4123 Test 2

List the Computational Estimation Strategies.

- Compatible Number Estimation - Front End Estimation - Rounding

List the 3 types of fraction models, and give an example of each.

1. Area Models - example fraction circle. 2. Length Models - example Cuisenaire Rods. 3. Set Models- examples counters.

What are the basic fact strategies for addition?

1. Facts with zero 2. One-more-than or Two-More-Than 3. Doubles 4. Doubles plus one 5. Doubles Plus Two 6. Make-A-Ten 7. 10 frame facts 8. Remaining Facts

Define the term measurement.

A number that indicates a comparison between that attribute of the object being measured and the same attribute of a given unit of measure

What does it mean if a proportional story problem is looking for the Unit Rate?

A rate of two measures in the same setting

What is a ratio?

A ratio is a multiplicative comparison of two quantities of measures, symbolically a ratio is an ordered pair of numbers that express a comparison between the numbers

What does it mean if a proportional story problem is looking for the factor of change?

A ratio of two corresponding measures in different situations

What is proportional reasoning?

A way of thinking about and recognizing multiplicative situations in realistic situation. It goes well beyond "setting up and solving proportions." Must distinguish between multiplicative and additive relationships

Understanding of ratios

Ability to compare ratios and to predict or produce equivalent ratios Ability to compare mentally different pieces of information and to make comparisons, not just of the quantities involved, but of the relationships between the quantities, as well Both quantitative and qualitative thinking Not dependent on a skill with a mechanical or algorithmic procedure

What are the measurement attributes throughout k-8 instruction?

Area, length

Describe what a unit fraction is.

As in, ¼, 1/3, or 1/5. A unit fraction is a fraction that is at its simplest form.

How should we as teachers introduce and teach decimals?

Begin with Rational Numbers that are easily represented by decimals; tenths, hundredths, and thousandths. Extend Understandings of the Base 10 System to numbers that are less than 1. Use models (Base 10 Blocks) to helps students make meaningful translations between fractions and decimals.

If Joe had 10 apples and Mark had 5 apples, how many more apples did Joe have than Mark?

Comparison

There are 6 apple trees in an orchard. Each tree has 7 apples on it. How many apples are in the orchard?

Equal Groups

What are the basic fact strategies for Subtraction?

Facts with zero One-less-than and two-less-than Doubles and Near Doubles Sums to 10 Ten Frame Facts Hard Subtraction Facts: Sums Greater than 10

Why are informal and standard units useful?

Informal units make it easier to focus directly on the attribute being measured. Can avoid conflicting objectives in the same beginning lesson. Informal units provide a good rationale for standard units.

What are the main differences between Invented Strategies and Traditional Algorithms?

Invented strategies are number oriented rather than digit oriented. Invented strategies are left-handed rather than right-handed. Invented strategies are flexible rather than rigid.

Mary takes 12 steps from her front door to the bus. Once Mary gets off the bus, she takes 83 steps to her classroom. How many steps does she take once she leaves her home to get to class?

Join

How should the attributes area and length be introduced?

Length should be first, begin with comparison activities, have students make own rulers Area comparison to help students distinguish between size and shape, length, and other dimensions Cutting a shape into two parts and reassembling it in a different shape can show that the before and after shapes have the same area. Area is a measure of covering

John has 25 cards to pass out for a new game he wants to play with Amy, Cindy, Luke, and Larry. How many cards should each person get?

Measurement

John had 6 cookies, and Kelly had 3 times as many cookies as John. How many cookies did Kelly have?

Multiplicative Comparisons

List the types of ratios. -

Part to Whole . examples. fractions, percentages, probabilities. Part to Part. examples part of the same whole, odds. Rates. example. a comparison of the measures of two different things or quantities; the measuring unit is different for each value.

Jon has 3 cars and Elizabeth has 2 cars. How many cars do they have?

Part-Part-Whole

Sam baked 12 cookies. He gave 4 cookies to each of his teachers. How many teachers does Sam have?

Partition

How should proportions be taught?

Provide ratio and proportion tasks in a wide range of settings. Encourage reflective thought, discussion, and experimentation in predicting and comparing ratios. Connect proportional reasoning to existing thought processes, the concept of unit fractions is very similar to unit rates. Recognize that the use of symbolic or mechanical methods, such as the cross-product algorithm, for solving proportions does NOT develop proportional reasoning.

What are the 6 conceptual thought patterns when comparing fractions?

Same-size whole Same number of parts but parts of different sizes More and less than ½ More and less than one whole Distance from ½ Distance from one whole

John has 8 apples. He gives Mary 3 of his apples. How many apples does John have left?

Separation

Explain how the Fraction wheel model tells you the decimal equivalents (tenths and / or hundredths) for each fraction

The model had 10 small wedges that each represent 1/10th. The small tick marks divide the model into tiny wedges that each represent 1/100th. One wedge represents .1 because it is 1/10th of the whole and .01 represents 1/100 because it is 1 one-hundredth of the whole (100).

What is a Base-10 fraction?

These are fraction with denominators that are a power of 10

How to determine the area of a rectangle

To find the area of a rectangle you would count the number of centimeter squares inside rectangles. (COVER UP) Then you can look at the base and height of the small rectangle and see that the base can be multiplied by the height and this will equal the same number you found when you counted up the squares.

What are the main functions of the top and bottom parts of a fraction?

Top- tell how many items are being considered, this number counts the parts or shares. Bottom- what kind of item is being considered; this number tells what is being counted.

What are the 2 requirements for fractional parts? -

Whole must be made up of the correct number of parts. Each of the parts must be equal; all parts must be the same size.

How to determine the area of a Parallelogram

You can find the area of a parallelogram because you discovered the area formula for the area of a rectangle. You are able to see that you can manipulate the small Parallelogram to form a rectangle by taking one of the slanted slides to the other side of the parallelogram to form a rectangle.

How to find the Area of a Triangle

You can find the area of a triangle because you know how to find the area of a parallelogram. You can manipulate the triangle to resemble a parallelogram by drawing a congruent right isosceles triangle. You can attach the two triangles together to form a parallelogram. Because you know how to use the dimensions of the base and the height when finding the area of the parallelogram you know that you have to do the same with the parallelogram. You know you only need to find half of the parallelogram because you are only finding one triangle.

Explain how to model each fraction using the Rational Number Wheel

You use one wheel to represent the whole. You look at the denominator to determine how many equal parts to split the wheel into. The numerator tells you how many parts of the whole to consider and represent. You then move one of the wheels to represent or cover up parts of the whole (other wheel).

How to find the Area of a Trapezoid

You use what you know about the area of a parallelogram. You are able to see that you can manipulate the trapezoid to resemble a parallelogram by drawing a congruent trapezoid and attaching it to one end of the original trapezoid to form a parallelogram because I know that the area of a parallelogram, I can use base times height as a starting point for finding the are of the trapezoid. However I looked at the base differently since the bases were different sizes and find that the base of the trapezoid was the top plus the bottom. I know that I divide by 2 because I am only finding one trapezoid.

What are the basic fact strategies for Multiplication?

Zeros and Ones Doubles Fives Nifty Nines Helping Facts- using known facts to derive other facts