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    • ▾4th grade
      • ▸Place value of whole numbers
        • •Place value of multi-digit whole numbers
        • •Adding and subtracting multi-digit numbers
        • •Multiply and divide by 10
        • •Represent a number using base ten blocks, units, tens, and hundreds
        • •Convert between written forms of numbers
        • •Round whole numbers
        • •Estimating sums and differences by rounding
        • •Estimating products by rounding
      • ▸Multiplication and division
        • •Multiplying one-digit numbers by 10, 100, and 1000
        • •Multiplying one-digit numbers by multiples of 10, 100, and 1000
        • •Multiplying 10s
        • •Multiplication
        • •Quotients and remainders
        • •Pattern in the units digit of multiples
        • •Solve multiplication and division word problems
        • •Multi-step word problems
      • ▾Factors, multiples, and patterns
        • •Factors and multiples
        • •Divisibility tests
        • •Prime and composite numbers
        • •Number patterns
      • ▸Equivalent fractions and comparing fractions
        • •Equivalent fractions
        • •37 trick
        • •Compare fractions with unlike numerators, denominators, or both
      • ▸Fraction arithmetic
        • •Round fractions
        • •Add and subtract fractions with like denominators
        • •Add fractions with denominators of 10 or 100
        • •Multiply fractions by whole numbers
      • ▸Understand decimals
        • •Represent decimal numbers using base ten blocks
        • •Compare decimals to hundredths
      • ▸Geometry
        • •Intro to parallel and perpendicular lines
        • •Lines of symmetry
        • •Rotational symmetry
        • •Intro to angles
        • •Measuring and drawing angles
        • •Coterminal angles
        • •Naming angles
        • •Adjacent angles and the additive property of angles
      • ▸Units of measurement
        • •Converting larger units of volume to smaller ones
        • •Converting larger units of length to smaller ones
        • •Converting larger units of time to smaller ones
        • •Word problems involving measures
     › 4th grade › Factors, multiples, and patterns

    Factors and multiples

    Students will learn how to identify factor pairs for any number 1-100. For example, 3 and 6 is a factor pair of 18 while 2 and 4 is not. Here's an interesting problem: Find the dimensions of the rectangle that has whole number side lengths, area 12, and perimeter 16. Students can find the answer by making a table, as seen here. After that, teach students how to solve Shikaku puzzles, then give your students some puzzles to solve. Puzzles of various difficulty are conveniently organized here. Additionally, here are some random Shikaku puzzles I've stumbled across. After your finished with Shikaku, explore the game found here and here. After that, give your students this challenge. Before attempting the challenge, students must be able to multiply two-digit numbers by two-digit numbers. They don't need to know the divisibility rule for 13, despite the name of the problem. Next, give your students the puzzle titled Pattern 30 on this page. Next, give your students this challenge. The solution can be found using the reasoning provided by NRICH, or by drawing a graph of all numbers which may be adjacent. From this, it's easy to see the longest simple path has length 9. Either way, the reasoning is that if we try to include 7, we miss out on 3, 6, and 9, or 4 and 8. Which set we miss out on depends on our subsequent choices. Conclude by leading the investigations found here, here, and here. Two more instances of the Tax Collector game being played can be seen here. Also, go to this page and give the puzzles found on the slides Hungry Monsters and Hungry Monsters Pt. 2.

    At this point, 4th graders don’t know the divisibility tests, so without this or the sieve of Eratosthenes, there’s no way they can test primality.

    Watch these Khan Academy videos:

    • Finding factors of a number
    • Finding factors and multiples
    • Recognizing prime and composite numbers
    • Prime numbers

    Do these Khan Academy exercises:

    • Factor pairs
    • Relate factors and multiples
    • Identify factors
    • Identify multiples
    • Identify composite numbers
    • Identify prime numbers

    Next, give your students this challenge:

    Make the equation below true by replacing each letter with a unique digit (0-9).

    $$P + P + P = I = G + G$$

    Here's the solution:

    \(P + P + P = I,\) and \(I = G + G.\) Thus, \(I\) must be divisible by 3 and 2. The only single digit number with this property is 6. Now we have \(P + P + P = 6 = G + G,\) so \(P\) is one-third of \(I,\) and \(G\) is one-half. So \(P = 2\) and \(G = 3.\) In conclusion, the equation is \(2 + 2 + 2 = 6 = 3 + 3.\)

    Conclude by leading this investigation:

    Lazy Lemur Puzzles
    by MathPickle

    4.OA.B.4: Find all factor pairs for a whole number in the range 1-100. 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. Determine whether a given whole number in the range 1-100 is prime or composite.

    Lessons and practice problems