Second Grade - MATH
5: Math
Unit 1: Number Sense
Lesson 4
The Power of 10
Students solve contextual word problems that require adding repeated tens (e.g., Kevin reading 10 books per month through April = 40 books; Steffi adding 10 minutes per week for 3 or 5 weeks = 30, 50 minutes). Students also work variant problems that require a two-step addition (e.g., Kevin reads 6 in January then 10 each month after, totaling 56 through June; Steffi starts with 8 minutes then adds 10 each week totaling 38 or 58 minutes). Students are directed to use number grids, an abacus, drawings, and written work to show their counting and calculations when finding answers.
Unit 2: Addition and Subtraction/Fact Power!
Lesson 1
Using Arrays to Add
Students create and name arrays and draw them on grid paper, using counters, sticky notes, and dice to represent rows and columns. Students write repeated-addition equations to express totals for arrays (e.g., 3+3+3+3 = 12 and 6+6 = 12) and complete worksheets that ask for two number sentences per array. Students explain what an array is and write number sentences to match drawn arrays during Activities 1, 2, and 4.
Lesson 2
So Many More Ways to Add
Students practice adding numbers using multiple representations (number lines, pictures, counters, abacus) when they show and solve addition sentences such as 4 + 3 = 7 and create number collections for 9 and 15. Students write number sentences for real-world counts (e.g., chairs in rooms, pictures on walls) and draw stories to represent adding-to/putting-together situations (Lucy had 4 dogs and then got 3 more). Students work with one- and two-digit addends on number-line problems (e.g., 6 + 10, 8 + 12) and record equations from dice rolls, reinforcing addition within 20 and beyond.
Lesson 3
Problem Solving with Addition
Students repeatedly add amounts from a menu (Activity 1 and Day 3) and find totals within a $20–$30 limit, writing number sentences such as 3+5, 4+2, and 6+3. On Day 2 students solve the "Clues to Addition" word problems by writing completed number sentences (e.g., 6+7=13) and are encouraged to use drawings, tally marks, counters, or an abacus. Activity 4 presents missing-addend equations (2 + ___ = 5) and menu problems where students find the unknown item given a total (e.g., 7+6+?=15), and Activity 5 (Option 2) has students determine missing addends during the beanbag game. Activity 6 has students write addition number sentences horizontally and vertically, reinforcing equation representation with blanks for unknowns.
Lesson 4
Time to Subtract!
Students solve one-step subtraction problems within 100 on activity pages (e.g., 18-7, 22-10, 18-6, 15-9, 15-4) using objects, number lines, and fingers. Students write subtraction number sentences horizontally and vertically (Activity 4) and use manipulatives (counters, abacus) to show differences. Students apply subtraction to real contexts by comparing guesses to actual counts in "Subtraction in the Kitchen" and by listening to subtraction sentences and finding the matching difference in the Bowling for Differences game.
Lesson 5
Problem Solving with Subtraction
Students solve one- and two-step subtraction word problems (e.g., the donut problem: 12 - 8 = 4 and 4 - 2 = 2) and write completed number sentences for each problem. Students use and are asked to try different strategies (fingers, drawings, counters, number line) and to write subtraction number sentences for menu problems. Students create their own subtraction word problems from given number sentences and revise them if they are not answerable.
Lesson 6
Tricks to Build Fact Power
Students practice addition and subtraction facts within the lesson (fluency within 20, examples up to 22) using flashcards, dominoes, and timed drills. Students model number sentences with counters and an abacus (e.g., 4 − 4 with counters; breaking 6+7 into 5+1 and 5+2 on an abacus) and draw a picture to represent one of the equations on the "Working With Zero" page. Students are asked to make up simple word problems that include zero (e.g., Rover barked 8 times yesterday and 0 times today), and they play games that require using addition or subtraction to make 10 (which practices solving for missing addends).
Lesson 8
Adding and Subtracting to Solve Problems
Students solve one- and two-step word problems in the 'A Day at the Fair' activities where they add and subtract ticket costs (e.g., find total cost of a game and a ride, determine leftover tickets after purchases). The Option 2 problems include comparison questions ("Which costs more... How many more tickets?") and multi-step scenarios that require organizing thinking and using addition/subtraction within 20. Activities also provide practice with mental computation and fluency (Fact Power, Brain vs. Calculator) that supports solving the word problems.
Final Project
Mathematical Ocean Adventure
Students are asked (in the Skills list) to use addition and subtraction within 100 to solve one- and two-step word problems. Students complete timed "Fact Power" worksheets that require many addition and subtraction calculations, giving practice with fluency. Students create a Mathematical Ocean Adventure story in which they must include two addition problems, two subtraction problems, an array, show math in mathematical language (e.g., 3+5=8), and write answers on an answer page.
Unit 3: Geometry
Lesson 5
Shaping Up!
Students use tally marks on the Shape Scavenger Hunt to record counts and write totals for each shape. Students answer direct addition questions such as "How many triangles and circles did you find altogether?" and comparison/subtraction questions such as "What's the difference between the number of squares and the number of rectangles that you found?". Students combine specified numbers of shapes when challenged to create pictures that include e.g., two squares and four triangles, requiring them to add counts.
Unit 4: Place Value I
Lesson 6
More Practice With Numbers to 1000
Students pick two number cards (1–50), write addition sentences (e.g., 34+15 and 15+34), and find the sums using chosen strategies, which practices addition within 100. Students practice subtracting within 100 when asked to find differences (39-26, 15-4, 48-44). Skills and activities explicitly require adding and subtracting two-digit numbers and using base-10 blocks or place-value cards to represent numbers.
Unit 5: Measurement: Length
Lesson 1
Why Do We Use Standard Measurement Units?
Students practice adding and subtracting within 100 when they are asked to point to numbers that are 10 more or 10 less than a given number and to find numbers that are 20 or 40 more than a given number. Students write numbers 1–100 on a number grid and count by 5s and 10s, reinforcing place-value reasoning used in these addition and subtraction tasks. The measurement activities prompt students to compare lengths and discuss differences in measurements, which could involve thinking about numerical differences.
Lesson 2
Inches
Students measure and compare lengths in inches, identifying inches, feet, and yards and using a ruler to record measurements. Students put two pieces of straw together to show 9 inches and answer questions like "How long will this line be if I add another inch?" and "How long will this line be if I erase one inch from it?", which involve adding to and taking from. Students answer comparison questions (e.g., which is longer, an inch or a foot; is a yard longer or shorter than an inch), practicing comparing quantities.
Lesson 6
Creating With Measurement
Students are given four vertical number sentences within 100 (89 - 17, 56 - 24, 29 + 55, 36 + 45) and told to use strategies and materials of their choosing to find the sums and differences. These tasks require students to practice addition and subtraction with numbers less than 100. The lesson also includes counting and number-grid activities that reinforce place-value and counting by tens and hundreds.
Lesson 8
Comparing Lengths
The Skills list explicitly states students should "Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units." In the Kitchen Measurement activity students measure items, identify the longest and shortest, and are asked to "calculate the difference in length" and "write a subtraction sentence and calculate the difference." In the Comparing Ribbons activity students measure two pieces and write subtraction sentences such as "9 in. - 7 in. = 2 in." to find differences.
Lesson 9
Gummy Worms and Measurement Data
The lesson's Skills list explicitly states students should "Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units." In Activity 2, students measure gummy worms, record lengths before and after stretching, and compute the "Difference in Lengths," with the teacher asking "Do we add or subtract to find differences?" and providing a whiteboard, abacus, and counters for students to perform subtraction. Activity 4 has students measure lines in inches and plot those measurements, keeping values that are small and well within 100.
Lesson 10
Measurement Practice and Problem Solving
The Skills list explicitly states students will "Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units." Activity 2 asks students to write number sentences and find sums or differences and invites them to draw pictures and use counters or an abacus. The Measurement Problems and answer key provide multiple one-step measurement word problems within 100 (e.g., 3+6=9; 4+6=10; 11-5=6; 15-8=7; 29-26=3; 1+2+3=6) that require students to add or subtract lengths and label units.
Unit 6: Place Value II
Final Project
Traveling Adventure!
Students read a map with labeled distances and answer travel word problems that require them to decide whether to add or subtract, write a number sentence, and compute the result. Students solve one- and two-step problems that add multiple legs of a trip (e.g., adding three segment distances to find total miles) and solve comparison problems that ask for differences between two routes. Students record operations in a "+ or -" column, write number sentences, label answers with "miles," and may use manipulatives or paper methods to calculate.
Unit 7: Telling Time
Lesson 3
Units of Time
Students complete an "Addition and Subtraction Practice" worksheet containing multiple addition and subtraction problems (e.g., 67 + 75, 91 - 78, 456 + 368) and are instructed to use mental math, regrouping, and borrowing. The Skills section lists "Add and subtract within 1000," and Activity 3 points students to an online game where they can practice subtracting a 2-digit number from a 2-digit number. Students are also told to check answers with a calculator, reinforcing computational practice.
Lesson 8
Time Problem Solving
Students answer the Swimming! problems that ask them to add lap times (e.g., "How long altogether did Karen, Greg, and Ally swim laps?") and to subtract durations (e.g., "How much longer did Emmy swim laps than Scott?"). The swim table gives start times and lap durations all under 100 minutes, and students are asked to compare durations (who swam longest/shortest, who swam more than half an hour). Activity 1 has students order and match activities to time amounts (5, 15, 30, 60 minutes), reinforcing comparisons and unit relationships.
Final Project
Making a Schedule
Students cut out activity boxes labeled with times (1 hour, 30 minutes, 15 minutes) and place them into hourly schedule blocks, explicitly combining two 30-minute activities or four 15-minute activities to make one hour. Students are prompted to refer to a written list of "ways to make an hour" and to answer questions such as which 30-minute activities were paired to create an hour and which 15-minute activities made a half hour. Students are asked to check and "prove" that the activities in each hour block add up to an hour before gluing them down.
Unit 8: Money
Lesson 1
Penny, Nickel, and Dime Review
Students count groups of pennies, nickels, and dimes to determine totals (Activity 2 asks them to write amounts such as 44¢, 56¢, 63¢). Students make amounts using coins and compare amounts (Activity 1 asks which plate has the most/smallest and which plates can buy a named amount). Students draw coin representations for given amounts on the activity sheet, using drawings to show different ways to make the same total (Activity 3).
Lesson 2
Introducing Quarters!
Students add coin values to find totals in multiple activities: they match groups of coins to written cent amounts (e.g., 1 quarter + 1 dime + 3 pennies = 38¢) and cut/glue values for 1–4 quarters (25¢, 50¢, 75¢, 100¢). In the Penny, Nickel, Dime Exchange Game, students roll, collect pennies, count totals, and exchange coins as they work to reach 25 cents, practicing repeated addition within 100. The lesson's skills list explicitly states students will "Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies," indicating an intention to use addition/subtraction in money contexts.
Lesson 3
More Practice With Coins
The Skills section explicitly states that students will "Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies," and several activities require students to compute coin values (Activity 3: cut out groups of coins, figure the value, and match equivalent amounts). In Activity 2 and the Wrapping Up, students assemble given cent amounts using coins (e.g., make 99¢ with specific coins), and the Exchange Game has students add collected pennies and exchange to reach 100 cents, requiring repeated addition within 100.
Lesson 4
Fun With Money
Students add coin values to find totals in multiple activities: in "Which Path?" they compute the value of coin sequences to match amounts like 87¢, 68¢, 54¢, and 71¢. In "Sticker Shopping" students count each person's coins and match them to sticker prices (e.g., 78¢, 86¢, 98¢). In "What's in My Wallet?" students draw coins and use guess-and-check to find combinations of a given number of coins that total amounts under a dollar (e.g., 4 coins total 60¢).
Lesson 6
Work With a Dollar and More
Students count and combine coin and bill values in multiple activities (e.g., writing amounts like $1.28, identifying 75¢ and $1.43 in boxes, and completing 'Counting Dollars and Cents' problems). Students play a game where they roll to collect cents and trade up to larger coins and dollar bills, accumulating totals toward $2 (practicing repeated addition of cent amounts). The lesson's skills list explicitly states students will "Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies," indicating an intent to apply addition/subtraction with money.
Lesson 7
Money Problem Solving
Students roll dice to create two-digit cent amounts, write the smaller and larger amounts in cents, and compute "how much more" to go from one to the other (Activity 3). Several examples use cent amounts like 34¢ to 82¢ and 30¢ to 72¢, requiring subtraction within 100. The wallet riddles and coin-exchange activities ask students to make or decompose monetary totals and to show equivalent amounts, which has students add and subtract coin values and reason about unknown compositions.
Lesson 8
Time to Shop!
Students write amounts in dollar notation and show those amounts using bills and coins (e.g., $5.31, $2.52, $3.17, $10.34) during the introduction and wrap-up. Students find and record prices for real grocery items and categorize them as less than or more than $3, then answer questions about which items are most and least expensive. Students play the "Do You Have Enough Money?" game for two rounds, answering 10 questions about whether they have enough money to buy items and practice showing amounts in different ways.
Final Project
A Cereal Box About Money
The Skills section explicitly states that students will "Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately." Suggested activities include "What's in My Wallet? riddles," a matching game that pairs collections of coins with their amounts, and a game matching objects with the person who bought each one based on cost. The Project Coins and Bills sheet provides specific counts of bills and coins for students to use, and students cut out or draw coins/bills to show money amounts on their index cards and cereal box.
Unit 9: Data and Graphing
Lesson 2
Pictographs
Students answer put-together and compare questions using data from pictographs and tally charts (e.g., "How many people like to watch tennis and soccer the most?" and "What's the difference between how many people like to watch swimming and how many like to watch soccer?"). The Furniture Pictograph activity asks students to count items and compute totals and differences (e.g., "How many tables and chairs in all?", "How many more chairs than beds?"). The Skills section explicitly states students will "Solve simple put-together, take-apart, and compare problems using information presented in a bar graph," and activities require counting symbols that represent numbers (including symbols representing tens).
Lesson 3
Bar Graphs
The lesson's Skills list explicitly states that students will "solve simple put-together, take-apart, and compare problems using information presented in a bar graph." Multiple activities ask students to read values and compare quantities from bar graphs (e.g., identify which ice cream flavor the greatest/fewest people like, determine how many people liked classical music—20, and see that rock is between 50 and 60). Activity 4 requires students to fill in a missing value (Science Fiction) and plot numerical data on a bar graph, which engages students with numeric information from graphs.
Lesson 4
Line Plots
Students read and interpret a dot/line plot showing counts of pets and answer questions that require comparing categories (e.g., which pet is greatest/fewest) and totaling categories (e.g., "How many birds and fish do students in this class own? (5)"). Students measure line segments in centimeters, record numeric measurements, and mark Xs on a line plot to show frequency counts, which requires counting and aggregating measured values. The Measurement Line Plot answer key shows aggregated counts above each number (e.g., stacks of Xs), providing practice with summing counts.
Lesson 5
More Graphing Practice
Students count letters in names, record tally marks, and write totals in a chart, practicing counting and combining counts. Students construct bar graphs and pictographs from collected data and answer questions such as "How many names have three letters?" and "How many windy days were there?", practicing reading quantities from graphs. Students are asked (in the skills list and questions) to solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
Lesson 6
Some Problem Solving
The lesson includes a skills statement that says students should "Solve simple put-together, take-apart, and compare problems using information presented in a bar graph." In Activity 1 students use the "Cupcakes Sold in a Day" bar graph to create word problems that match given answers (e.g., create a question whose answer is 12), and in Activity 2 students place items on a bar graph and answer questions about the graph.
Final Project
My Book of Graphs
The lesson asks students to collect data, create bar graphs, and includes the skill: "Solve simple put-together, take-apart, and compare problems using information presented in a bar graph." Step 4 and Step 6 instruct students to label axes with numbers and decide on counting intervals (1s, 2s, 5s), which has students work with numeric values on bar graphs. Step 9 prompts students to answer comparison questions such as "What does this graph show the most of?" and "What does this group show the least of?"
