Fifth Grade

Welcome to 5th Grade math!


Highlights from this year include:

  • Students read, write, represent, compare, and order numbers in the millions
  • Students review multiplication strategies such as using multiplication patterns when
    multiplying with multiples of ten; doubling and halving, using the distributive property
    with an area model, and mental computation

Numbers in Base-10

Students learn that we often use exponential notation when writing very large
numbers. E.g. we can write 103 = 1,000 (which we read as “ten to the third power
equals one thousand”).

When working with seven- and eight- digit numbers, students see that they now
have three main groups of three when saying number names: millions, thousands,
and ones.



Students explore multiplication patterns to see how problems involving small numbers can reveal answers to problems involving much larger numbers. E.g. if a student knows 3 × 4 = 12, then they can easily see why 3 × 40 = 120.


Students use an area model (rectangle) to understand the distributive property
of multiplication. This provides a good basis for working mentally, and for
developing steps for the written algorithm. Students see 47 × 6 and think “47 × 6 is the same as 40 × 6 and 7 × 6. That’s 240 and 42. So 47 × 6 equals 282.”


Students extend and compare strategies for multiplying mentally that were
introduced in Grade 4. In Module 3, students will use the standard algorithm
to multiply larger numbers that are diffi cult to do mentally.

• Doubling and halving is a strategy to simplify multiplication. Students double one
factor and divide the other factor in half. E.g. students see 12 × 15 and think 6 × 30.

• Breaking up one or both of the factors can simplify some multiplication problems.
35 × 16 is easier to think about as 7 × 5 × 4 × 4. Applying the associative property
of multiplication allows students to multiply the factors in any order. E.g. 5 × 4 =20,
20 × 4 = 80, 80 × 7 = 560.

• Students are encouraged to use mental strategies if the numbers seem manageable.


For home:

• Look for opportunities to use mental math when shopping. For example, say “Cans of
green beans are on sale for 89¢. How much would 10 cans cost? What about 12 cans?” Be sure to ask your
child how they know.

• Remove the picture cards from a deck of cards, give your child three cards and ask them to multiply the
three numbers. Discuss which two numbers are easiest to multiply first and why. E.g. with the numbers
3, 5, and 6, your child might multiply 5 × 6 first (30), then multiply the answer by 3 (30 × 3 =90).

• Ask your child to answer questions such as, “If 6 × 7 is 42, what is 6 × 70?” Have them explain their thinking (e.g. “70 is 10 times more than 7, so the answer will be 10 times more than 42”).


In the equation 12 × 25 = 300, 12 and 25 are the factors, and 300 is the product.

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