distributive property

Geometry Part 8: Area and Perimeter (cont’d)

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by C. Elkins, OK Math and Reading Lady

This post features 3 more area and perimeter misconceptions students often have. I have included some strategies using concrete and pictorial models to reinforce the geometry and measurement standards. Refer to Geometry Part 7 for 2 other common misconceptions.

Also, check out some free resources at the end of this post!!

Misconception #3:  A student only sees 2 given numbers on a picture of a rectangle and doesn’t know whether to add them or multiply them.

  • Problem:  The student doesn’t know the properties of a rectangle that apply to this situation — that opposite sides are equal in measurement.
  • Problem:  The student doesn’t see how counting squares can help calculate the area as well as the perimeter.

Ideas:

  • Give the correct definition of a rectangle:  A quadrilateral (4 sides) with 4 right angles and opposite sides are equal.
  • Give the correct definition of a square:  A quadrilateral (4 sides) with 4 right angles and all sides are equal. From this, students should note that squares are considered a special kind of rectangle.  Yes, opposite sides are equal – but in this case all sides are equal.
  • Using square tiles and graph paper (concrete experience), prove that opposite sides of a rectangle and square are equal.
  • Move to the pictorial stage by making drawings of rectangles and squares. Give 2 dimensions (length and width) and have students tell the other 2 dimensions.  Ask, “How do you know?” You want them to be able to repeat “Opposite sides of a rectangle are equal.” With this information, students can now figure the area as well as the perimeter.
  • Move to the abstract stage by using story problems such as this:  Mr. Smith is making a garden. It will be 12 feet in length and have a width of 8 feet.  How much fence would he need to put around it? (perimeter) How much land will be used for the garden? (area).
  • Measure rectangular objects in the classroom with some square units.  Show how to use them to find the perimeter as well as the area using just 2 dimensions.  Ask, “Do I need to fill it all the way in to determine the answer?”  At the beginning – YES (so students can visualize the point you are trying to make). Later, they will learn WHY they only need to know 2 of the dimensions to figure the area or perimeter.

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Multiplication Strategies Part 2: Decomposing and distributive property to learn facts

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by C. Elkins, OK Math and Reading Lady

In part 2, I will show you some ways to help students decompose a multiplication problem into 2 (or more) easier multiplication problems. Most students know problems with factors of 2, 5, and 10. The decomposing will allow students to use what they know to work on the unknown / unmemorized fact.

I frequently see students struggle with solving an unknown multiplication problem. Often they choose skip counting, but if they miss just one number in the sequence, the answer comes out wrong. I also see them use their multiplication chart, but this doesn’t do much to help them apply number sense. Other times I see students draw circles with dots inside, but this is time consuming and it often becomes just a counting practice. This method is using the distributive property. Students can break apart one of the factors into “friendly” addends. I usually advise making one of the addends a 2, 5, or 10 since those are usually easier to compute or are already memorized. Here are some examples:

 

 

I have also attached a class activity sheet in which students cut out grids, glue them on the worksheet and then decompose them. Get it free here: Distributive property teaching chart  Another resource for teachers is my multiplication strategies guide which shows some ways to break down each factor’s family. Get it here free: Multiplication fact strategies chart  Finally, here is a link to a TPT source with a freebie for using the distributive property with arrays: Distrib. Property of Multip. freebie by Tonya’s Treats for Teachers

Have a great Spring Break for Oklahoma teachers!! I will be back in 2 weeks with more multiplication strategies.