[FREE] End of Year Math Assessments (Grade 4 and Grade 5)
The assessments cover a range of topics to assess your students' math progress and help prepare them for state assessments.
In order to access this I need to be confident with:
ArithmeticUnderstanding multiplication
Rounding numbers Factors and multiplesHere you will learn about the commutative property, including what it is, and how to use it to solve problems.
Students will first learn about the commutative property as part of operations and algebraic thinking in 3rd grade.
The commutative property says that when you add or multiply numbers, you can change the order of the numbers and the answer will still be the same.
For example,
This is also true when multiplying numbers.
For example,
The commutative property can be used to create friendly numbers when solving.
Friendly numbers are numbers that are easy to add or multiply mentally – like multiples of 10.
For example,
\begin{aligned} & 3+25+7 \\\\ & =3+7+25 \hspace{0.3cm} \text{ **Change the order of 25 and 7} \\\\ & =10+25 \hspace{0.65cm} \text{ **Adding 3 and 7 first, gives us 10 - a friendly number} \end{aligned}The commutative property lets us change the order and create friendlier numbers.
10 + 25 is easier to solve mentally than 3 + 25 + 7 = 28 + 7.
For example,
\begin{aligned} & 2 \times 8 \times 5 \\\\ & =2 \times 5 \times 8 \hspace{0.3cm} \text{ **Change the order of the 8 and 5}\\\\ & =10 \times 8 \hspace{0.65cm} \text{ **Multiplying 2 and 5 first, gives us 10 - a friendly number} \end{aligned}The commutative property lets us regroup and create friendlier numbers.
10 \times 8 is easier to solve mentally than 2 \times 8 \times 5=16 \times 5.
The commutative property can also be referred to as the commutative property of addition and the commutative property of multiplication, or more generally as the commutative law.
How does this relate to 3rd grade math?
In order to use the commutative property:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEGive an example of the commutative property using 4 + 9.
All the numbers are being added, so the commutative property can be used.
2Change the order of the numbers and solve.
4 + 9 = 13 \; \longrightarrow \; 9 + 4 = 13Changing the order in the equation does not change the sum.
Give an example of the commutative property using 10 \times 6.
Check to see that the operation is addition or multiplication.
All the numbers are being multiplied, so the commutative property can be used.
Change the order of the numbers and solve.
Changing the order in the equation does not change the product.
Use the commutative property to create a friendly number and solve 6 + 32 + 14.
Check to see that the operation is addition or multiplication.
All the numbers are being added, so the commutative property can be used.
Change the order of the numbers and solve.
Use the commutative property to create a friendly number and solve 3 \times 8 \times 3.
Check to see that the operation is addition or multiplication.
All the numbers are being multiplied, so the commutative property can be used.
Change the order of the numbers and solve.
Notice that when multiplying, friendly numbers can also be single digit numbers. If you know your basic facts, it is easier to solve 9 \times 8 than solving 3 \times 8 \times 3=24 \times 3.
Use the commutative property to create a friendly number and solve 41 + 17 + 9.
Check to see that the operation is addition or multiplication.
All the numbers are being added, so the commutative property can be used.
Change the order of the numbers and solve.
Use the commutative property to create a friendly number and solve 3 \times 5 \times 4.
Check to see that the operation is addition or multiplication.
All the numbers are being multiplied, so the commutative property can be used.
Change the order of the numbers and solve.
Notice that when multiplying, friendly numbers can also be numbers that are basic facts. If you have memorized the basic multiplication facts from 1-12, it is easier to solve 12 \times 5 than solving 3 \times 5 \times 4=15 \times 4.
This commutative property topic guide is part of our series on properties of equality]. You may find it helpful to start with the main properties of equality topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:
1. Which of the following equations shows the commutative property?
The commutative property says that changing the order in the equation does not change the product.
11 \times 6=66 \; \longrightarrow \; 6 \times 11=66
2. Which of the following equations shows the commutative property?
The commutative property says that changing the order in the equation does not change the sum.
\begin{aligned} & 5+11+9 \hspace{0.7cm} \longrightarrow \hspace{0.7cm} 9+11+5 \\\\ & =16+9 \hspace{2.1cm} =20+5 \\\\ & =25 \hspace{2.65cm} =25 \end{aligned}
3. Which of the following equations shows how to solve 2 \times 9 \times 5 using the commutative property?
The commutative property says that changing the order in the equation does not change the product.
\begin{aligned} & 2 \times 9 \times 5 \\\\ & =2 \times 5 \times 9 \hspace{0.3cm} \text{ *Change the order of 9 and 5} \\\\ & =10 \times 9 \hspace{0.65cm} \text{ *Multiplying 2 and 5 first gives us 10 – a friendly number} \end{aligned}
4. Which of the following equations shows how to solve 37 + 28 + 23 using the commutative property?
The commutative property says that changing the order in the equation does not change the sum.
\begin{aligned} & 37+28+23 \\\\ & =37+23+28 \hspace{0.3cm} \text{ *Change the order of 23 and 28} \\\\ & =60+28 \hspace{1cm} \text{ *Adding 37 and 23 first gives us 60 – a friendly number} \end{aligned}
5. Which of the following equations shows how to solve 8 \times 4 \times 5 using the commutative property to create a friendly number?
The commutative property says that changing the order in the equation does not change the product. Friendly numbers are numbers that are easy to multiply mentally – like multiples of 10.
\begin{aligned} & 8 \times 4 \times 5 \\\\ & =8 \times 5 \times 4 \hspace{0.3cm} \text{ *Change the order of 4 and 5} \\\\ & =40 \times 4 \hspace{0.6cm} \text{ *Multiplying 8 and 5 first gives us 40 – a friendly number} \end{aligned}
6. Which of the following equations shows how to solve 16+18+22 using the commutative property to create a friendly number?
The commutative property says that changing the order in the equation does not change the sum. Friendly numbers are numbers that are easy to multiply mentally – like multiples of 10.
\begin{aligned} & 16+18+22 \\\\ & =18+22+16 \hspace{0.3cm} \text{ *Change the order of all the numbers} \\\\ & =40+16 \hspace{1cm} \text{ *Adding 18 and 22 first gives us 40 – a friendly number} \end{aligned}
No, you can solve the numbers as they appear in the equation, without changing the order. The commutative property just gives you flexibility to add or multiply in a different order.
Yes, the commutative property can be used with integers, rational numbers and any real number, as long as they are all being added or multiplied.
The associative property of addition states that you can change the grouping of numbers when adding (using parentheses) and the sum will still be the same. The order of operations changes, but not the written order of the numbers in the equation. The commutative property of addition says you can change the written order of the numbers when adding and the sum will still be the same.
It is one of the properties of numbers for mathematical operations. This property states that any number added to 0 will still result in the same number (0 + a = a) or any number multiplied by 1 will still result in the same number (1 \times a=a).
At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.
Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.
Find out how we can help your students achieve success with our Elementary math tutoring programs.