No Series: Third Grade Mental Math


Common core State Standards

  • Math:  Math
  • 3:  Grade 3
  • NBT:  Numbers & Operations in Base Ten
  • A:  Use place value understanding and properties of operations to perform multi-digit arithmetic
  • 2: 
    Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

Third Grade Mental Math

Lesson Objective: Use the strategies of decomposing, jumps of ten, and splitting
Grade 3 / Math / Number Sense


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Discussion and Supporting Materials

Thought starters

  1. How does mental math deepen students understanding of the basic operations?
  2. What strategies does Ms. Saul use to encourage independent thinking before sharing responses?
  3. Notice how students use a common vocabulary to describe strategies.?


  • Private message to Janis Maltos
Thank you for making this video. I appreciate how the teacher said, 'Before we begin our mental math lesson, lets discuss why we do mental math." Then the kids shared with a partner before sharing as a class. By having students understand the purpose of what they are learning to do, they became more engaged and interested.
Recommended (1)
  • Private message to Marshall Jones
I can see how having students talk about mathematics,as well as work out real world problems,can be valuable.
Recommended (1)
  • Private message to Matthew Wilburn
Amazing video. I love the strategies and I LOVE the hand signals but more than anything, I think I love the class worked together. More of a learning community than a classroom. Outstanding!!!
Recommended (2)
  • Private message to Brandi Parker
I am a mother of 3 & the methods they are teaching now are very different than what & how I was taught. My youngest is struggling with her math & I did a Google search for "mental math" & this website & video came up. I am so very thankful as a PARENT to be able to tap into the ways they are teaching & actually help my child. There have been nights where she would spend 4 hours after school on one page of her workbook & I didn't understand how she was supposed to apply what she had learned in class, now I am able to watch various videos & not feel helpless as a parent. Thank you so much for this wonderful website. I learn something new everyday & homework isn't such a battle anymore. Thank you again-
Recommended (2)
  • Private message to Mohsin Merchant
Where did you learn these skills, any scientific research behind that..
Recommended (0)

External Resource Materials


  • Classroom Close Up: 3rd Grade Math: Mental Math with Jennifer Saul

    Jennifer: Two days a week, we do what we

    Classroom Close Up: 3rd Grade Math: Mental Math with Jennifer Saul

    Jennifer: Two days a week, we do what we call Mental Math. Often times, students feel dependent on either the graphic organizers we give them or the worksheets or the paper and the pencil.

    "So, before we start our mental math, I'd like a review of why we do Mental Math. First, tell your partner why do you think we do Mental Math? Why even bother?"

    What's good about doing Mental Math is that students can take apart and put together numbers, and make calculations themselves. So, it helps them feel very independent.

    "So, what's a reason why it's good to be able to do Mental Math?"

    Student: "Because you can do it in your head."

    Jennifer: "You can do it in your head, like where, when you're in a store, or at Great America. Yeah. You can always do math in your mind."

    Student: "Store...your car...or your car or your house."

    Jennifer: "OK. Alright. Back in three, two, one. Who would like to share something that they said or their partner said about why we do Mental Math? Sara?"

    Sara: "We do Mental Math because there's math all over the world."

    Jennifer: "There's math all over the world. And, all over the world, is there always a pencil and a paper?"

    All: "NO!"

    Jennifer: "But is there always our brain, if we're there?"

    All: "YES!"

    Jennifer: Then I present them with a problem.

    "So my question is, if I go to the East Palo Alto library, and the Redwood City library, what would be the total number of books we would have about planets? Think."

    We have been teaching them strategies to break apart and put together numbers in their head. And, it involves a lot of academic discourse, and the students are able to use the vocabulary we teach them to explain their process, first to their partners.

    "Knee to knee. Eyes to eyes. I'd like Partner A to start."

    Student: "I got 90. I used decomposing. I broke 60 into 60 and 5."

    Student: "I used 60 jumps of ten."

    Jennifer: The three strategies we've learned so far are decomposing..

    Sara: "I used decomposing. I broke 65 into 60 and 5. I broke 25 into 20 and 5...."

    Jennifer: This is breaking numbers out into their expanded form.

    Sara: "...added the 20 and I got 80. I added the 5 to the 5, and I got 10. I connected the 10 to the 80 and I got 90."

    Jennifer: "Show if you agree. Somebody solve it with another strategy, another Mental Math strategy. Carlos?"

    Carlos: "I got 90. I used splitting. I split 65 to 50 and 15. I added the 50 to the 25. That equal 75. I added the 75 to the 15."

    Jennifer: The next one is splitting, breaking numbers apart for any number of reasons. Some reasons might be to create doubles, it might be counting 25's, quarters, whatever might make sense.

    Carlos: "That equal 90."

    Jennifer: "Between decomposing and splitting, why are they different? Lisette?"

    LIsette: "Because when you decompose, the..the..the..the 10's have to be, have..have to have a zero."

    Jennifer: "So, good. She's got us started in the right direction. So, when you decompose you're breaking into the tens. Estaban?"

    Estaban: "In decomposing, it's expanded form and, and in splitting, it's not."

    Jennifer: "Who else was remembering it's expanded form? We're breaking up tens and ones. Splitting? There's...this isn't 45, so that's not splitting into the tens and the ones. You can split any way you want, for lots of different reasons.

    And, then the third strategy, is jumps of ten.

    Student: "I took a jump of ten."

    Jennifer: "You did jumps of ten? Ok. Let's count your jumps. Ready? 1...

    Basically picturing a numberline, and hopping up tens, and then adding on whatever's left from the ones place at the end.

    The students are allowed to choose favorite strategies where it just maybe works for their brain better. And, they realize that they are a vital part of the process. Without their brain, the learning can't happen.


Jen Saul
English Language Arts Math Science Social Studies Arts / 3 / Teacher


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