Math Methods Exam #3 Flashcards
Distinguish between ratios and proportions
Ratio is a multiplicative comparison of two or more numbers in a number whereas, proportion is an equivalence relation between two or more ratios
Ratio-Multiplicative comparison
Proportion- equivalence relation
Recognize foundational concepts that children need to master in order to work effectively with percents
Fractions, decimals, ratios & proportions
Solve each of the following types of percent problems using BOTH the ratio and equation methods
-Find the percent of a given number
-Finding what percent one number is of another number
-Finding the total percent (100%) when only a percent is known
+What is 20% of 50
+what percent of 10 is 5/10
+After a sale an item was marked $40, if the sale was 50% off how much was the original price?
A. 40
B. 50
C. $80
Describe ways of developing proportional reasoning with students
Using concrete examples (the Giant Activity) give students the opportunity to compare objects and their size. Having students compare shapes of two different sizes and write the proportions for them.
Describe how you would concretely model the concept of percent with children
Using 100 pennies to show students that 1/4 of a dollar is the same at $.25. Another way would be to show students what a percent bar looks like and breaking down the different percentages by marking them at 25% 50% 75% and 100%. Poker chips are another way to show percentages by having students find the percentage they have of each color.
Discuss the use of repeating and growing patterns in helping children understand algebraic concepts
A repeating pattern has a core element that is repeated over and over. One of the simplest repeating patterns is red, blue, red, blue… A growing pattern increases or decreases by a constant difference but doesn’t repeat.
Describe how you would help students develop an understanding of variables, relations, and functions.
I would show them that variables are just placeholders of the number that we are solving for by writing out equations for them using variables and modeling how we solve for them. relations if you add 2 postiive you’ll get a postive. If you add a negative to a positive you’re going to subrtract. Function (think function machine)
Describe one activity that you could use in your classroom to help children think about the concept of change and represent it mathematically.
students tracking the decrease in mass of two carrots that have been sitting out one with the starting weight of 40g and the other 80g. They would track the data on a table and then graph it at the end of every week.
Describe how you would would use Algebra Tiles to help children visualize the following types of algebraic relationships and problems
-Adding and subtracting integers
-Modeling Algebraic expressions
-Solving linear equations
-Adding or subtracting
-Multiplying polynomials
-Factoring polynomials
use one side of the tiles to represent negative integers and the other side to represent positive integers.
Describe the 5 levels of geometric thinking defined by Clements and Battista. Be able to give an example for each level
Level 0 (Pre-recognition) ~ Children only focus on some visual cues- Shown a triangle, children may focus on straightness and say it’s a square
Level 1 (Visual) ~ Children view a geometric shape as a whole. They can describe attributes based on visualization but not based on analysis of the attributes- Children may say it is a rectangle because it “looks like a door”. It has 4 sides because they can count them
Level 2 (Descriptive/Analytic)~ Children focus on the relationship between parts of a shape and defining attributes- Children may describe a rectangle is a four-sided figure with opposite sides equal and parallel with 4 right angles
Level 3 (Abstract/ Relational)~ Students interrelate geometric attributes, form abstract definitions, distinguish among necessary and sufficient sets of attributes for a class of shapes- Students know that a sufficient definition of rectangle is “a quadrilateral with two pairs of parallel sides and a right angle
Level 4 (Formal axiomatic)~ students use deduction to prove statements. This is the level needed to be successful in a formal, high school geometry class- Students, given axioms, can write a deductive proof
Define and give examples of the following types of transformations used in transformational geometry
-Translation
-Rotation
-Reflection
Translation~ [Slide] every point on the plane moves in the same direction by the same distance
Rotation~ [Turn] revolution or complete rotation
Reflection~[Flip] turned over a straight line to become a mirror image
Give examples and describe how to develop the following geometric ideas with children:
-Congruence
-Similarity
-Representing locations (coordinate graphing)
-Symmetry
Congruence- showing students two of the same shape one on its side and one upright to show that they are the same shape and size making them congruent
Similarity- Having students make observations about what they notice is the same about 2 shapes that are the same but different sizes
Representing locations- having students identify the coordinates of different plots
Symmetry- showing students that symmetry means when an object is folded on a symmetry line it looks the same on both sides
Give examples of comparing a measurement attribute such as length using each of the following types of comparison
-Perceptual comparison
-Direct comparison
-Indirect comparison
Perceptual comparison- comparing lengths of two objects of different lengths and thickness (hold up a crayon and pencil and ask students what they notice is different)
Direct comparison - hold two objects up that are the same but are different lengths (ask students which one they think is longer)
Indirect comparison- comparing two ideas without a concrete way to show the difference (ask students which they think is taller, the teacher desk or their student desk
Be familiar with the 9 concepts about units of measure discusses in your texts. Be able to recognize them. Be able to discuss one of them in depth, describing how you would develop the idea with children (pg.328-332)
-A unit MUST REMAIN CONSTANT
-A measurement MUST INCLUDE BOTH A NUMBER AND UNIT
-Two measurements may be EASILY COMPARED IF THE SAME UNIT IS USED
-ONE UNIT MAY BE MORE APPROPRIATE THAN ANOTHER TO MEASURE AN OBJECT
-There is an INVERSE RELATIONSUP BETWEEN THE NUMBER OF UNITS and the size of the unit
-STANDARD UNITS NEEDED TO COMMUNICATE EFFECTIVLEY
-A SMALLER UNITS GIVE MORE EXACT MEASUREMENTS
(Give students a strip of paper that is 28cm and one that is 29cm have them make observations to guess which one they think is longer and then have them measure in cm to see which one is truly longer.
-UNITS MAY BE COMBINED OR SUBDIVDED to make other units
-UNITS MUST MATCH THE ATTRIBUTE that is being measured
Construct and discuss the uses of each of the following types of graphs
-Line plots
-Stem-and-leaf plots
-bar graphs
-pie graphs
-line graphs
-box plots
line plots- Used to display NUMERICAL DATA with a SMALL RANGE
Stem-and-leaf-plots- displays data and provides a different representation and typically is ORGANIZED IN 10s
Bar graphs- used for DISCRETE NOT CONTINUOUS that would be a histogram, or separate and distinct data
Pie graph- A circle that REPRESENTS the WHOLE with wedges to REPORT MORE SPECIFIC DATA
Line graphs-show TRENDS OVER TIME
Box plots- shows the SPREAD OF DATA to show variability
