Cuisenaire® Rods Staircases provide context for exploring common difference and describing quantities in relationship to other quantities. The following 10 activity mats and 100 worksheets are designed to emphasize these concepts.
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 completely avoided.
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.
When students observe basic behavior of quantities, they manipulate quantities with better understanding.
This product is included in the PDL's Interactive Math Notebook for Cuisenaire Rods
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Cuisenaire® Rods is a registered trademark of hand2mind, Inc. and is used with permission from hand2mind, Inc.
*Cuisenaire® Rods not included.
*IMPORTANT PRINTING NOTE* Some PDF software default the file to fit page. This changes the size of the activity so when you print, the cuisenaire rods will not fit within the desired area. Please change your settings so that they do not change the size of the page. This setting varies on your software. For Adobe, change the settings to NONE. For others, the setting should be changed to "use actual PDF dimensions for paper size."