Multiplication and Division ‣
Multiplication is a huge part of third grade and I believe the most important. It is the joining of equal groups. The students are required to show multiplication using many different models. When students experience a variety of models, they have more chances to understand the concept of multiplication. ‣
Repeated Addition​
is adding the same number over and over to find the solution. ‣
Arrays​
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are organized rows or columns that mirror repeated addition. ‣
Area Models​
are related to arrays and will help the students with the concept of area later in the year. Area models use square units in rows and columns. ‣
Equal Groups​
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is the easiest method for students to master. It is a way to represent multiplication using a picture. ‣
Equal jumps on a number line ​
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show the same interval over and over. The last number the arrow lands on represents the product, or the answer to the multiplication problem. The number of jumps represents the number of times the interval is being multiplied. ‣
Skip counting​
is a skill the students have been working on for years in school. This skill will help them with the memorization of their multiplication facts. ‣
Strip diagrams ​
are kinds of pictorial models that tell the math story in the problem. As students draw strip diagrams that match the story, they begin to understand the mathematics in the story more clearly. ‣
Partial Products ​
is a way to break the traditional algorithm into manageable steps. You still start by multiplying the ones place, but you write down the total answer underneath. Then you multiply times the tens place, which becomes simpler because it ends in a zero. Then you add the two answers together to get the final total. ‣
Traditional Algorithm​
is the “normal” method that has been taught for many years. You start by multiplying the ones place, but only write the digit in the ones place in the answer. The digit in the tens place is written above tens place. Then you would multiply the tens place, but add the number above before you write the answer underneath. This is the last way we teach the students because until they understand the concept of multiplication, this way is just a list of steps. ‣
The students in third grade are required to multiply a two digit number by a one digit number. They will learn how to multiply a two digit number by a two digit number in fourth grade. ‣
What does recalling facts with automaticity mean?​
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It means that students can recall their basic facts within about 3 seconds and without counting. Students may use basic fact strategies if it helps them recall their facts more quickly. Notice that students only have to recall their multiplication facts with automaticity, not their division facts. Students who master this skill are far more successful because their energy can be solving the entire problem and not just one piece. ‣
There are many ways to memorize facts. I personally like creating a set of flashcards for studying. It is also something that can be practiced in the car orally. Students may use the multiplication chart below to find the answer to the basic facts. ‣
Multiplication and division are inverses of each other. That is, they form “fact families.” They are families because they are related to each other through their operations—multiplication and division. Here are a few examples of fact families: 4, 5, and 20 8, 6, and 48 1, 7, and 7 The relationship between multiplication and division helps students determine a quotient. If a student knows that 4 x 5 = 20, they can determine the quotient of 20 ÷ 4 by determining what factor makes 20 when multiplied by 4. ‣
Divisibility Rules: ​
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In second grade, students used objects to tell if numbers were even or odd. Students counted out objects such as counters and put them in pairs. Even numbers produced pairs of counters; odd numbers always had one leftover counter. Students used a pattern of manipulatives to tell if a number is even or odd. Third grade builds on second grade by introducing divisibility rules. Even numbers are divisible by 2; odd numbers are not. ‣
The students will solve one and two step word problems using multiplication and division. Below is an example of a typical third grade word problem. Katy and her dad took 2 of Katy’s friends to the movies with them. The cost of the movie was $5. Candy was $4. Katy’s dad did not get candy, but everyone else did. If Katy’s dad paid for all 3 of them to go and for the candy, how much did Katy’s dad spend? Important vocabulary your student should know: product row
zero property
associative property dividend quotient
identity property
commutative property
array
factor
divisor
distributive property divisor
column
area model
divisible