How Many Dots Do You See?

Spatial Reasoning Skills

  • Visualization 
  • Mental Rotations 
  • Complexities of Symmetries, Transformation and Coordinates 
  • Mapping, Location and Orientation 
  • Composing and Decomposing 2-D and 3-D figures 
  • Perspective Taking

Curriculum – Geometry and Spatial Sense

  • Recognizing transformations 
  • Describing relative locations and paths of motion 
  • Describing location using positional language

Context

Students are shown dots on cards in typical dot patterns or arrangements and are encouraged to state how many dots they see. The game has many variations and the games can be played for five minutes at the carpet, as a warm-up and for practice.

Purpose: Students use visual pattern/arrangement to recognize quantity with accuracy and speed; students use these patterns to compose and decompose numbers. This activity promotes subitizing (suddenly seeing and knowing a quantity) which, in turn, supports counting-on strategies and adding fluency. For example, when a child sees an arrangement of three dots on a card, he or she may know that the quantity is three without counting each dot, and then he or she can add on the remaining dots on a second card.

Materials

  • Dot Cards (see images below for examples when making dot cards)

Lesson
Introduction

  • Gover configurations of dots with students 
  • Prompt a discussion around memorization 
    • Ask students what are some common ideas or concepts that we remember
    • Strategies for remembering numbers and images

Lesson

  • Game 1: Dot Dash
    • Students can work with a teacher, volunteer or a partner to state the number of dots they see when a card is shown to them. The key is for the student to only count the dots if they need to. They can visualize—look at the dots, then verbalize—say how many dots there are, then verify by counting the dots.
  • Game 2: How many dots CAN’T you see?
    • Show the students a card with some of the dots revealed and some covered. Tell the students how many dots there are in total. Ask students: “How many dots do you see?” Then ask “How many dots can’t you see?” This helps children to visualize the number of dots that are not visible. This game can also be played at the carpet with little bears or objects and a blanket. (For example: “There are 7 bears in total but the blanket is covering some of them. How many can we see? How many can’t we see?”)

Closure

  • Gather students for a summarization of the two game-based activities
  • Consider the following prompts for discussion:
    • Did you remember how many dots?
    • How did you remember the dots?

Extensions

  • Consider the following extensions: 
    • As students gain experience with this activity, encourage them to use two dot cards at a time and add the dots together. They may want to count all dots to verify the total, but then some will count on from the first dot card to the second dot card, while others may simply add the two quantities together.
    • As a further challenge, try Game 3: How many dots on my card? Have students play this game as a group of 3. One student (student A) does not have dot cards. This person has to be able to add all of the dots together and state a total to the other two students. The other two students (B and C) each place one dot card on their foreheads.
    • Student A calls out the total and students B and C look at each other’s dot cards without looking at their own—to see what is missing from the total (which is the number of dots on their card). Students B and C can discuss what the number sentence will be.