We can help our children experience math in the real world by providing thousands and thousands of experiences with real objects in the physical world. But what’s next?
Last week we focused on providing some of those real life experiences for littles through intentional, math-focused conversations embedded into your daily routines. Even as you progress through the stages of developing early problem solving skills, don’t neglect those conversations! The topics of conversation might adapt as your child masters certain skills, but every math-focused conversation you have strengthens that child’s understanding of math and adds to their body of experience with real objects in the physical world.
The next stage of problem solving involves using what we call quantitative pictures. It sounds fancy, but quantitative pictures is simply a picture that contains lots of things to count! You could use a picture from the Hidden Picture section of the Highlights magazine (if you have it, or you can get a few for free online: https://www.highlightskids.com/games), or you could use a page from a coloring book or favorite picture book. National Geographic even has pictures of animals and things in nature that could be counted.
Asking Questions about Real Life Situations
One of my favorite resources to use is a book called Math Talks by my friends Char Forsten and Tori Richards. So many of our teachers use and love this book. Sadly, it has been out of print for a while, but we are super excited to announce that we have the exclusive rights to the digital version of this book! You can download the eBook from our SIS4Teachers store and use it right away!
The title of this book catches people off guard sometimes because “math talks” sound a lot like the “number talks” that we talk about. Of course, both types of talks deal with numbers, but in different ways. Math talks use real pictures in a quantitative way and focus on using different types of questions (from beginning to challenging) to help students think about numbers.
For our littlest learners, questions about a quantitative picture could be very basic: What do you notice? How many children do you see? Our advanced students could look at the same picture and we could ask more complex questions: If two more children join these children on the beach, how many children would there be?
In Math Talk, not only do you get a great selection of full-color images and a range of questions to ask about it, you also get a black and white version of the image that is almost like a coloring sheet. This is great if you want students to literally interact with the picture by coloring the different objects you are asking questions about.
Using Quantitative Pictures
In these videos, I’m going to show you how you can use quantitative pictures to help make word problems come to life for students of all ages! I’ll be using two of the examples from Math Talks, At the Apple Orchard and At the Beach, and you’ll be able to see how you can use one picture for a really wide range of students just by varying the questions from basic, to intermediate, to advanced, and finally to more challenging.
Download At the Apple Orchard: bit.ly/AttheOrchard
Download At the Beach: bit.ly/SISAttheBeach
I like to display my quantitative pictures on a document camera or even a smartboard so we can interact with them in different ways, depending on the level of students. Younger students might just need to come up and be touching and counting. Older kids might start to draw or circle objects in the picture if you’re doing this in a whole class setting.
This is a great opportunity to double-dip and work in some vocabulary words as well! Depending on what grade you’re teaching, directional words work really well with quantitative pictures. Talk about objects that are above or below, next to, behind, etc. Use plenty of adjectives to describe physical characteristics of objects you’re looking at – large, small, round, flat, etc. – as well as comparison adjectives – big, bigger, biggest.
Beyond Early Childhood
Math Talks lists sample questions, those aren’t the only questions you can ask about the picture! By applying different mathematical concepts – part/part/whole addition, multiplication, division, fractions, etc., you can extend the use of a quantitative picture beyond the early childhood years. With a little practice (and a few sample questions as a guide!), you can apply whatever concept you’re teaching in math to a quantitative picture!
Once students are confident and comfortable examining quantitative pictures of math in real life situations, we want to look at how we can take this progression of problem solving to a more hands-on level of actually where children act out the problem with concrete objects, create a pictorial representation, and then record it in an abstract equation. Join us next week to talk about how we do this with story mats!