Category Archives: Number Sense

This category would include converting between multiple equivalent forms such as decimals, percents and fractions; properties; operations involving real numbers; and combining like terms.

Teaching Integers…Successfully!

As you delve deep into your curriculum, integer operations usually sits close to the beginning of the year for most 7th, 8th, and Algebra courses. I would like to take the time to share with you a resource that a colleague of mine found a few years ago and I’ve used ever since.

Integers Made Easy: Just Walk It Off

Julie Nurnberger-Haag does a wonderful job teaching students how to add, subtract, multiply and divide integers using a life-size number line in her article Integers Made Easy: Just Walk It Off. Students follow a very small set of guidelines for performing operations on integers using a number line place on the floor, large enough for students to walk about. Supplies needed are painters tape, notecards, and integer problems. This can be done outside using sidewalk chalk as well; however, you must have exceptional control over your class in order for this activity to be meaningful to students.

I have enclosed a word document similar to one I use in class for students to record their specific steps they performed to arrive at the solution. Students may not like the writing portion, but this is just another avenue for students to put the information into long-term memory. In many cases, it slows the student down and requires them to really think about what they are doing and why they’re doing it. Have student practice verbalizing their steps out loud to you as a means of explaining their answers. You could even do as a small assessment in this manner.

Walk It Off

Later in the year, when students get confused with their integer rules, either you or a fellow classmate will have a way to explain how to arrive at the correct solution.

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Number Sense Foldable

In my last post here I left discussing the importance of creating strong number sense skills for students. I provided instructional notes and a foldable example. I have attached below a Smart Notebook file that walks through creating this with students. If you do not have this software, you can save this file and then open it using the Smart Notebook Express Web Application. This is a free viewer/editor and is easy to use. The Number Sense file that is attached here is posted to the Smart Exchange site that is designed for educators to share files.

Smart Notebook Express Web Application

Number Sense (Notebook File)

Teaching and Assessing Number Sense

It is important for algebra students to know the characteristics of the different sets of real numbers, including natural numbers, whole numbers, integers, rationals and irrationals. They should be able to determine the smallest subset the value belongs, as well as all subsequent sets. Students should understand and be able to interpret the Venn diagram of the real number system.

I have included two documents here. One is for instructional purposes and may even be used for student notes. The other is a test that I have used with algebra students. The test goes a bit further than the instructional piece that I have included in that I also assess students ability to evaluate and operate using real numbers. Students will need to be able to apply the order of operations and integer rules to evaluate algebraic expressions.

Instructional Piece on the Real Number System RealNumberSystem

Algebra Test NumberSenseTest 

Instructional Strategies:

  1. Have students create a foldable to record this information. See instruction sheet Instructional Strategy Number Sense Foldable
  2. Create a large Venn Diagram on the whiteboard, provide students with notecards with a real number, one at a time have them place their card in the appropriate spot within the Venn.
  3. Create a large number line within the classroom. Provide each student with a real number written on a notecard and a clothes pin. Have students place their card appropriately on thenumber line. Once everyone has  finished, have each child call out their number, what set(s) the number belongs and why they placed it where they did on the number line.

Number Sense Ideas…Coming Soon!

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