminded that adding sometimes requires composing ten and carrying, and they may use base-10 blocks as they work.
