math methods final updated

Demonstrate the development of area formulas

Area -measure of two dimensional space inside a region Goal- help students distinguish between size, shape, length, and other dimensions. Students who have the informal notion that area is the "amount of 2-D 'stuff'" contained inside a region can invent for themselves most of the formulas that they are often asked merely to memorize. Each formula they reinvent helps strengthen their understanding (and memory) for the other formulas they know. Rectangle ex

Describe an introductory lesson on place value to second graders

Base 10 riddles Materials: Riddle cards Directions: Present riddles orally or written Purpose: This activity allows you to gauge where the students present level of understanding is.

Explain the distributive property and how it applies to the teaching of algebra

Distributive Property: When multiplying a sum or difference of terms, you can multiply each term or addend inside a parenthesis separately. How it applies to the teaching of algebra: It allows students to problem solve.

Describe how you would teach basic algebra to second graders

First, meaning is needed for: Number combinations Place value Algorithms Relational thinking: Operational View Equal sign means "do something" Relational-Computational View Equal sign symbolizes a relation between two calculations Relational-Structural View Equal sign signifies a numeric relationship

Describe how the place value system is central to the understanding of decimal fractions

Five levels of Place Value Understanding: Single Numeral. The student writes 36 but views it as a single numeral. The individual digits 3 and 6 have no meaning by themselves. Position Names. The student correctly identifies the tens and ones positions but still makes no connections between the individual digits and the blocks. Face Value. The student matches 6 blocks with the 6 and 3 blocks with the 3. Transition to Place Value. The 6 is matched with 6 blocks and the 3 with the remaining 30 blocks but not as 3 groups of 10. Full Understanding. The 3 is correlated with 3 groups of 10 blocks and the 6 with 6 single blocks.

What steps would you take to teach number sense to kindergartners

Four Categories of Early Number Relationships Spatial Relationships Actors to 5 and 10 One More/Two More/One Less/Two Less Part-Part-Whole Interactive Ways Make numbers with clay Trace in shaving cream Write on an interactive whiteboard Calculator keypad

Explain the foundational concepts of fractional parts, including iteration and partitioning

Fractional Part: is the excess beyond that numbers integer part. Interating: Counting fractional parts, helps students understand the relationship between the parts and the whole Partitioning: Sectioning a shape into equal sized parts When teaching Consider the following: Emphasize number sense and meaning of fractions Provide a variety of models and contexts Emphasize that fractions are numbers Dedicate time for understanding of equivalence Link fractions to key benchmarks and encourage estimation.

Explain how you would each teach computational estimation

Front-end Methods: This strategy focuses on the leading or leftmost digits in numbers ignoring the rest. After an estimate is made on the basis of only these front-end digits, and adjustment can be made by noticing how much has been ignored. Rounding Methods: This is the most familiar form of estimation and is a way of changing the problem to one that is easier to work with mentally. Good estimators follow their mental computation with and adjustment to compensate for the rounding. To round a number simply means to substitute a "nice" number that is close so that some computation can be done more easily. Using Compatible Numbers (Grouping): When adding a long list of numbers it is sometimes useful to look for two or three numbers that can be grouped to make 10 or 100. General Principles: Use real examples such as shopping, distance, budgets, costs, and more. Use the language of estimation Use context to help determine the reasonableness of the estimate. Accept and offer a range of estimates as an option Focus on flexible methods, not answers.

Describe the van Hiele levels of geometric thinking

Level 0: Visualization Level 1: Analysis Level 2: Informal Deduction- Think about properties of geometric objects without focusing on one particular object/shape. Engage in "if then" thinking if all four angles are right angles the shape must be a rectangle Level 3: Deduction Level 4: Rigor

Explain how percents or percentages are related to fractions and decimals

Percents or percentages have a direct fraction or decimal that represent said percent

What steps would you take to teach long division to fourth graders

Prior knowledge needed before the student is ready to learn long division" Multiplication tables Basic division concept, based on multiplication tables Basic division with remainders Teach in several steps: Division is even in all digits. Here students practice just the dividing part A remainder in the ones. Now students practice the multiply and subtract part and connect tht with finding the remainder. A remainder in the tens. Students now use the whole algorithm, including "dropping down the next digit" using 2-digit dividends. A remainder in any of the place values. Students practice the whole algorithm using longer dividends.

Describe a process for teaching fraction operations with understanding

Problem-Based Number Sense Approach: Allows students understand why procedures for computations make sense Use contextual tasks Explore each operation with a variety of models Let estimation and invented methods play a big role in the development of strategies Address common misconception regarding computational procedures

Describe how you would teach multiplication to third graders

Representations Compensation strategies Manipulate numbers to make calculations easier Adjustment or compensation Half-then-double strategy used when 5 or 50 involved Close compatible number Cluster problems- using facts and combinations already known in order to figure out more complex computations. Standard Algorithms Area Model Open Array

Summarize the four major geometry goals for students

Shapes and properties Transformations Locations Visualization

Describe the best model for teaching elapsed time

Solving problems involving addition and subtraction of time intervals. Empty number line is a computational model.