5.OA.1- Order of Operations (PEMDAS)
PEMDAS is a mnemonic to help students memorize the order in which to solve problems. Students will not need to master working with exponents at the fifth grade level, however, it is good to know how to recognize exponents and to understand that they have an order in which they would solve an operation involving them.
It is also important for students to understand the difference between braces, brackets, and parentheses. Use the interactive dictionary on the Word Wall page to understand the differences. Students should know and understand that these symbols represent what they will do FIRST when solving a numerical expression.
Students get most confused with Step 3 and Step 4, multiplying/dividing from left to right and adding/subtracting from left to right. Students forget that it doesn't matter which order you do the multiplication and division as long as they do whichever comes first from left to right, and the same for addition and subtraction as well. See the Unit 1 page for help and examples.
PEMDAS is a mnemonic to help students memorize the order in which to solve problems. Students will not need to master working with exponents at the fifth grade level, however, it is good to know how to recognize exponents and to understand that they have an order in which they would solve an operation involving them.
It is also important for students to understand the difference between braces, brackets, and parentheses. Use the interactive dictionary on the Word Wall page to understand the differences. Students should know and understand that these symbols represent what they will do FIRST when solving a numerical expression.
Students get most confused with Step 3 and Step 4, multiplying/dividing from left to right and adding/subtracting from left to right. Students forget that it doesn't matter which order you do the multiplication and division as long as they do whichever comes first from left to right, and the same for addition and subtraction as well. See the Unit 1 page for help and examples.
5.OA.2- Order of Operations (Read, Write, and Interpret)
It is important that students understand how to verbalize numerical expressions. This will help them to visualize what is represented and what is expected from them to understand about that representation. They will also need to be able to reproduce abstract representations in order to solve real world problems.
This anchor chart helps students to recognize and apply key words when interpreting numerical expressions and/or solving word problems. Students get confused with this standard because they often have a hard time distinguishing the order in which operations occur. They also struggle with how to say an expression once parentheses are introduced. For example, in the expression 2 x (3+4), students might say "Two times three plus four" which is really (2 x 3) +4, instead of saying the appropriate "Two times the sum of 3 + 4".
See the Unit 1 page for help and examples.
It is important that students understand how to verbalize numerical expressions. This will help them to visualize what is represented and what is expected from them to understand about that representation. They will also need to be able to reproduce abstract representations in order to solve real world problems.
This anchor chart helps students to recognize and apply key words when interpreting numerical expressions and/or solving word problems. Students get confused with this standard because they often have a hard time distinguishing the order in which operations occur. They also struggle with how to say an expression once parentheses are introduced. For example, in the expression 2 x (3+4), students might say "Two times three plus four" which is really (2 x 3) +4, instead of saying the appropriate "Two times the sum of 3 + 4".
See the Unit 1 page for help and examples.
5.OA.3- Number Patterns
In this standard, students will extend their knowledge of patterns, relating them to numbers and how coordinate pairs influence one another. This standard goes hand-in-hand with 5.G.3 and 5.G.4, where students will then use these number patterns to plot coordinate pairs on a plane. They will also begin to see the relationship of plotted points and make sense in them. The biggest mistake I find when students are completing or understanding these number patterns in In/Out tables, is that they tend to find a "rule" for the first pattern they see instead of checking that rule against all other information provided. Make sure to check the rule you have found with each of the numbers given to make sure it is true for all!
In this standard, students will extend their knowledge of patterns, relating them to numbers and how coordinate pairs influence one another. This standard goes hand-in-hand with 5.G.3 and 5.G.4, where students will then use these number patterns to plot coordinate pairs on a plane. They will also begin to see the relationship of plotted points and make sense in them. The biggest mistake I find when students are completing or understanding these number patterns in In/Out tables, is that they tend to find a "rule" for the first pattern they see instead of checking that rule against all other information provided. Make sure to check the rule you have found with each of the numbers given to make sure it is true for all!
5.NBT.1- Place Value
By fifth grade, students should be pretty familiar with whole number place value. Watch the 4th grade review video on place value if you don't have it down. In this standard, students will extend their knowledge by recognizing and understanding place value with decimals. Students in fifth grade are expected to work with numbers to the thousandths place. This standard is usually fairly easy for students to understand due to their knowledge of money. They know that it takes 100 pennies to make a dollar, so $1.85 means that they have 85/100 cents to the next dollar. Where students get confused is understanding place value when you take the dollar sign away and add a thousandths place. The number 1.008, for example, means that there are no tenths, no hundredths, and eight thousandths. When ask to represent this number with a visual, students have a hard time producing this. See the Unit 1 page for examples, videos, and practice. 5.NBT.2- Powers of 10
Understanding place value is really understanding powers of 10. In our world, very brilliant mathematicians from long ago have decided for us to use a base ten system. We have the numbers 0-9, and when you get to 10, it is simply a regrouping representing one ten and zero ones. If we were to have decided to go with a base 3 system, we would count 0,1,2,3, and then regroup to the tens place- 10, 11, 12, 13, and then 20, 21, 22,23, and then 30,31,32,33, and then we would have to move to the hundreds place, so 100, 101, 102, 103, 110, 111, etc. A very confusing concept for students to understand, but worth explaining, because students need to know why and how we regroup in order to fully understand powers of 10 and our base ten system. Students are generally pretty receptive to being able to multiply and divide by power of 10, since it is really just adding and taking away zeros once they see that pattern; however, students get confused on the practicality of the answer. Is there answer getting bigger or smaller and why? If we are multiplying a decimal by a power of 10, our answer should be bigger, and if we are dividing, it should be smaller. Students often make the mistake of by not attending to precision or not making sense of their computation. 5.NBT.3a- Read & Write Decimals
Reading and writing decimals can often times be a very difficult task for students, especially for English Language Learners. It is important that students understand right away the difference between standard form, expanded form, and word form. Students particularly get confused when there is a zero in one of the place values. For example, in the number 23.06, students often have difficulty accounting for that zero and what it means. A common error is saying that this number represents "twenty-three and six tenths" instead of the correct "twenty-three and six hundredths". See the Unit 1 page for examples, videos, and practice. 5.NBT.3b- Comparing Decimals
Coming soon! 5.NBT.4- Rounding Decimals
Coming soon! 5.NBT.5- Multi-digit Multiplication Algorithm
Coming soon! |