PDL's Number Building Staircases FREE

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Grade Levels
PreK - 1st, Homeschool
Formats Included
  • PDF
10 pages
Play Discover Learn


Cuisenaire® Rods Staircases provide context for exploring common difference and describing quantities in relationship to other quantities. The following activity mat (color or black/white) and 5 worksheets are designed to emphasize these concepts. This product is designed to be used with Cuisenaire® Rods.

To purchase the FULL product with 10 activity mats and 100 worksheets, check out PDL's Number Building Staircases for Cuisenaire® Rods.

Why common difference is Important?

Common difference is a strategy students may use to subtract quantities with greater ease. For example, which is easier to subtract 15 minus 9 or 16 -10. Both have the same common difference.

If students understanding that adding one to both numbers still creates the same answer, then students may avoid other strategies that are more complex.

This strategy continues for larger numbers. For example, take the problem 156 – 98. If the student adds 2 to both numbers, an easier problem is made available to the student. 158-100. Even for more complex problems like 1426 -679 can be solved using the same strategy. Adding 321 to both numbers creates the problem 1747 -1000.

Developing the student’s awareness for common difference prepares the student later to use this strategy for subtraction. You can see that understanding common difference carries the student a long way. It also provides for less error because regrouping is reduced.

Other topics explored

Many worksheets are provided to help create context to see the interconnectedness of multiplication, fractions and division. Students explore addition in the context of staircases as well to help them see the relationship between addition and subtraction.

Reading Meaning into Notation

The ability to read meaning into notation is a key factor of success in mathematics. Worksheets include both written word notation as well as symbol notation to help students read meaning into notation. For example, Five and four have a difference of one is the written word notation. 5 – 4 = 1.

Avoid Operating Language

Subtraction is what you do to a quantity. Difference is how you describe a relationship between two quantities. This entire packet avoids operation language like subtraction. Instead, the focus is on describing relationships of quantities to develop understanding of numeric behaviors.

We don’t go out into nature and manipulate (i.e. operate on) it without first learning to observe and describe the nature we see. Observing and describing quantities and their relationships develop student understanding on how quantities behave in relationship to each other.

Cuisenaire® Rods is a registered trademark of hand2mind, Inc. and is used with permission from hand2mind, Inc.

*Cuisenaire® Rods not included.

Total Pages
10 pages
Answer Key
Teaching Duration
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