How Tall is a Giant?

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INTRODUCTION TO SCALING – Prerequisite for 5.NF.B.5a/b – This lesson addresses only one dimension when considering scale thus it may be used as a precursor to thinking about multiplication as scaling using a pair of factors.

CONTEXT – The height of a giant can vary greatly. The evidence of this comes from Giants, a tabletop RPG supplement written by Bruce Humphrey and published in 1987 by Mayfair Games Inc. According to this “reference for the society of giants,” there are many races of giants and though scholars have scoffed at their physical impossibility, their existence cannot be denied. Instead of delving into the biology of giants (see Giants pages 5 and 6 if you must), our focus today is on their height.

Fire Giants, 12 feet tall, impetuous and powerful warriors

Titans, 24 feet tall, first giants and progenitors of the other giants

Sea Giants, 18 feet tall, noble and personable giants from the depths

Frost Giants, 15 feet tall, resilient hermits from the icy realms

Hill Giants, 10 feet tall, aggressive and stubborn hunters

Investigate

Q1:  How many feet taller is each race of giants when compared to a 6 foot tall human?

Q2:  How many times taller is each race of giants when compared to a 6 foot tall human?

Q3:  How many times shorter is each race of giants when compared to a 60 foot tall sauroposeidon?

Q4:  How many times taller is each race of giants when compared to a 6 inch tall tufted titmouse?

Activity:  Draw a picture of yourself and a representative of each giant race, all to scale in regards to height.

Create

Activity:  Make a new race of giants. What will they be called? What characteristics will they have? How tall will they be? How will the height of the new race compare to the heights of other giants and animals?

No Squares Here

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Recognize and Categorize Shapes – Grade 4

Everyone wants to count triangles in this figure but what about rhombi, parallelograms and trapezoids? Hexagons and pentagons? Dodecagons anyone? The abundance of parallel lines make this a good figure for 4th graders to study, both as a review of some of the shapes addressed in previous grades and as an opportunity to classify quadrilaterals based on the presence of one or two sets of parallel lines.

2.G.A.1 – recognize triangles, quadrilaterals, pentagons and hexagons

3.G.A.1 – recognize rhombi as examples of quadrilaterals

4.G.A.2 – recognize parallelograms and trapezoids* by their attributes

Investigate

Q1:  What shapes do you see?

Q2:  How many of each shape are there? Count all same sized shapes as one shape. [For example, there are 4 different sized triangles, all equilateral.]

Q3:  How would you organize each of these shapes into categories?

Q4:  How many categories do the rhombi belong to? Make your case.

*Although students are composing trapezoids as early as grade 1, it’s not until grade 4 that students are expected to consider its defining attributes. Use the inclusive definition of the trapezoid, a quadrilateral with at least one set of parallel sides.

Understanding the Equal Sign

Challenge

Children may misperceive the equal sign as an instruction to compute rather than understanding the equal sign as a symbol that shows two expressions have the same value. These children will often place a 5 in the blank when given 2 + 3 = _ + 4. Practice with addition facts may actually strengthen this misconception if children are repeatedly given left to right “4 plus 2 makes 6” formatted facts. This can become a significant stumbling block in a child’s development of algebraic reasoning.

Teachers

  • Explicitly teach the equal sign means “the same value as.” In lower grades you may say, “6 marbles is the same as 4 marbles and 2 marbles.”
  • Avoid the input-output model to describe equations. The equal sign is not an operation that “makes” a number.
  • Use a variety of equation formats. For example: 3 = 5 – 2 or 9 = 9 or 2 + 6 = 10 – 2

Students

  • Represent a variety of equation formats with concrete objects and pictorials.
  • Describe their own representations of equations using “same value as” to express equality.
  • Solve for unknowns in equations such as 8 + _ = 3 + 9.

Source: Teaching the Meaning of the Equal Sign to Children with Learning Disabilities: Moving from Concrete to Abstractions by Ruth Beatty and Joan Moss at the University of Toronto. Published in The Learning of Mathematics, NCTM’s 69th Yearbook, 2007.