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Lesson 53: Notice & Name – Absolute vs. Relative Thinking – Discussion
Posted by Jon on December 6, 2019 at 6:20 amDescribe absolute thinking and relative thinking in your own words. What are key characteristics you want to keep your eyes open for to determine which type of thinking your students are using in your classroom?
Share your reflection below along with any wonders you still have.
Kyle Pearce replied 1 year ago 21 Members · 27 Replies 
27 Replies

I’d like to know what bank James uses. $14 a month in interest?!?

Hahaha! I was wondering how long we’d go before someone commented on that!!! Extreme examples, I know 🙂


Absolute thinking is addition and subtraction.
Mulitplicative thinking is when you compare an attribute such as volume of two objects.
If kids are thinking multiplicatively, you’d notice them perhaps using repeated addition or subtraction. Maybe they’d be using the words “times”, “groups of”, “sharing”” or ” divided by”.
I, too, would like to find an investment with such great interest!

Absolute thinking involves addition and subtraction while relative thinking uses multiplication and division.
I’ll invest in the Bank of Jon and Kyle! 🙂

Absolute thinking is looking only at the numbers. Like a cup of coffee cost $1.00 and then it was changed to $2.00. The absolute change is the difference between the two prices or $1.dollar. However, if we look at the relative cost of the increase it would require us to look at $1.00/$1.00 or 1 whole = 100% increase in price.

Additive thinking describes how much a quantity changed by adding or subtracting another quantity. Multiplicative thinking describes how much a quanitity change by sarting with the quantity and making all changes relative to it.

Additive thinking is based on addition and subtraction while multiplicative thinking is based on multiplication and division.
Students who are trying to make the leap to multiplicative thinking might being trying to use repeated addition or subtraction. I find many students struggle with breaking away from just additive thinking and they want to stay with addition as it is a comfort zone for them.

With relative thinking there is a relationship between two objects or sets and there is an exponential growth (or decrease) in a particular attribute they both share.
With additive thinking, there is a difference in a number of items or units when comparing two groups. The difference involves subtraction.

Instead of writing more I would just say the best example is the Coffee cup pricing that Jeanette used. It is perfect. It demonstrates how one can look at price change in both manners.

Absolute thinking results in a quantity (either more or less) that stands on its own – it is absolute. It needs no reference to another quantity or value. (It can be expressed using the language of addition or subtraction).
Relative thinking results in a relationship to describe one quantity in reference to another quantity. It requires a reference to another quantity or value. It can be expresses using the language (and symbolic notation) of division or multiplication.
I enjoyed the sorting activity. This transition from additive to multiplicative thinking is such a critical, and fragile one for students. This shows up so often in grades 5 and 6 when students are reading a table and not able (yet) to read the table in both directions. When they look vertically (if headings are at top), they’ll say that “it is going up by 1.” I’ve had to show them to read the relationship of the horizontal cells. The number of miles is 8 times greater than the number of minutes, for example.

Using a measure of unit as a reference point to describe how one quantity is greater than or less than another is additive thinking.
Using multiplication or fractional language to describe how one quantity relates to another quantity is multiplicative thinking.
The key characteristic to keep an eye out for:
the point of reference….is it the unit or the other quantity

Love your key to watch out for. Definitely helpful as people look to notice and name additive and multiplicative thinking!


That was a fun game to play. I can see it taking off, “Additive or Multiplicative?” Great Jeopardy topic too.
My take is that additive is really in terms of how much greater or fewer, while multiplicative is more about the relationship of a quantity that one has on another and watching it change in proportion over time. Additive does not need to change in proportion.

Great way of thinking about it. It certainly brings back the absolute vs relative change discussion from module 1.


When comparing two quantities you are using multiplicative thinking or relative thinking. When adding or subtracting one quantity from another you are using additive or absolute thinking.

using the earlier example in unit 1 about the $100 that became $400 and the $1000 that became $1500, in additive or absolute thinking the first earned $400 and the second earned $500. In multiplicative thinking the first earned four times as much as it started with (or 400%) while the second earned 1 1/2 times what it started as or 150%. Also you are risking 1/10 less in the first scenario which is also multiplicative thinking

Nice reflection and summary! When dealing in money, we tend to flip flop additively and multiplicatively without even realizing it. Hopefully these activities help you better notice and name these types of thinking in action! 🙂


The difference between additive and multiplicative thinking is clear to me, but I have not really highlighted it with my students. I’m excited to have conversations with them about how we are thinking differently, not just using a different operation, when we solve problems multiplicatively. And yes, many students are stuck in additive thinking. It seems to me that they don’t trust multiplicative thinking, it is a leap of faith they aren’t willing to risk (for fear of the dreaded MISTAKE). I’m excited to learn more about how we bridge or scaffold kids over the multiplicative thinking.

Trust is a great way to put it. When we aren’t flexible with our number and operation sense, we don’t trust the mathematics. Helping students by using math talks and keeping the calculator to the side is so critical for students to develop this fundamental number sense.


Having read Diane Hamilton’s reflection, I too, love her analogy of trust. Maybe when we have made students take timed fluency tests is when we have broke trust as their teacher. Anxiety builds because they haven’t had enough experiences to trust their knowledge of the facts. I know that they say the mother bird pushes her baby out of the nest to fly but only when the bird is ready to test its feathers.
So I am thinking another way to think of additive or absolute thinking is you can hear the counting….3 more. Multiplicative or relative you aren’t sure if one is counting or giving a ballpark estimate…”about” 3 times as many. I never thought about multiplication being a big enough jump to trust the mathematics.

Additive thinking using absolute values compares using the ideas of more or less and stating the difference or the total in a specific value. Multiplicative thinking uses relationships and proportions between two or more objects.

Absolute thinking uses terminology of “more than/less than.” It’s additive thinking where we are looking for differences of a single unit.
With relative thinking we are evaluating one object in terms of another. I will hear students talking about about “groups of” or “times.” It’s multiplicative thinking. They might still be counting on their fingers, but each finger would represent a multiple rather than an individual number.

Absolute thinking is counting off the difference or sum, while relative thinking is utilizing the patterns of multiplication and division to describe the relationship.
When students are using key words like more than/less than they are still thinking additively, while using words like times bigger would indicate relative thinking.

Relative has a relation to one of the quantities as the “unit”. Then it is multiplied. The absolute is additive and seems to usually use a indirect unit.

Would love to hear more about your thinking around an “indirect unit”.
