Math 2A Lesson Plans

What this unit is about...

1) ratios - ratios are comparing two numbers. 
	There are three forms of ratios:
		a) three cats to five dogs = 3 to 5
		b) three cats to five dogs = 3:5
		c) three cats to five dogs = 3/5
	There are three kinds of ratios:
		a) part to whole - three cats of eight pets
		b) part to part - three cats to five dogs 
		c) comparing two different kinds of things
			 - three cats to two chairs
2) differences - The difference between two sets
	a) there are two more dogs then cats
	b) there are two less cats then dogs
3) fractions (Must be part to whole ratios)
	a) 3/8 of the pets are cats
	b) 5/8 of the pets are dogs
4) percentages (Must be part to whole ratios)
	a) (3/8 x 100) = 37.5% of the pets are cats
	b) (5/8 x 100) = 62.5% of the pets are dogs
5) scaling (up or down to make equivalent ratios)
	a) There are 1.666 times as many dogs as cats
	b) there are  cats = 0.6 times dogs

NOTE: Percents are useful for making comparisons because everthing is changed to 'out of 100.'

NOTE: Fractions and percents can only be used when referring to the part of a whole. For example, comparing 3 cats to 5 dogs cannot be indicated with a fraction or a percent. While it is true that 3/5 IS a fraction, in this case it is not a comparison that makes sense as a fraction of a percent. As a RATIO it is OK. Consider: 3/5 = 0.6 as a decimal and 60% as a fraction. But in the context of the problem of 3 cats and 5 dogs, what exactly would the 60% mean? Of course, if we talk about the WHOLE group of 8 pets, then 3/8 for the cats would mean 37.5% of the pets.

OBJECTIVE: •GS02 1.3.3; 1.3.4 a) Items may ask students to identify or name ordered pairs describing the location of points or objects in any of the four quadrants on a two-dimensional coordinate grid. b) Items may ask students to identify, plot, and/or label points or shapes on a coordinate grid given ordered pairs. c) Items may ask students to identify or name ordered pairs describing the location of figures that have been translated and/or reflected on a 2-dimensional coordinate grid. d) Items may ask students to identify whether an object has been transformed by a translation and/or a reflection or by a rotation with or without a coordinate grid. e) Items may ask students to identify a picture or diagram of a rotation of 90° or 180° about the center or a vertex of a figure or a combination of two translations and/or reflections of a simple figure, with or without a coordinate grid. f) Items may ask students to plot or draw a combination of two translations and/or reflections of a simple figure on a coordinate grid or to draw a 90° or 180° rotation about the center or a vertex of a figure in the first quadrant. g) Items may ask students to describe the transformation of one object to another on a 2-dimensional coordinate grid, in terms of a combination of two translations and/or reflections. h) Items may ask students to describe a translation, reflection, or rotation so that another person could draw it. i) Items may ask students to explain a series of transformations in a diagram or picture. Also NS04 1.1.6 Computations. ACTIVITIES/ASSESSMENT: P89-90 Quiz 2 (timed)and/or [1.2.5] Apply formulas to find measurements of circles, triangles, and rectangular prisms. Handout NOTES: HOMEWORK: Figures as assigned.

OBJECTIVE: [1.2.5] Apply formulas to find measurements of circles, triangles, and rectangular prisms. d) Items may ask students to determine circumference, perimeter, and/or area of a circle, rectangle, and/or triangle. e) Items may ask students to determine volume and/or surface area of a rectangular prism. f) Items may ask students to determine linear dimensions of a circle, triangle, or rectangle based on a given circumference, perimeter, or area. g) Items may ask students to determine linear dimensions of a rectangular prism based on a given volume or surface area. h) Items may ask students to compare angle measurements or the volumes of rectangular prisms. Note: Students are expected to determine and label units. ACTIVITIES/ASSESSMENT: Valentine Perimeter and Heart; Finish triangle/circle/rect prism worksheet and introduce changing a length. NOTES: Valentine = square + 2 ½ circles HOMEWORK: Assigned figure with changed dimension

OBJECTIVE: See 2-14 above. •To use geometric scaling to estimate population counts •To apply proportional reasoning to situations in which capture-tag-recapture methods are appropriate for estimating population counts •To use ratios and scaling up or down (finding equivalent ratios) to find the missing value in a proportion[1.1.4] •To use rates to describe population and traffic density (space per person or car) ACTIVITIES/ASSESSMENT:Page 52 Prob. 5.1 Estimating Population ; Distribute Problem solving worksheet - select 10 - Due on February 22. Extra Credit for all 15. NOTES: Distribute progress report 3-1; HOMEWORK: Dimension change figure #2.

OBJECTIVE: See 2-15 above. ACTIVITIES/ASSESSMENT: Page 54 Problem 5.2 (Estimating population)(this is a capture-recapture exercise); Next assignment - read pages 55 to 57. Washington State data: population 5,894,367, Area: 66,582 mi². Write a summary report defining population density using this data as a final example. NOTES: HOMEWORK: Page 59 #1

OBJECTIVE: See 2-15 above. ACTIVITIES/ASSESSMENT: Pages 55 to 57. Washington State population density. Page 66 #5 NOTES: HOMEWORK: Work on the select 10 problem solving set.