Students count up and back by tens on an interactive number grid and color the numbers they land on to show patterns. Students check addition sentences (e.g., 11 + 10 = 21) by counting on the grid and by manipulating an abacus, moving beads to represent tens and ones. Activities ask students to mentally add or subtract 10 from two-digit numbers and to solve contextual problems by adding or subtracting tens.

The lesson's Skills list specifies that students will mentally add 10 or 100 to a given number 100–900 and mentally subtract 10 or 100 from a given number 100–900. The Photo Journal project asks students to create photographs and captions that demonstrate counting by 10s and number patterns. Students are directed to use correct mathematical language in captions and to explain choices as they work. The project also has students sort and label examples of greater than/less than and odd/even, which involve number relationships tied to place value concepts.

Students practice addition using number lines, drawings, counters, arrays, and an abacus (e.g., showing 4+3 on a number line, drawing 4 dogs then 3 more, and modeling sums with counters). Students explore the commutative property by comparing 3+4 and 4+3 with dice, dominoes, and a worksheet that has them record turn-around facts. Students use the abacus with a 1s and 10s side to combine 8+7 and 6+8, explicitly making a group of ten and moving a bead to the tens place, demonstrating place-value-based regrouping.

The Skills section explicitly lists explaining why addition and subtraction strategies work, using place value and properties of operations. Students are asked to use multiple strategies (number line, counters, abacus, fingers, pictures) to solve subtraction problems and to try out and compare at least two approaches. Students are prompted to reflect verbally and in writing (e.g., "Which way do you prefer to solve subtraction problems? Why?" and "Which difference was the most difficult to find? Why?") and to do place-value tasks such as naming 10 more and 10 less.

Students model and explain the identity/zero property using counters (e.g., showing 5 + 0 and 5 - 0 with counters and explaining why the total stays the same) and complete a "Working with Zero" sheet. Students explain and apply the commutative (turn-around) property when reasoning that 7 + 8 and 8 + 7 both equal 15 and practice doubles and doubles-plus-one strategies with cards and foldables. Students use an abacus and decomposition into fives to show how sums like 6 + 7 make 10 + 3 and play games and activities (dominoes, Circles of Ten) that build forming tens and composing numbers to 10.

Students use dominoes to write two addition sentences (2 + 3 = 5 and 3 + 2 = 5) and are told this proves the commutative property of addition. Students generate the four-number-sentence fact families (two additions and two subtractions) for given triples (e.g., 2, 3, 5) and write the corresponding equations on a sheet. Students make and use triangular fact-family cards, cover a number, and deduce the missing number, and they practice strategies named in the materials (doubles, doubles plus one, making 10s, zero) on timed "Fact Power" worksheets and matching games.

Students generate all addition sentences that sum to 5 and are prompted to consider what 0 does to 5 and to notice "turn-around facts," which highlights the identity and commutative properties. The activity asks students to use more than two addends and notes that order does not matter in those columns, which engages students with associative ideas. Students also solve one- and two-step word problems (A Day at the Fair) and represent problems with drawings and equations, practicing addition and subtraction in context.

In the Introduction, students practice additional addition and subtraction flashcards and are reminded of specific strategies including the turn-around (commutative) property, doubles, doubles plus one/two, fact families, and making 10. Students are asked which flashcards correspond to these strategies and are encouraged to sort the flashcards by strategy and practice the facts with those strategies in mind.

Students read and produce examples of named addition properties and strategies (the zero property, the commutative property, doubles, doubles plus one, making 10s, and fact families). Students model adding multiples of 10 and two-digit addition with base-10 blocks and an abacus and are explicitly asked to explain why the ones place stays the same when adding a multiple of 10 and why adding tens is like adding ones. Students practice composing 10 and regrouping (e.g., circling 10 ones to form a ten, using the place-value mat in Race to 100, and performing vertical addition with carrying such as 28+17) and check answers with manipulatives.

Students are prompted to use an abacus and base-10 blocks to add by ‘‘taking and giving'' to make ten (e.g., transforming 9+6 into 10+5 and 59+3 into 60+2). The text explicitly asks students to explain what they are doing as they move beads and to talk aloud while using the nine- and eight-tricks. The lesson also names and uses the commutative property (turn-around facts) when showing 4+9 = 9+4 and asks students to write intermediate steps (e.g., 10+4) to show their thinking.

Students are asked to explain subtraction examples and name which strategies they used (e.g., after completing the "Using Subtraction Strategies" sheet they are asked, "Which strategies did you use?"). Students use and manipulate base-10 blocks and an abacus to subtract tens and two-digit numbers and are asked specific place-value questions such as, "What happens to the digit in the tens place when you subtract 10 from a number?". Students discuss the role of zero with the prompt, "Why does the number stay the same when we subtract zero from it?", and they practice subtracting ones and tens while aligning digits and explaining each step (e.g., subtracting ones then tens for 57-22).

Students represent three-digit numbers with hundreds flats, ten rods, and unit blocks and decompose/recompose numbers (for example, showing 358 as 300 + 50 + 8). Students use manipulatives to decide whether vertical subtraction sentences are true or false and are given addition and subtraction problems to solve (35+14 and 76-25). Students practice counting and grouping by tens and hundreds (bundling 10s to make 100 and 10 hundreds to make 1000).

Students create addition sentences from drawn number cards and are told they can compute answers using materials or strategies of their choosing (Introduction and Wrapping Up). The lesson has students represent three-digit numbers with base-ten blocks and place-value cards (Activity 1 and Activity 2) and asks students to identify the value of digits (Activity 4). The introduction explicitly reminds students that the order of addends does not matter, pointing to the commutative property of addition.

Students count up and back by tens on the Number Grid 101–200 and fill in missing numbers, repeatedly noting that the digit in the tens place increases or decreases by one. Students use base-10 blocks on a place-value mat to build numbers (e.g., 180), add a ten-rod to make 190, and then add another ten-rod and trade ten tens for one hundred to make 200. Students are asked to identify resulting numbers, circle them on the grid, and write sequences (e.g., 180, 190, 200, 210), linking the manipulative trade to the change in written digits.

Students practice two-digit addition and subtraction in Row 3 activities (Dicey Two-Digit Addition and Subtraction, Close Call: Two-Digit Addition, Close Call: Two-Digit Subtraction) where they create and compute sums and differences. The materials explicitly allow use of base-10 blocks and other manipulatives so students can work with place value representations. Directions prompt adults to model strategies aloud (for example, describing carrying in ones place) and remind students about arranging larger digits first for subtraction. The wrap-up asks students to describe their "favorite tricks for adding and subtracting two-digit numbers," prompting reflection on strategies.

Students create 1–100 number grids and are asked to count by 100s to 1000, with the teacher prompting that 10 number grids are needed because there are 10 hundreds in 1000. Students are asked to identify numbers that are 10 more or 10 less than a given number and to find numbers 20 more and 40 more than given numbers. Students practice counting by 10s (starting at 4) and by 5s, which engages with place-value based increments.

Students complete number grids from 1–100 and 101–200 and count up and down by tens from chosen starting numbers, practicing grouping by tens. Students identify the hundreds, tens, and ones digits of a three-digit number and state the value of each digit. Students compute a simple addition of tens when asked, "If you add 20 to this number, what number will you have?"

The Introduction directs the student to complete a number grid from 301 to 400 and asks questions such as which digits are in the hundreds, tens, and ones places. The Skills section explicitly lists understanding that the three digits of a three-digit number represent amounts of hundreds, tens, and ones and reading/writing numbers to 1000. The Wrapping Up asks the student to solve vertical addition and subtraction problems (34+25, 76-23, 56+18, 98-83) using strategies and methods of her choosing.

The Skills section explicitly states students will "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." The Wrapping Up prompts have students count by 100s and answer specific questions asking for the number 1 more, 1 less, 10 more, and 10 less than given numbers (e.g., "Can you point to the number that is 10 more than 295? (305)"). Students also complete number grids (writing numbers to 500 and up toward 1000) and point to and identify numbers on those grids.

Students count by 10s and 100s from given numbers and are asked which digit changes when counting by tens or hundreds, linking counting behavior to the hundreds/tens/ones places. The lesson has students write numbers to 600 and explicitly states that the three digits of a three-digit number represent hundreds, tens, and ones. Students are given vertical addition and subtraction problems (89-17, 56-24, 29+55, 36+45) and told to use strategies and materials of their choosing to find sums and differences.

Students measure lengths and then compute differences by subtracting the before/after measurements (Activity 2), using tools such as a whiteboard, abacus, and counters to find differences. The Skills list explicitly includes using addition and subtraction within 100 to solve word problems and understanding that three-digit numbers represent hundreds, tens, and ones. The secret number game has students identify digits in the hundreds and tens places, reinforcing place value understanding.

Students write number sentences and find sums or differences for measurement word problems within 100 (Activity 2 and provided answer key). Students are encouraged to draw pictures and use counters or an abacus to solve problems, supporting place-value-based procedures. Students practice reading and writing numbers to 1000 and learn that three-digit numbers represent hundreds, tens, and ones (Skills and Wrapping Up).

Students are asked to tell how they found each sum or difference and to describe what strategies or tricks helped them find the answers, prompting explanation. Students model numbers on an abacus and base-10 blocks and are guided to exchange 10 tens for 1 hundred, explicitly linking place-value exchanges to sums (e.g., 60+40=100 and 42+80=122). Students use expanded form and are asked to use or name the Commutative Property (turn-around facts) when finding sums and are prompted to break numbers apart (e.g., 35+23 = 35+20+3) to show why strategies work.

Students are prompted to describe aloud how to subtract and to begin with the ones place, and they model borrowing by trading one ten rod for ten unit blocks using a place-value mat. Students practice crossing out and rewriting digits to show borrowing on paper and are asked to model and explain that process with base-10 blocks. Students use fact families (e.g., 4, 6, 10) and addition sentences to check subtraction work, explicitly connecting subtraction to addition as an inverse relationship.

Students use an interactive abacus to add and subtract 10 and 100 while being asked to explain transitions (e.g., why 105 is 10 more than 95 because the tens place goes from 9 to 10). Students are prompted to notice which place changes when adding or subtracting 100 and to explain how they know (the hundreds place goes up or down by 1). Students complete a table of given numbers with +10, +100, -10, and -100 and write number sentences, checking their work with the abacus.

Students model adding hundreds with base-10 blocks and are asked to identify which place is changing (e.g., 572 + 300 keeps tens and ones the same and only the hundreds place changes). Students use the abacus and exchange 10 ones for a ten and 10 tens for a hundred while finding sums, and are asked questions such as "Why did you have to compose 10 and regroup?" to elicit explanation. Students use expanded form (300+20+1 + 400+30+4) and are prompted to describe digit values and the steps in place-value addition while teachers model think-aloud strategies.

Students are asked to explain how to add and subtract multiples of 100 in their own words and to justify that only the hundreds place changes when adding or subtracting hundreds. Students use base-10 blocks and a laminated place-value mat to model three-digit subtraction problems (including borrowing) and are prompted to explain why no borrowing was needed when each digit in the minuend is larger. Students are prompted during games and activities to consider and discuss strategies that focus on aligning digits by place value and minimizing differences in the hundreds place.

Students draw place-value cards and answer questions about hundreds, tens value, and what is 10/100 more or less, which engages place-value reasoning. In the Close Call addition game, students form three-digit numbers, use base-10 blocks/abacus/place-value mats to compute sums, and are instructed to hear an adult talk aloud about strategies (for example, ‘‘I need to begin adding here in the ones place, and I'll need to carry to the tens place because the numbers here in the ones place add up to more than nine''). The subtraction version directs students to arrange larger numbers in the ones and tens places and to use manipulatives and strategy talk to find differences.

Students choose whether to add or subtract, write number sentences, and compute sums or differences for travel-distance problems. Students are allowed to use an abacus, base-10 blocks, and a laminated place-value mat while solving problems. Prompts ask students to explain decision-making (e.g., "What about this question makes you think you need to add or subtract?" and "How did you decide which numbers to work with?") and to check regrouping/borrowing.

Students complete an "Addition and Subtraction Practice" worksheet with multi-digit problems (e.g., 456+368, 962-746, 788+104) and check answers with a calculator. The teacher notes instruct students to use mental math, manipulatives as needed, and to "compose 10/regroup and borrow" and to "line up the places correctly." Students also play addition/subtraction games (Amusement Park Addition, Snowball Smash) to practice the operations.

Activity 2 (Swimming!) requires students to add and compare minute amounts (e.g., "How long altogether did Karen, Greg, and Ally swim laps? (50 minutes)" and "How much longer did Emmy swim laps than Scott? (15 minutes)"). The directions explicitly allow students to use manipulatives such as an abacus or base-10 blocks and a whiteboard to compute answers. Activity 1 asks students to order activities by duration and to "explain her thinking" when choosing which activities take more or less time.

Students list and demonstrate concrete combinations that make an hour (1 hour; 2 half hours; 4 quarter hours; 1 half hour and 2 quarter hours) and use a geared clock to test these decompositions. Students place activity cards labeled with durations of 1 hour, 30 minutes, or 15 minutes into hourly schedule blocks, pair 30-minute activities, and group 15-minute activities to create half-hours and hours. Students are asked to explain their thinking and to "prove" that the activities in each hour block add up to an hour.

Students practice counting by 10s and 5s and are asked questions about what happens to the tens and ones digits when counting by 10s. Students count coin collections by first counting the highest-value coins (dimes by 10s, nickels by 5s, pennies by 1s) and write each partial amount as they go. Students make and justify equal-value exchanges (5 pennies = 1 nickel, 2 nickels = 1 dime, 10 pennies = 1 dime) and are prompted to trade coins to use the smallest number of coins.

Students model grouping and place value when they exchange 5 pennies for a nickel and 10 cents for a dime during the Penny, Nickel, Dime Exchange Game. Students use base-10 blocks to show the value of a quarter in more than one way and use an abacus to check values for 1–4 quarters. Students count by 5s and 10s to add coin amounts and complete vertical addition and subtraction problems within 1000 using methods and materials of their choosing.

Students are asked to mentally add and subtract multiples of 100 (e.g., 356+400, 742-300, 829-100) and are reminded to "think about what's happening to the hundreds place," which prompts place-value reasoning. The Skills list explicitly includes "Mentally add 100 to a given number 100-900 and mentally subtract 100 from a given number 100-900." Students also practice exchanging pennies for nickels, dimes, and quarters (e.g., exchanging at 25¢, 50¢, 100¢), which requires grouping and place-value-like thinking about amounts.

Students add coin values in multiple activities (Which Path?, Sticker Shopping, Counting Money Game) by totaling series of pennies, nickels, dimes, and quarters to reach specified cent amounts. Students draw and exchange coins to make given totals in the "What's in My Wallet?" riddles, using equivalence of coin combinations to represent the same value. Students write vertical number sentences (618+355, 654-246) and use chosen methods and materials to compute sums and differences.

Students count groups of coins by place-value units (count the dimes by 10s and the nickels by 5s) to show they total 100 cents. Students represent amounts with dollar and cent notation (e.g., $1.25 = 1 dollar and 25 cents) and place the dollar amount before the decimal and cents after. Students compose amounts in multiple ways (show $1.00 with different coin combinations) and match pictured collections of bills and coins to written dollar amounts, which requires adding coin values.

Students connect a dollar bill to 100 cents by comparing a dollar bill with a hundred flat, explicitly linking money to base-10 place value. In the Rolling to Two Dollars game, students add coin values and repeatedly exchange coins for larger units (e.g., trading 100 cents for a dollar or exchanging smaller coins for a quarter) while aiming to minimize the number of coins. Activity directions ask students to count bills first and count coins starting with the highest values and include prompts (e.g., advice to count by 10s and 5s) that surface strategic approaches to adding coin amounts.

Students play a money-exchange game in which they collect pennies and exchange them for larger coins and bills so they always have as few coins as possible, practicing composing smaller units into larger ones. Students count half-dollars and are prompted to pair them to make dollars (e.g., two half-dollars = $1) and to reason that an extra half adds 50 cents. Students create amounts from dice rolls (e.g., $3.64) and represent those amounts with bills and coins, practicing combining place-based money units to form totals.

Students are asked to mentally add and subtract 10 and 100 to and from given numbers (Skills and Introduction questions asking which number is 10/100 more or less than a given number). Students convert three-digit numbers into expanded form, breaking numbers into hundreds, tens, and ones (Activity 1 and the expanded-form practice sheet). Students compare and order numbers up to 1000, sometimes using expanded form to reason about magnitude (Activity 2 and the comparing numbers practice).

Students are asked to explain what is happening in problems like 30+40 and 300+400 and to identify which place value changes in 456+30 versus 456+300. They are prompted to explain the role that zero plays in addition and subtraction and to explain which digits change in subtraction examples such as 548-20 and 548-200. Students use base-10 blocks if needed, practice composing ten/carry and borrowing, and line up digits when adding and subtracting within 1000.