HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 1

Unit 1: Number Sense

Students practice mentally adding and subtracting tens and hundreds (skills bullet: mentally add 10 or 100 to a given number 100-900 and subtract 10 or 100). Students repeatedly count up and back by 10 from various two-digit numbers using an interactive number grid and complete worksheets that require writing the results. Students use a concrete model (abacus) to show adding 10 (the 11 + 10 example describes moving beads across place-value rows) and they color number patterns to make place-value patterns visible.
Students are asked to count within 1000 and skip-count by 5s, 10s, and 100s as listed in the Skills section. Students are asked to mentally add 10 or 100 to and mentally subtract 10 or 100 from numbers 100–900. The photo-journal tasks require students to demonstrate counting by 10s and to use correct mathematical language in captions, supporting some place-value reasoning.
Unit 2

Unit 2: Addition and Subtraction/Fact Power!

Students use concrete models and drawings to add (number lines, counters, pictures, arrays, dice, dominoes). Students use an abacus and are asked to flip it to the side labeled 1000, 100, 10, and 1 and to model sums that require composing tens (for example, showing 8 + 7 by grouping ten ones and moving one bead to the tens wire). Students write number sentences and use the commutative property activities to relate concrete actions to written equations.
Students practice subtraction word problems using drawings, counters, fingers, and number lines and are asked to write completed number sentences for each problem. Students create their own subtraction word problems from given number sentences and use subtraction clue words to decide when to subtract. Students solve contextual subtraction problems with numbers up to the tens and use simple monetary examples (e.g., $18, $10) and are prompted to record equations that represent their strategies.
Unit 4

Unit 4: Place Value I

Students use concrete models (base-10 blocks, abacus, place-value mat, and manipulatives like Cheerios and pretzel sticks) to represent numbers and to compose tens when adding. Students practice strategies based on place value and properties of operations (making tens, doubles, commutative property) in mental-addition activities and apply them to two-digit problems. Students relate those strategies to a written method by performing vertical addition (e.g., 28 + 17), showing regrouping and writing the carried 1 over the tens place.
Students model subtraction with concrete tools (base-10 blocks and an abacus) for problems such as 35 - 10, 49 - 5, and 57 - 22, showing tens and ones and removing tens or unit blocks. Students use number lines and counting strategies (counting back, counting up) and practice role-of-zero, neighbors, half facts, and other subtraction strategies on worksheets. Students are shown a written vertical method and directed to line up tens and ones and subtract the ones place then the tens place (the 57 - 22 example is stepped through in writing).
Students use a laminated place-value mat and base-10 blocks to build three-digit numbers (e.g., show 180, add a ten rod to make 190, then trade 10 ten rods for 1 hundred flat to make 200). Students count up and back by tens and hundreds on a 101–200 number grid and fill in missing numbers by moving tens and hundreds (e.g., counting 110, 120, …, 200 and writing sequences such as 180, 190, 200, 210). Students practice composing tens into a hundred concretely when they discover 10 ten rods equal 1 hundred flat and adjust the digits on the mat accordingly.
Unit 5

Unit 5: Measurement: Length

Students practice reading and writing numbers to 1000 and create number grids, including counting by hundreds to reach 1000. Students use the 1–100 number grid to count by 10s and 5s and to answer questions such as finding the number 10 more or 10 less than a given number and finding numbers 20 or 40 more than a given number. The activities require students to identify place-value relationships (e.g., ‘‘10 more than 63'' → 73) on the number grid.
Students practice counting and filling number grids up to 300 and are asked to extend that understanding to 1000 by determining how many more hundreds are needed, showing work with hundreds blocks of numbers. The skills list explicitly requires students to "Read and write numbers to 1000" and to "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." In the Wrapping Up section, students identify specific three-digit numbers from clues about the hundreds, tens, and ones places, demonstrating place-value identification.
The Skills section asks students to read and write numbers to 1000 and to understand that the three digits of a three-digit number represent hundreds, tens, and ones. The Introduction has students complete a number grid from 301 to 400 and prompts them to name the digits, identify the hundreds/tens/ones places, and describe number features. The Wrapping Up asks students to solve vertical addition and subtraction problems (e.g., 34+25, 76-23), giving some practice with written computation format.
Students complete number grids (e.g., 401–500) and are asked to count by hundreds from 100 to 500, showing facility with hundreds, tens, and ones. In the Wrapping Up students identify numbers that are 1 more, 1 less, 10 more, and 10 less (for example, 10 more than 295 = 305), which requires adding or subtracting tens and ones across a hundreds boundary. The Skills list explicitly states students will read and write numbers to 1000 and understand that three-digit numbers represent hundreds, tens, and ones.
Students are asked to write numbers to 600 and the skills list explicitly includes reading and writing numbers to 1000 and understanding that three digits represent hundreds, tens, and ones. Students practice counting by 100s using examples such as predicting that 226 and 326 follow 126, reinforcing place-value changes in the hundreds and tens places. 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.
The Skills section instructs students to "Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units," and Activities 1 and 2 require students to write subtraction sentences (e.g., "9 in. - 7 in. = 2 in."). The Skills and Wrapping Up sections ask students to "Read and write numbers to 1000" and to "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones," and the secret-number game has students ask and answer place-value questions about three-digit numbers. The Introduction has students complete number grids from 701 to 800 and count by 2s and 5s, reinforcing three-digit number familiarity.
Students practice place-value reasoning with three-digit numbers by completing number grids up to 900, counting by hundreds, and playing a secret-number game that asks about the hundreds, tens, and ones digits. Students read and write numbers to 1000 as listed in the skills and use questions that focus on the digit in each place (e.g., "Does this number have a 4 in the hundreds place?"). Students compute differences between before-and-after gummy-worm measurements using tools such as a whiteboard, abacus, and counters, selecting subtraction approaches of their choice.
The Skills list explicitly tells students to "Read and write numbers to 1000" and to "Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones." The Measurement Problems activity has students write number sentences and find sums or differences (examples provided are addition and subtraction word problems, e.g., 3+6, 11-5, 1+2+3, 29-26). The Wrapping Up section has students count to 1000, count by 10s and 100s, and identify numbers that are 10 or 20 more/less than a given three-digit number.
Unit 6

Unit 6: Place Value II

Students model addition with concrete tools (abacus and base-10 blocks) and draw base-10 representations to add numbers (e.g., showing 42 then adding 80 to get 122). Students practice composing tens into hundreds (60+40 --> exchange 10 tens for 1 hundred) and use expanded form and regrouping on paper (examples: 35+23 broken into 35+20+3; 26+33+54 shown with carrying to make 113). Students are asked to line numbers up vertically, add ones then tens, and explain the strategies they used when finding sums of three- and four two-digit addends.
Students draw two cards (1–99) and create addition and subtraction sentences, write each sentence on grid paper, and find the sum and difference. Students are encouraged to work without manipulatives but may use base-10 blocks, a place-value mat, or an abacus if needed. Students are reminded that they may need to regroup or borrow as they work, and they record their work on laminated grid paper, linking concrete/models to written work.
Students use hundreds, tens, and ones place-value cards to build three-digit numbers from digit clues, practicing identification of hundreds/tens/ones. Students manipulate an interactive abacus (a concrete model) to add and subtract 10 and 100 from three-digit numbers, watch place-value digits change (examples: 683+10, repeated +10 to cross from 95 to 105, adding/subtracting 100 up to 1000), and explain which place changes. Students complete a table of given three-digit numbers filling in +10, +100, -10, and -100 and are asked to write number sentences (including answers), connecting actions to written expressions.
Students use base-10 blocks to model adding hundreds (Activity 1) and are asked to add numbers like 572 + 300 using those concrete hundreds, tens, and ones. Students use an abacus to build and add three-digit numbers and are prompted to compose 10 and regroup when wires exceed 9 beads (Activity 2 and checks). Students write addition vertically and use expanded form to add ones, tens, and hundreds in order (Activity 3), and they practice many three-digit addition problems on worksheets and in the Close Call game. The materials also prompt students to read addition sentences aloud and to check sums with manipulatives and the written method, linking strategy to a written algorithm.
Students use base-10 blocks, a laminated place-value mat, and vertical (written) alignment to model and solve three-digit subtraction problems (e.g., 453-138) and to practice borrowing. Students practice adding and subtracting multiples of 100 and are asked to describe how only the hundreds place changes when adding or subtracting hundreds. Students generate subtraction sentences (dice/card activities and Close Call game), line up digits in columns, compute differences, and are asked to explain their steps aloud or in writing.
Students create and read three-digit numbers from place-value cards and answer questions about hundreds, tens, ones, and what is 10/100 more or less, reinforcing place value. Students form two three-digit numbers and write addition or subtraction number sentences in the Close Call games, using base-10 blocks, an abacus, place-value mats, or grid paper as concrete models. The lesson models and prompts students to talk aloud about strategies (for example, starting in the ones place and carrying to the tens place) and to record sums and differences on score cards and the practice worksheet of sixteen three-digit problems.
Students solve word problems that require adding and subtracting three-digit distances (examples: 184+100+174, 188+147+174, 309-136) and record number sentences and answers. Students are instructed to determine whether to add or subtract for each question and to write the arithmetic expression in the Number Sentence column. Students are allowed to use concrete place-value tools (abacus, base-10 blocks, laminated place value mat) or drawings as they work. Students are prompted to check regrouping/borrowing with questions such as "Did you regroup (or borrow) correctly?" which connects modeling to written methods.
Unit 7

Unit 7: Telling Time

Students are given four three-digit addition and subtraction problems (435+182, 526-148, 751+249, 883-566) and asked to find sums and differences within 1000. The problems are written in vertical format on laminated grid paper, and students are allowed to use methods and materials of their choosing to compute and then check and correct answers. Students are asked to read each number sentence aloud after finding the correct answers.
Students complete an "Addition and Subtraction Practice" worksheet that includes multiple three-digit addition and subtraction problems (e.g., 456 + 368, 400 + 562, 962 - 746). The instructions tell students they may use manipulatives as needed, encourage mental math, and explicitly remind them that they may need to "compose 10/regroup and borrow" and to "line up the places correctly." The lesson's skills list explicitly includes "Add and subtract within 1000."
Students write and compute three-digit addition and subtraction number sentences in vertical format (e.g., 617+175, 853-175, 375+468, 892-679) and find sums and differences within 1000. Students are allowed to use methods and materials of their choosing to find the sums and differences and then check answers with a calculator. Students are asked to read each number sentence aloud after obtaining correct answers, reinforcing the connection between the computation and its written form.
Students are asked to compute four three-digit addition and subtraction problems written in vertical format (478+390, 958-300, 275+500, 757-199). The activity lets students use methods and materials of their choosing to find sums and differences and then check answers with a calculator and read each number sentence aloud. The problems include cases that require composing or decomposing (e.g., 478+390 and 757-199).
Unit 8

Unit 8: Money

Students count groups of coins by tens and fives (e.g., counting dimes by 10s and nickels by 5s) in Activity 2 and are asked to write each amount as they work. The introduction asks students to count by 10s and 5s to 200 and to note how the tens and ones digits change when counting by tens. Activity 4 has students exchange coins (5 pennies for a nickel, 2 nickels for a dime, 10 pennies for a dime) which requires composing and decomposing units of ten.
The Skills list explicitly includes "Add and subtract within 1000." In the Wrapping Up section students write the number sentences 525+173, 427-348, 561+159, and 975-566 in vertical format and are told to use the methods and materials of their choosing to find sums and differences. Materials provided earlier (base-10 blocks, abacus, laminated grid paper) are available for students to use as concrete models while solving these three-digit addition and subtraction problems.
The Skills and Introduction ask students to mentally add and subtract 100 to numbers from 100–900 and present horizontal problems such as 356 + 400, 742 − 300, 829 − 100, etc., with a prompt to think about what happens to the hundreds place. Students are reminded to use what they know about adding and subtracting multiples of 100 and to think about the hundreds place in each number sentence.
The lesson explicitly lists "Add and subtract within 1000" in the Skills section and asks students to write the three-digit problems 618+355 and 654-246 in vertical format and find the sums and differences. Students are allowed to "use the methods and materials of her choosing" and to check answers with a calculator. Multiple activities ask students to use real coins and to draw coins to solve money riddles, providing opportunities to use concrete models and drawings for addition work.
Students count and combine coins and bills to find totals (e.g., writing amounts for collections such as $1.28, $1.63, and completing worksheets with totals like $2.72, $3.77). Students use a hundred flat and dollar bills to connect 1 dollar = 100 cents and represent 100, and they play a game where they collect cents toward $2.00 using coin values (1, 5, 10, 25) while exchanging smaller coins for larger ones. Students are instructed to trade coins to have the smallest number of coins and to exchange a dollar in coins for a dollar bill, which requires composing/decomposing units (pennies→nickels→dimes→quarters→dollars).
The Skills list explicitly includes "Add and subtract within 1000," and the Introduction gives four three-digit vertical number sentences (425+377, 927-378, 586+356, 946-563) for the student to solve. Students are asked to write the number sentences in vertical format on laminated grid paper and to use the methods and materials of their choosing to find the sums and differences, then check answers with a calculator and read each number sentence aloud.
Unit 9

Unit 9: Data and Graphing

The Introduction asks students to write and solve three-digit addition and subtraction number sentences in vertical format (376+173, 683-348, 489+159, 577-566) and to use methods and materials of their choosing to find the sums and differences. Students are instructed to check and correct their answers and to read each number sentence aloud. The use of laminated grid paper for vertical format provides a written algorithm practice context.
Unit 10

Unit 10: Skills Review

Students practice adding and subtracting 10 and 100 mentally as stated in the Skills list and reinforced by introduction questions (e.g., "Which number is 10 more than 746?", "Which number is 100 less than 445?"). Students practice place value by converting three-digit numbers to expanded form via the video and the "Review: Expanded Form" worksheet. Students practice ordering and comparing numbers to 1000 through the Counting Caterpillar game and the "Review: Comparing Numbers to 1000" worksheet.
Students practice adding and subtracting within 1000 through guided problems (e.g., 265+174, 563+128, 354+532, 448+396) and worksheet items including three-digit sums and differences. Students use place-value reasoning explicitly when discussing problems like 456+30 vs. 456+300 and when adding/subtracting multiples of 10 and 100, and they are invited to use base-10 blocks (concrete models) and laminated grid paper (drawings) to solve problems. Students are reminded about composing tens/carrying and borrowing and are required to write vertical algorithms and line up digits correctly (dice-generated three-digit subtraction).