HOMESCHOOL AND DISTANCE LEARNING
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5: Math

Unit 1

Unit 1: Number Sense 1-20

Students practice decomposing numbers 11–15 into ten and ones as stated in the Skills section ('Decompose numbers 11-20 to show that they are made up of 10 and other ones'). Students use an abacus to represent 11 as 10 beads on one wire and 1 bead on the next wire and count all beads to prove the quantity. Students model amounts like 13 cents as 2 nickels and 3 pennies and exchange nickels for pennies to check totals, reinforcing understanding of grouped values and ones.
Students practice representing numbers 16–20 on an abacus and are asked to show 20 as two tens (Activity 2), noting that two tens make 20 and that groups of five form rows of beads. Students color beads on number pages for 16–20 to represent tens and ones and trace/write the numerals and number words. Students also place number cards 11–20 in order on a number line and answer questions about what number comes before or after a given two-digit number.
Students decompose numbers 11–20 into 10 and additional ones by drawing number cards and using the abacus to write the ones part (Activity 3). Students model two-digit numbers with base-10 blocks, lining up 10 unit blocks and matching them to a ten rod and representing numbers such as 12 as one ten and two ones (Activity 4). Students practice numerical order from 1–20 with an online counting game, reinforcing relative order of numbers (Activity 1). Students also compare groups of coins and identify when two amounts are the same, indicating practice with equality of quantities (Activity 2).
Students arrange and order numbers through multiple activities (Ordering Number Fun, Rabbit Hop, Ordering Owls) that include numbers 1–20 and two-digit numbers 10–20. The Introduction and Ordering Owls activity have students line up 1–10 above 11–20 and prompt them to notice that numbers in the rows end in the same digit, connecting to tens/ones ideas. Activities 4 and 5 have students compare two quantities or two numeral cards (e.g., 8 and 12, or flipped owl cards) and state which number is greater or less, sometimes using a number line to justify.
Students create and answer "Which number is greater" cards that include two-digit examples (for example, 12 vs 17 and 12 vs 15). Students sort and complete "Do the Math!" cards into a greater-than/less-than group and practice ordering and comparing numbers within the 1–20 range. Students play the game and respond to comparison questions during gameplay, staying on a space for correct answers and moving back for incorrect ones.
Unit 3

Unit 3: Addition and Subtraction to 10

Students use a number strip and an abacus to show and count by tens, placing counters above 10, 20, 30, …, 100. Students use 10 dimes to represent groups of ten and answer questions such as "Which number is 10 more than 10?" and "Which number is 10 less than 40?" Activity prompts ask students to count, read, and write numbers to 100 and to show amounts on the abacus and number strip.
Unit 5

Unit 5: Addition and Subtraction to 20

Students are asked to represent amounts using tens and ones in Activity 2 (e.g., show 10 in two ways and show 11 dollars using 1 ten and 1 one). The activity lists practice showing 12, 13, 15, 17, and 20 using combinations of tens, fives, and ones, which requires students to think of a ten as a group of ten ones and to compose two-digit totals. The Student Activity Page for the zoo gives counts including a two-digit number (10) and problems that ask which is more/less, prompting comparison of quantities in context.
Unit 7

Unit 7: Place Value

Students use a place-value mat to build and write two-digit numbers, exchanging ten unit blocks for a ten rod and recording the tens and ones digits (e.g., making 10 as 1 ten and 0 ones, then 11, 12, … 19). Students are asked to model numbers such as 20 and 30 with ten rods and to compare the value of digits in different places (e.g., "Which is greater, 2 in the tens place or 2 in the ones place?" and "Would you rather have 30 cents or 3 cents?"). Students also practice showing numbers 1–30 with base-ten blocks using a virtual manipulative, reinforcing tens/ones meanings.
Students identify and name the tens and ones digits in two-digit numbers (Introduction; Activity 3; Activity 4) and represent two-digit numbers using abacus, base-10 blocks, place value cards, and a place-value mat (Activity 1; Activity 3). Students match equivalent representations of numbers (digits, words, abacus, base-10 blocks) on the "Matching Numbers" sheet, showing recognition of equal values across forms. Worksheets ask students to circle numbers with specific digits in the tens or ones place, reinforcing attention to the meaning of tens and ones ("Which Place?" sheet).
Students use dominoes and base-10 drawings to represent two-digit numbers and write the tens and ones for each domino (Activity 1). They are asked to name the numbers they create and to determine the smallest and biggest number on the sheet by first comparing tens and then, if needed, ones: "When we compare two-digit numbers, we look first at the tens place. If the digits in the tens place are the same, then we look at the ones place." Activity 3 also has students create multiple two-digit numbers and answer "What is the smallest number... What is the biggest number...", reinforcing comparison by tens and ones.
In the Introduction, students draw two digit cards to create two two-digit numbers, write them (e.g., 57 and 75), state them as "5 tens and 7 ones" and "7 tens and 5 ones," and draw base-10 blocks to represent each number. Students then compare the two representations and state which number is greater (the example explicitly has students conclude 75 is larger than 57).
Students practice place value explicitly when they use ones and tens place value cards to make two-digit numbers (Activity 2) and when they say equivalents for groups of ten in the Wrapping Up. The Skills section states that students should understand that the two digits of a two-digit number represent amounts of tens and ones and that numbers like 10, 20, ... 90 refer to tens. Students construct specific two-digit numbers (e.g., 72, 36, 99) by placing ones over the 0 on the tens card, reinforcing the meanings of tens and ones.
Students cut out and compare base-10 cards and are asked to tell which card shows the bigger number (examples given: 8 and 18; 30 and 70; 55 and 70). Students use base-10 blocks and are encouraged to name numbers as tens and ones (for example, "4 tens and 2 ones") and to count ten rods to determine which number has more tens. In Activity 3 students draw random numbers from 1–100, put them in order, and respond to prompts such as "Which of these numbers has more tens?" and "Which of these numbers has more ones?"
Students sort number cards into groups marked "Greater than", "Less than or equal to", or ranges (e.g., "Between 30 and 60"), practicing identification of larger and smaller numbers. Students select pairs of cards and point to the greater and the lesser number, then build the > symbol with craft sticks and place it between numbers (e.g., 10 > 1). Students examine two-digit pairs (24 vs. 33, 37 vs. 39) to compare the digits in the tens place and, when tens are equal, compare the ones place using a decision-tree. Students record comparisons by gluing < or > into boxes on a worksheet and by writing < or > between numbers on the Domino Place Value sheets and in the wrap-up activity while reading the number sentences aloud.
Students are asked to place the correct symbol (> = <) between given pairs of two-digit numbers (22 __ 28, 30 __ 20, 15 __ 15) and to explain how they know which is greater, less, or equal. The introduction prompts students to talk about the digits in the tens and ones places (e.g., "30 is greater than 20 because it has more tens"). Activities have students use base-10 blocks, an abacus, and number grids to model adding or subtracting tens and to visualize how tens and ones change, supporting comparisons based on place value.
Students represent two-digit and three-digit numbers in multiple forms (base-10 blocks, abacus beads, tens + ones, and digit form) by showing numbers such as 8, 15, 50, 112 and filling BINGO cards with those representations. Students write and read expressions like "5 tens + 2 ones" and match them to numerals and visual models. Students place each representation on cards and check off numbers on a provided number list as they complete them.
Unit 8

Unit 8: Measurement

Students are asked to represent given two-digit numbers (examples: 26 and 57) using ten rods and unit blocks and to record them in a Hundreds/Tens/Ones chart. Students complete related place-value tasks such as finding 1 more, 1 less, 10 more, and 10 less for the given numbers and can show numbers with base-10 blocks or other representations. The "Today's Number" routine repeatedly has students identify the tens and ones for specific two-digit numbers.
Students are asked to represent 99 and 15 with ten rods and unit blocks and to state the numbers as 0 hundreds, X tens, Y ones. Students practice finding one more/one less and ten more/ten less for those numbers. Students are asked to create number sentences to show 15, reinforcing place-value decompositions into tens and ones.
The lesson has students represent two-digit numbers with ten rods and unit blocks (e.g., "Today's number is 79" with "7 ten rods and 9 unit blocks" and "0 hundreds, 7 tens, 9 ones") and a second example with 48 showing "4 ten rods and 8 unit blocks." Students reason about place-value changes by finding 1 more/1 less and 10 more/10 less (e.g., 79 → 89 or 69; 48 → 58 or 38), which requires understanding tens and ones. These activities require students to decompose and manipulate tens and ones when describing numbers.
The 'Today's number is 63' section asks the child to show 6 ten rods and 3 unit blocks and to state 0 hundreds, 6 tens, 3 ones. It asks students to identify 1 more and 1 less (64, 62) and 10 more and 10 less (73, 53), reinforcing the meanings of the tens and ones digits. Students are also asked to show 63 in a way of their choosing, reinforcing place-value representations.
Students are asked to represent the two-digit number 66 by showing 6 ten rods and 6 unit blocks and to state 1 more (67), 1 less (65), 10 more (76), and 10 less (56). Day 2 suggests giving a child a two-digit number and asking them to name the numbers that are 1 more, 1 less, 10 more, and 10 less. These activities require students to understand and use the meanings of tens and ones digits.
Unit 9

Unit 9: Addition to 100

Students practice identifying tens and ones and writing the two-digit number in the "Tens and Ones Practice" activity and the "Writing Place Value" page, where they decompose numbers into tens + ones and expanded form. Students are asked to create a two-digit number larger than 40 and to make the largest and smallest two-digit numbers from two drawn digit cards, which requires reasoning about tens versus ones positions. Students also use base-10 materials to represent and read two-digit numbers in multiple activities.
Students represent two-digit multiples of ten on an abacus and with base-10 blocks (e.g., showing 30, 80, 10, 50, 100, 40) and reason in terms of tens (e.g., thinking of 20+30 as 2 tens + 3 tens). Students draw two number cards and are instructed to write subtraction sentences beginning with the larger number (e.g., if they draw 40 and 70, they write 70-40), which requires them to identify which of the two numbers is greater. Activities also have students add and subtract multiples of ten and complete number bonds for sums like 60, 80, 50, and 30 using tens.
Unit 10

Unit 10: Skills Review

Students are asked to compare two-digit numbers as a listed skill and to order drawn number cards from least to greatest in Activity 1. As they sequence numbers, students are prompted to use the tens and ones places to decide order (the prompt asks how the tens and ones places can be used to decide the order). In the Wrapping Up, students draw two cards, read the numbers, and identify which number is greater multiple times.