KCM EXPLORATION POST

By Cindy Aossey

Quick looks, sometimes called dot talks, are a special kind of number talk in which students are briefly shown an image of a quantity, and students are prompted to determine the total.

If students are new to number talks, we recommend starting with dots rather than a computation task. The overall structure of the experience is the same as a number talk in that (1) the teacher provides a prompt, (2) students have individual think time, (3) the teacher collects responses, and (4) the teacher collects and annotates strategies. Students use established hand signals to indicate their readiness to share, agreement, etc., and the teacher weaves in partner talk to offer more thinking time and discourse as needed. (See related posts for more information about number talks). Talking about dots allows students to learn and grow more comfortable with the steps of a number talk, while also building mental images of numbers and how they can be composed and decomposed.

In their book Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 3-10 (2015), the authors, Cathy Humphreys and Ruth Parker, recommend starting with a simple dot arrangement such as the figure below. Give it a try! Give yourself a quick peek at the image. How many dots are there? How did you figure it out?

To encourage students to attend to structure and use groups, the dot image should be shown briefly (about ½ second). Students can be given additional, slightly longer looks (about 1-2 seconds) as needed. Note - young learners (typically Kindergarten and early Grade 1) may still be developing their understanding of counting principles, including cardinality. For children at this age, you might start by showing the image briefly (1-2 seconds), ask students to mentally imagine the dots, then display the dot image so that students have as long as they need to count the quantity. While discussions with older students should focus on non-count-by-one strategies, discussions with young learners should include counting by ones, with discussion of how students track the dots and that the last number of the count is the size of the collection.

You will likely find that students of all ages are eager to respond. Most likely, the class will quickly reach consensus that the number of dots is 7. But then something really interesting can happen as you start to collect responses. I bet you and your students will be amazed at how many different strategies there are! At this point in the dot talk, I like to display the dot image so students can refer to it as they share their strategies and listen to the strategies of others.

See below for a sampling of the responses you might receive from older students and how you might annotate each response. For each, imagine what a student might have said and how they might have gestured to communicate their thinking. Alternatively, especially for younger students, a teacher might choose to have a recording page consisting of multiple copies of the prompt so that each response can be recorded.

Was your strategy recorded above? If not, how would you annotate your own strategy? Can you think of another strategy not shown?

Through this experience, students are learning to listen to and learn from each other - an essential aspect of number talks. They are learning to look for structure and think about how a quantity is composed. They are building mental images of numbers. For example, they are learning that 3 can be visualized as three dots in a horizontal line, a diagonal line, or in a triangle structure. They are seeing how a simple visual and an expression can be used to communicate the structure they are seeing. And finally, they are building their comfort and confidence with the number talk routine.

Young students will benefit from frequent experiences with small quantities in different arrangements. Older students can move quickly to much larger quantities with arrangements that encourage place value and/or multiplicative reasoning. Include images that can be more easily quantified by mentally “moving” dots or “pretending” dots, then adjusting - these create foundations for flexible calculation strategies.

Don’t limit yourself to dots! Use your classroom manipulatives to create concrete representations of quantity. Contextual images, such as eggs arranged in cartons, grocery store shelves, chairs set around tables, or an array of window panes, help students notice multiplicative structures all around them. See the chart below for more suggestions.

Resources

• Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 3-10 by Cathy Humphreys and Ruth Parker (2015)
• Virtual Resources: Number talks
• Multiplicity Lab
• Visual Patterns