Students are asked to identify multiples in the Basic Skills Review (e.g., "Circle the multiples of 3: 6, 8, 11, 15, 20, 24, 28"), so they practice determining whether specific numbers are multiples of the one-digit number 3. Students complete basic multiplication problems (7×10, 5×9) which reinforces their understanding of multiples and products. These items require students to recognize and mark multiples among given whole numbers.

Students are asked to identify and circle the multiples of 7 from a list (14, 24, 35, 42, 50, 57, 63), which has them determine whether specific whole numbers are multiples of a one-digit number. Students also solve multiplication problems (7 × 40 and 50 × 9), reinforcing the concept of multiples and repeated addition.

The Basic Skills Review #3 item asks students to "Circle the multiples of 9," giving students practice identifying multiples of a one-digit number among whole numbers (several listed are within 1–100). The review also includes multiplication practice (70 × 3 = 210), which reinforces recognizing products and multiples.

Students use factor and multiple language when solving digit-clue puzzles: one clue asks for a digit that is a "factor of 9," another requires digits in the tens and ones places to be "multiples of 3," and several clues require students to use multiplicative relationships (e.g., one digit is three times or two times another). Students apply these ideas to choose specific single digits that satisfy the multiplicative constraints in the Number Detective and "What's the Number?" activities.

Students work with a multiplication table (0–12) and color facts they know, which lets them locate products and the pairs of multiplicands that produce them. The introduction asks students to point to a factor and the product in 7 × 4 = 28, so students identify individual factors and recognize the relationship between factors and multiples. Several word problems require students to divide totals by a one-digit number (e.g., 54 guests ÷ 6 per table, 56 dollars ÷ $8 per ticket, 96 dollars ÷ $8 per poster, 35 animals ÷ 7 boxes), prompting students to determine whether a number is a multiple of a one-digit number and to find quotients that correspond to factor/group size relationships.

Students model division with counters and solve division problems (e.g., 30÷3, 24÷8, 25÷5, 18÷3) and use multiplication to check answers and remainders. Students are prompted to identify when a number is divisible by another and are asked to list all numbers that divide 24, with the teacher helping them see 24 is divisible by 2, 3, 4, 6, 8, and 12. Multiple activities require students to divide various whole numbers (many under 100) by one-digit divisors and decide quotients and remainders, which shows use of division to determine multiples.

Students are asked in the Skills list to "Find all factor pairs for a whole number in the range 1-100," and to "Recognize that a whole number is a multiple of each of its factors" and "Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number." In Activity 1 students write multiples (e.g., multiples of 2, 5, 7) and complete a table marking whether given numbers are multiples of 8 or 3. In Activity 2 students list factors for numbers (a table for numbers 1–12 is completed) and use the multiplication table to confirm factor lists, linking factors and multiples.

Students draw factor rainbows for numbers like 12 and 18 and use counters to divide numbers into equal groups, showing they find factor pairs and see that factors multiply to the original number. Students complete worksheets that ask them to list the factors of numbers (e.g., 8, 9, and the table for 13–30) and circle or color numbers that are factors of given targets. Students play a true/false game (e.g., "2 is a factor of 10") that requires deciding whether a number is a multiple of a given one-digit number.

Students sort numbers into prime and composite columns and highlight prime numbers on provided "Factors" tables (2, 3, 5, 7, 11, 13, 17, 19, 23, 29). Students complete activities that ask them to circle prime numbers in lists, explain why 1 is not prime, explain how 9 is both a multiple of 3 and a factor of 36, and identify factors for specific numbers (for example, noting 33 has factors 3 and 11). Students use the "Rolling for Prime" activity and a Random Number Generator (lower limit 2, upper limit 100) to generate numbers and decide whether each is prime or composite.

Students create factor rainbows (18, 20, 21) and use the Factorize interactive to make rectangles whose side lengths multiply to given target numbers, recording factorizations (e.g., 1 x 47). The Student Activity Page and Answer Key ask students to circle and list all factors for numbers such as 24, 36, 40, and 42 and to use division/calculators to check divisibility (e.g., "Is 36 divisible by 4?"). Activities 3 and 4 have students use a laminated 100-chart and the Sieve of Eratosthenes to cross out multiples and circle prime numbers up to 100, and the wrapping-up games reinforce prime vs. composite identification.

Students create Number Chains (Activity 1) using number cards and for each card decide whether the next number is a factor or a multiple of the previous number. Students sort number cards 1–100 into "prime," "composite," or "neither" (Activity 2), giving direct practice identifying primes and composites. Students list divisors and note multiples for specific numbers (Activity 3), e.g., listing all factors/divisors for 56 and for 25, and use a 1–100 chart and games to practice identifying multiples of one-digit numbers.

Students practice identifying prime numbers by circling primes on the "Basic Skills Review" (e.g., tasks listing 3, 6, 20, 23, 37, 18). Students identify factors of a specific number by circling factors of 24 from a list. Students solve multiplication and division problems (e.g., 30 ÷ 6, 24 ÷ 4, 5 × 80 = 400) and complete word problems that require using multiplication/division (e.g., $2 per day to reach $20, teams of 2 with 4 people each).

Students are asked to identify prime and composite numbers and to determine divisibility (e.g., Which of these numbers are prime? Which are divisible by 2? by 3?). Students complete tasks that find multiples (first six multiples of 3; circle the multiples of 4) and use a factor rainbow to find factors of 30 and list all factors of given numbers (factors of 21, factors of 36). The skills list and multiple student pages explicitly include "Identify multiples and factors" and "Determine whether a given whole number in the range 1-100 is prime or composite."

The lesson's Skills list explicitly includes: "Recognize that a whole number is a multiple of each of its factors," "Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number," and "Determine whether a given whole number in the range 1-100 is prime or composite." The project requires students to create three stories/cartoons that focus on factors, multiples, prime numbers, and composite numbers, and the evaluation checklist asks whether the collection "Teaches about factors," "Teaches about multiples," "Teaches about prime numbers," and "Teaches about composite numbers."

Students complete 'Basic Skills Review #7' where they are asked to "Circle the composite numbers" from a provided list (2, 3, 5, 15, 9, 4, 7, 11, 18). Students also complete the item "Circle factors of 30" selecting from given choices (3, 5, 9, 6, 10), and the answer key identifies the composite numbers (4, 15, 18) and factors of 30 (3, 5, 6, 10).

Students are asked to "Circle the prime numbers" from a provided list (the answer key shows 7, 13, 19) and to "Circle factors of 36" (the answer key lists 2, 6, 9). Students solve multiplication-relationship items such as "4 x n = 28" (n = 7) and compute products like "70 x 5 = 350," which connect factors and multiples. These items require students to recognize some factors, identify some prime numbers, and use multiplication to find missing factors.

Students complete items on the "Basic Skills Review #9" page that ask them to "Circle the composite numbers" from a given list (with answer key identifying 9, 16, 21 as composite). The same sheet asks students to "Circle the factors of 24" from a choice list (answer key: 2, 6, 8). A division equation (40 ÷ x = 8) requires students to find x = 5, which connects division to identifying a factor.

In Activity 4 (Basic Skills Review) students are asked to "Circle the numbers that are multiples of 7" and "Circle the numbers that are multiples of 8," using lists of whole numbers that fall within the 1–100 range. The review also includes division/remainder tasks (e.g., remainder when 40 is divided by 9) and a division equation in the answer key, which require students to reason about multiples and divisibility. These items require students to determine whether specific whole numbers are multiples of given one-digit numbers.

The lesson explicitly asks students to identify numbers as factors or multiples (card activity with numbers 1–10) and includes grouping colored tiles to test whether a number of tiles is a multiple of 4 or 6. The skills list names recognizing that a whole number is a multiple of each of its factors and determining whether a whole number 1–100 is a multiple of a given one-digit number. Students write lists of multiples for many single-digit numbers (Multiple Patterns and More Multiple Patterns) and answer questions about patterns and even/odd products.

Students are asked to "List the prime numbers between 1 and 12" on the Basic Skills Review page, and the answer key lists 2, 3, 5, 7, 11. The Basic Skills Review also includes division and multiplicative reasoning problems (e.g., remainder of 68 ÷ 9 and solving 6000 × N = 240,000) that require students to work with factors and multiples in calculation. Multiple activities have students generate and compute multiplication problems (domino activity, two-digit multiplication, expanded-form multiplication), which gives practice with multiplication facts and multiplicative structure.

Students are instructed to list multiples of denominators when finding a common denominator (for example, Jess lists multiples of 3 and 5: 3, 6, 9, 12, 15, 18). Students convert fractions by multiplying numerator and denominator by the factor needed to reach the common multiple (e.g., 2/3 -> 10/15, 3/5 -> 9/15). The Methods for Comparing Fractions and the Changing Denominators activities explicitly ask students to find a common multiple and create equivalent fractions using that multiple.

Students are asked to write all the factors of 24 and to list factors for numbers used in examples (e.g., factors of 4, 16, 10, 25, 12, 18). Students use factor lists to find the greatest common factor (GCF) and then divide numerator and denominator by that factor to simplify fractions (Method #2 and answer key examples). Matching and practice problems require students to recognize equivalent fractions by identifying common factors and performing divisibility steps (e.g., dividing by 2, 3, 5, 7).

Students divide concrete counters (25 and 31) into equal groups to decide when a number divides evenly or leaves a remainder. In the "Showing Division" activity students complete division problems such as 18 ÷ 6, 20 ÷ 4, 24 ÷ 6, 100 ÷ 10, and 32 ÷ 8 and find the quotients. In the "Connecting Multiplication and Division" activities students convert multiplication facts into corresponding division statements and complete tables (e.g., 45 flies ÷ 5 exhibits = 9), reinforcing the relationship between factors and multiples for specific examples.

Students compute division problems with numbers in the 1–100 range (examples: 24 ÷ 12 = 2, 15 ÷ 3 = 5, 63 ÷ 9 = 7, 24 ÷ 8 = 3) and repeat this practice using number cards and a division facts game. Students match division sentences that have the same quotient (e.g., 64 ÷ 8 matched to 32 ÷ 4), which requires them to check whether one number divides evenly into another. The activities ask students to determine quotients and remainders and to check answers with a calculator, so students repeatedly test divisibility by one-digit divisors.

Students repeatedly divide whole numbers (many between 1 and 100) by one-digit divisors: practice problems, long-division steps, and division tables include dividends up to 99 with divisors 2–9. Students solve real-world sharing problems (e.g., 24 cards with 3 friends, 65 tickets for rides costing 3) and determine quotients and remainders, and they are instructed to check answers by multiplying divisor and quotient and adding any remainder. The Division Tables and practice items require students to decide when division yields no remainder, implicitly testing whether a number is divisible by a given one-digit number.

Students practice dividing multi-digit dividends by one-digit divisors throughout the lesson (e.g., problems like 258 ÷ 6, 4698 ÷ 3, 5170 ÷ 4) and complete long-division problems with and without remainders. Students create their own division sentences using one-digit divisors and three- or four-digit dividends from playing cards and check their work with a calculator. The lesson asks students to find quotients and to note when quotients have remainders, which requires performing divisibility checks by one-digit numbers.

Students practice dividing multi-digit dividends by one-digit divisors in structured problems (e.g., 340 ÷ 4 = 85, 72 ÷ 3 = 24, long division examples and word problems). Students compute quotients and remainders, use multiplication to check division, and solve real-world division problems that require determining how many full groups and what is left over (e.g., 100 ÷ 7, 367 ÷ 8). Students create division sentences with a one-digit divisor and solve them, reinforcing use of division to test exact divisibility.

Students practice dividing whole numbers by one-digit divisors and finding quotients and remainders in multiple problems (examples include 46 ÷ 3, 73 ÷ 5, 83 ÷ 5, 6213 ÷ 4). Students identify dividends and divisors, set up division in several formats, and solve word problems that require determining how many groups and what remainder remains. The activities include many division calculations with dividends both below and above 100, with several explicit problems using numbers in the 1–100 range (e.g., 46, 72, 83).

Students practice simplifying specific fractions (for example 9/27, 8/24, and 15/25) and are asked to write fractions in simplest form. Students match and sort sets of equivalent fractions (for example grouping 6/12, 1/2, 2/4, 3/6, 10/20) and place fractions into equivalent groups. These activities require students to use divisibility and common factors to reduce fractions and identify equivalent forms.

Students are prompted to use factors and division to simplify fractions (for example, converting 25/100 to 1/4) and to recall simplification strategies from a 'How to Simplify Fractions' resource. The lesson has students simplify additional examples such as 5/100 (to 1/20), 24/100 (to 6/25), and 66/100 (to 33/50), which requires identifying and using common factors.

Students are asked to find side lengths from given areas and perimeters (for example, dividing an area of 81 sq m to get side length 9, dividing 35 by 5 to get 7, and solving perimeter problems like perimeter 34 cm with one side 4 cm). The 'Creating Perimeters and Areas' task explicitly asks students to show 4 different ways to create a rectangle with an area of 24 square cm, which requires generating multiple factor pairs (e.g., 1x24, 2x12, 3x8, 4x6). Several activities require students to compute widths or lengths by dividing whole numbers, providing practice that is related to identifying factor pairs for particular numbers.

Students are asked to draw all rectangles with an area of 16 square centimeters and the text explicitly lists the corresponding side pairs 1 cm x 16 cm, 2 cm x 8 cm, and 4 cm x 4 cm. Students solve similar tasks for areas like 36, 25, 24, and 40 by finding unknown side lengths from given areas and perimeters on the activity pages. Multiple problems require students to determine side lengths that multiply to a given area, which has them generate factor pairs for whole-number areas within the 1–100 range.