Minds On

Pascal’s triangle

Let's check out Pascal's triangle!

It is one of the most famous patterns in the world and one that continues to be studied by mathematicians all around the globe. There are still many secrets that have yet to be uncovered in this famous pattern.

This is Pascal’s triangle which is a famous pattern used by mathematicians. Rows go from top to bottom and left to right. There is 1 number in the first (and top) row, and it is 1. There are 2 numbers in the second row and they are 1 and 1. There are 3 numbers in the third row and they are 1, 2, and 1. There are 4 numbers in the fourth row and they are 1, 3, 3, and 1. There are 5 numbers in the fifth row and they are 1, 4, 6, 4, and 1. There are 6 numbers in the sixth row and they are 1, 5, 10, 10, 5, and 1. There are 7 numbers in the seventh row and they are 1, 6, 15, 20, 15, 6, and 1. There are 8 numbers in the eighth row and they are 1, 7, 21, 35, 35, 21, 7, and 1. There are 9 numbers in the ninth row and they are 1, 8, 28, 56, 70, 56, 28, 8, and 1. There are 10 numbers in the tenth row and they are 1, 9, 36, 84, 126, 126, 84, 36, 9, and 1. There are 11 numbers in the eleventh row and they are 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, and 1. There are 12 numbers in the twelfth (and last) row and they are 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, and 1.

Student Success

Think-Pair-Share

If possible, with a partner, reflect on the following questions:

  • What patterns do you notice in Pascal’s Triangle?
  • What interesting things can you explore?
  • If you haven’t tried it already, add the numbers in each row across. What do you notice?

Record your ideas in your notebook or another method of your choice.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Action

Repeating patterns

Pascal’s Triangle has many examples of growing patterns.

Let’s identify repeating patterns in a hundreds chart in the same way mathematicians continue to discover patterns in Pascal’s Triangle.

Let's explore a Hundreds Chart! Try using it yourself and ask for help if you need it!

Part 1: Hundreds chart

Use a hundreds chart to help you answer the following questions:

  • What do you notice about how the numbers are organized?
  • What happens to the numbers in the tenth column?
  • What do you notice about each of the rows?
  • How are the numbers organized?
  • What happens to the numbers in the first column?

Record your ideas in your notebook or another method of your choice.

Part 2: Counting patterns

You can use a hundreds chart, number line, or another manipulative of your choice to explore the following patterns.

Exploring the hundreds chart by 11

Let’s start at 1 and count up by 11 each time.

You can use the yellow sticker to help keep count.

Let’s explore the hundreds chart, and identify the numbers that are part of this pattern.

  1. Describe the pattern and record the numbers in this pattern.
  2. Observe your numbers in the tens and ones columns. What is happening to those numbers?

Record your ideas in your notebook or another method of your choice.

Exploring the hundreds chart by 9

Now, start at 10 and count forwards by 9 each time.

You can use the pink sticker to help keep count.

Let’s explore the hundred chart, and identify the numbers that are part of this pattern.

  1. Describe the pattern that you notice in your number chart. Record the numbers in this pattern.
  2. Observe your numbers in the tens and in the ones columns. What is happening to those numbers?

Record your ideas in your notebook or another method of your choice.

Exploring the hundreds chart by 8

Start at the number 80 and count backwards by 8 each time.

You can use the purple sticker to help keep count.

  1. What pattern do you notice? Record the numbers in this pattern.
  2. What do you notice about the numbers in the ones place? Is there a repeating pattern?
  3. Knowing the repeating pattern rule for the numbers in the ones place, what are the next 5 numbers after 80 in the pattern?

The next five terms are ____, ____, ____, ____, ____

Record your ideas in your notebook or another method of your choice.

Consolidation

Reflecting on the hundreds chart

Student counting and exploring a hundred chart on a device.
  • What is something you discovered in today’s lesson?
  • How could a hundreds chart be a useful tool to help you add and subtract in the future?

Complete the Hundreds Chart Reflection in your notebook or using the following fillable and printable document. You can also use another method of your choice.

Grade 3 Mathematics Algebra – Hundreds Chart Reflection

Press the Activity button to access the Hundreds Chart Reflection.

Activity(Opens in a new tab)

Reflection

How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.