HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 1

Unit 1: Number Sense

Students practice counting up and back by 10 using a 1–100 interactive number grid, number cards, and an abacus (Activity 1 shows 11 + 10 with bead movements; Option 2 has students draw cards 1–100 and record counting by tens). The Skills list and Day 2 explicitly state that students should be able to mentally add and subtract 10 from two-digit numbers without counting. Multiple activities and the student pages require students to write sequences that increment or decrement by 10 and solve word problems that add or subtract tens.
The lesson's Skills list explicitly names mentally adding or subtracting 10 or 100 to/from a given number 100–900. Students are asked to create or photograph 'Counting by 10s' number cards and to skip-count by 10s and 100s within 1000, which gives practice with tens- and hundreds-based number sequences. The project requires students to label captions using correct mathematical language, encouraging numerical descriptions that could reference tens and hundreds.
Unit 4

Unit 4: Place Value I

The lesson explicitly lists the skill "Mentally subtract 10 from any number" and models subtracting 10 using base-10 blocks (e.g., 35 - 10 = 25) and abacus work. Students are given multiple practice problems to find differences after subtracting 10 (56-10, 23-10, 67-10, 32-10, 55-10, 77-10) and are prompted to solve some problems mentally. The lesson also has students compare tens digits to subtract multiples of 10 (examples: 40-30, 50-20) and encourages recognizing the pattern that subtracting tens affects the tens place.
Students place and count hundred flats and write the hundreds digit (e.g., showing 100, 200, …, 900) and practice skip counting by 100s (Activity 2 and Day 2 activities). Students bundle tens to make hundreds in the Earth Day activity and decompose/compose three-digit numbers using hundreds, tens, and ones (Activity 1 and Activity 4 examples such as 358, 462, 536). Students are asked to cover the hundreds place and name the remaining two-digit number (e.g., cover the hundreds in 462 to get 62) and to write and read aloud three-digit numbers like 437, 186, and 529.
Students count up and back by 10 with three-digit numbers (e.g., asking them to count by 10s from 110 to 200 and to count back from 183 to 123). Students use base-10 blocks and a place-value mat to add 10 to 180 (making 190) and add another 10 to trade ten tens for a hundred to make 200, then continue to 210. Students practice filling in sequences by tens and by hundreds (examples: fill blanks 370–430, practice 590–650, 680–740, and count by 100s starting at 100 up through 300 and back from 800 to 700).
Students are asked in Wrapping Up to roll three dice, form a three-digit number, identify place-value values, and then "count up by 10 from the number he created, as high as he can go," which practices adding 10 to a three-digit number. The Skills list explicitly includes "Skip-count by 5s, 10s, and 100s" and "Count within 1000," indicating practice with increments of 10 and 100 and work with three-digit numbers. The Getting Started activity has students draw tens cards and count up by 10, with a prompt about moving beyond 100, which reinforces tens-place incrementation into the hundreds.
Unit 5

Unit 5: Measurement: Length

Students create a "Numbers to 1000 Collection" and are asked to count by 100s to 1000 and to read and write numbers to 1000, which gives experience with three-digit numbers and hundreds. The wrapping-up tasks ask students to count by 10s starting at 4 and to point to numbers that are 10 more than 63 and 10 less than 48, and to find numbers that are 20 or 40 more than given values, providing practice with adding and subtracting multiples of 10. The student activity pages and number grids provide repeated practice with place value up to 1000.
Students are asked to pick a number between 1 and 10 and count up aloud by 10s from that number to 200, pointing to the numbers on the 1–100 and 101–200 grids. Students are also asked to count down by 10s from a number between 191 and 200. Students answer place-value questions about a chosen three-digit number (greater than 150 but less than 170), including identifying hundreds, tens, and ones.
The Skills section 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." In the Introduction students complete a number grid starting at 301 and ending at 400 and are asked to identify the hundreds, tens, and ones places for numbers they write. The Wrapping Up asks students to pick numbers from grids 1–400 and describe digits and digit values, reinforcing place-value thinking for three-digit numbers.
Students are asked to count up by 100s from 100 to 500 and point to 100, 200, 300, 400, 500, which practices adding 100 repeatedly. The Wrapping Up section asks specific questions that require adding or subtracting 10 (for example, "10 more than 387? (397)", "10 less than 219? (209)", "10 more than 295? (305)"). The lesson has students complete number grids (including a grid starting at 401 and ending at 500), supporting practice with three-digit numbers and place-value positions for hundreds and tens.
Students write and arrange number grids so they have written numbers 1 through 600, providing practice with three-digit numbers. Students are asked to "pick a number below 400, and show me how to count up by 10s from it," giving practice with adding 10 repeatedly. Students are prompted to consider counting by 100s, identify which digit changes (hundreds), and predict that 126 + 100 = 226 and then 326, which models adding 100 mentally.
Students count by hundreds from 100 to 900 while pointing to number grids, and an introduction asks a student to begin a 100-grid at 801 and reason that it will end at 900. The lesson includes objectives to read and write numbers to 1000 and to understand that a three-digit number represents hundreds, tens, and ones. The secret-number game has students ask and answer questions about a number's hundreds, tens, and ones places.
Students count by 10s from 350 to 460 and count by 100s from 100 to 1000 in the Wrapping Up section, which requires adding tens and hundreds to given numbers. Students are asked to point to the number that is 10 more than 635 and the number that is 10 less than 863, providing explicit practice with adding and subtracting 10 for three-digit numbers. The lesson also includes instruction to read and write numbers to 1000 and to understand hundreds/tens/ones, supporting place-value reasoning for adding or subtracting 10 or 100.
Unit 6

Unit 6: Place Value II

Students are asked explicit questions about adding 10 to three-digit numbers (e.g., "What number is 10 more than 781? (791)" and "What number is 10 more than 864? (874)"). Students represent adding 100 physically on the abacus when they change 49 to 149 by moving a hundred bead. Students write and match expanded forms including examples like 900+30+6 and 481 = 400+80+1, reinforcing understanding of hundreds, tens, and ones.
The Skills section explicitly lists mentally adding and subtracting 10 or 100 for numbers 100–900. Activity 1 asks students to predict results (for example, asking "What number will be next?" when adding 10 from 95 to 105 and when subtracting 10 from 834 to 824) and to identify which place changes when adding or subtracting 100. Activity 2 provides a table of three-digit numbers (264, 730, 815, 108, 595, 444, 380, 692, 529, 371) for students to fill in +10, +100, -10, and -100, with instruction to check answers using the abacus.
The Introduction directs students to use a random number generator to produce a number between 100 and 900 and then to Add 10, Add 100, Subtract 10, and Subtract 100 for that number, repeated five times. Activity 1 explicitly tells students to try to solve adding multiples of 100 mentally and then use base-10 blocks to check their sums (example: 572 + 300). The Skills section lists "Add and subtract within 1000" and several student activity pages provide practice problems that involve adding hundreds and three-digit numbers.
Students practice adding and subtracting multiples of 100 in Activity 1 (e.g., 300+368, 645+200, 568-200, 683-500) and complete an "Adding and Subtracting Multiples of 100" activity sheet with problems such as 800-300 and 600+289. The lesson explicitly asks students to use base-10 blocks and to picture base-10 blocks without using them when subtracting 683-500, prompting mental visualization of changing the hundreds place. The "Counting by 10s and 100s" student page has students fill in sequences that increase or decrease by 10 and by 100 (examples include 560, 570, 580 and 970, 870, 770).
Students draw hundreds, tens, and ones place-value cards to create three-digit numbers and are asked explicitly to state "What is 10 more? What is 10 less? What is 100 more? What is 100 less?" Activity 2 asks students to complete addition and subtraction problems with three-digit numbers and instructs to "encourage him to use mental math as much as possible." The answer key and problems include examples that add or subtract whole hundreds (for example, 900 - 600 = 300 and 400 + 500 = 900), giving practice with 100 more/less adjustments.
Students read and write three-digit distances and solve addition and subtraction problems within 1000 (Skills: Read and write numbers to 1000; Add and subtract within 1000). Students write number sentences and compute sums/differences for travel problems (e.g., the answer key shows 184 + 100 = 284 and 188 + 147 + 174 = 509). The activity asks students to determine whether to add or subtract and to compute totals or differences using the map distances.
Unit 8

Unit 8: Money

The lesson asks the child to count by 10s and 5s to 200 and to count by 10s from 25 to 95, noting that the tens digit goes up by 1 and the ones digit stays the same. It prompts the child to begin counting with the highest-value coins and to count dimes by 10s, reinforcing repeated-ten counting. Activities require students to count amounts like 44¢, 56¢, and other totals by grouping tens (dimes) first.
The Skills list explicitly tells students to mentally add 100 to a given number 100-900 and mentally subtract 100 from a given number 100-900. The Introduction provides practice problems in which students compute sums and differences involving hundreds (e.g., 356+400, 742-300, 829-100, 238+500, 165+700, 920-800) and prompts them to think about what happens to the hundreds place.
Students count dimes by tens and nickels by fives to show that certain coin collections total 100 cents, and they glue and organize coins into groups (e.g., 10 dimes, 20 nickels, 4 quarters) to make a dollar. Students read and match dollar amounts such as $1.30, $1.55, $1.24, etc., to corresponding coin/bill combinations and show amounts like $1.25 and $1.45 using a dollar bill plus coins. The wrapping-up tasks ask students to represent amounts ($1.80, $1.65, $1.50, $1.70) in two different ways using a dollar bill and coins.
Students are asked to recognize that 1 dollar = 100 cents and to compute that 2 dollars = 200 cents and 3 dollars = 300 cents when prompted. Students play a game in which they roll and collect cents toward 200, exchanging coins for a dollar when they reach 100 cents. Students count and record multi-dollar amounts (for example $2.72, $3.77) by counting bills first and then coins, which requires aggregating cents into dollar units.
Unit 10

Unit 10: Skills Review

The Skills section explicitly states students will "Mentally add and subtract 10 and 100 to and from a given number 100-900." In the Introduction students write numbers and answer questions that require this reasoning, for example "Which number is 10 more than 746? (756)", "Which number is 10 less than 842? (832)", and "Which number is 100 less than 445? (345)". Students use a whiteboard to produce answers, indicating they perform mental adjustments rather than only procedural computation.
Students practice skip-counting by 10s and 100s aloud (e.g., count up by 10 from 30 to 120 and count up by 100 from 300 to 1000). Students work with explicit place-value examples that involve adding and subtracting multiples of 10 and 100 (e.g., 456+30, 456+300, 548-20, 548-200) and are asked to explain which place changes and why. Students complete a worksheet of problems that require adding and subtracting multiples of 10 and 100 (e.g., 378+400, 134+40, 800-200).