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Infer & Predict to Build Mathematical Comprehension!

 Being able to 'read between the lines' and make predictions is the bedrock to building understanding in both reading AND math. Maybe even more so in math! Inferring is something that we do all the time- without even realizing it. Personally, I think that fact right there makes teaching HOW to infer difficult. It's hard to put into words and explain something you do without even realizing it. I AM getting better at it, though. (With the help of ideas and activities I've found out here in bloggy land!)

In Mosaic of Thought, Keene & Zimmerman (1997) relate that "inferences are like lifting ideas out of a book and adding your own ideas to them". I don't know about you....but my kiddos have a rough time doing that -- especially in math! And that's a problem, because inferring helps kiddos:
  • draw conclusions
  • make reasonable predictions
  • answer questions they've generated
  • make connections
  • gain insight when struggling to understand complex concepts (hElLo!)
  • make critical or analytical judgements about text or mathematical data (again....HELLO!)
Think about all those things that inferring helps kiddos do in math. Super important...right?! I agree with Laney when she says, "[b]uilding the capacity of students to infer and predict in mathematics is even more essential that in reading instruction considering the fact that mathematics is a science of patterns" (p. 173).

So how can we help kiddos build these skills?
First, it's important that kiddos know these things about inferring & predicting:
  1. Mathematicians figure out unknown words, concepts, and problems by using their schema, paying attention to details, re-reading, and talking with others.
  2. Mathematicians use info from their work & their prior knowledge to determine problem-solving methods and to better understand the math concepts their working on. They are intentional.
  3. Mathematicians make predictions then confirm or contradict them as they work.
  4. Mathematicians know to infer when the information they need is not expressly stated, when they're looking at data, or with unfamiliar math ideas.
  5. Mathematicians look for patterns in their work from which they can draw inferences.
So- how can we help kiddos build these skills?
  • Modeling & Think Alouds There it is again....teacher modeling and think alouds are so important. Are you as intentional about doing them in math as you are in reading? Did you know that many students (& adults) fear math? Many feel like math makes no sense & it's just a matter of memorizing rules, procedures, & facts? Have you noticed when meeting with kiddos AND PARENTS that many feel that math achievement is solely related to ability rather than effort? I cannot tell you how many times I've heard parents say, "Well...I was never good in math either" with the implication that of course, because of that, their child won't be either. Math ability is NOT hereditary, people!! Those think alouds we do give kiddos experience and practice in how to make those inferences and predictions that form the bedrock of their mathematical comprehension...that gives them all those benefits listed up there!
  • Word Splash I've done these for Science and Social Studies before...but never thought about them for math! Basically, you choose key words or expressions for your concept, scatter them all over your chart paper, then have kiddos look for the common thread that connects them. Love how that makes them draw on their schema and look for those connections!

  •  What's the Question? Math Stretch Is this a coincidence, or what? I just ran across this awesome pin the other day...exactly what Laney is suggesting for helping kids build the ability to infer & predict. You give the answer....kiddos come up with the question. That makes kiddos pull on their own prior INFER what kinds of questions will go with the answer you've posted. This is definitely going in my room in a few weeks!

  • Facts or Inferences Math Stretch Have students read a math story problem. Kiddos then decide if statements are either facts or inferences based on the story. You could begin by making a chart on which you've listed the facts/inferences and then work together to label them. I made up this little organizer (which is EDITABLE!) that would be great for kiddos to use to practice this skill.  Just click the image to download your copy!
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And stop by to check out others' thoughts on Chapter 6 of Building Mathematical Comprehension...

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  1. Great post! It's amazing how many times Sammons has already stressed the idea of teacher modeling and think alouds....makes me think if I really do them often enough!

    Thinking of Teaching

    1. I know what you mean, Beth! I worry that when I do do them, I don't give it justice because I'm so worried about the time! Sometimes I'm just trying to get it all I do a good job when I'm doing that? Hmmmm

  2. I love that pin! I think I'll be making one of those too!

    Teach on a Limb