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Algebraic Thinking: Generalizations, Patterns & Fractions
Developing Fraction Concepts
Developing Strategies for Fraction Computation
Developing Concepts of Decimals and Percents
Solve These Problems
100
What are the five forms of Algebraic thinking?
What is the generalizations from arithmetic and from all of mathematics. Meaningful use of symbolism. Study of structure in the number system. Study of patterns and functions. Process of mathematical modeling.
100
Why do students find fractions difficult?
What is because fractions have many meanings, they are often written in an unusual way, instruction does not focus on the conceptual understanding of fractions and students over generalize their knowledge of whole numbers.
100
What guidelines should be kept in mind when developing computational strategies for fractions?
What is through the use contextual tasks, explore each operation with a variety of models, let estimation and informal methods play a big role in the development of strategies, and address common misconceptions regarding computational procedures.
100
What are decimals and how else can they be written?
What is it is a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point.
100
Convert 4/5 into a decimal.
What is 0.8
200
What is one of the most valuable methods when searching for generalizations in math?
What is to find the growing pattern represented with visual or concrete materials.
200
What is the goal of activities involving the concept of sharing? When would you implement these activities?
What is the goal of sharing activities is to have students understand the concepts of fractions, equivalence, and the ordering of fractions. These activities should be implemented when students are struggling to grasp the concepts mentioned above.
200
Why is it important to teach computational estimation with fractions?
What is estimation is one of the effective ways to build understanding and procedural fluency with fractions.
200
What is another name for percent?
What is percent is another name for hundredths.
200
Convert 1/4 into a percentage.
What is 25%
300
Why are the uses of symbols important in algebraic math?
Because symbols represent real events and are useful tool for solving important problems that aid in decision making.
300
What does partitioning mean?
What is partitioning is the sectioning of shapes into equal-sized pieces. It is important that students do not focus on the shape rather their focus should be on the equal-sized parts. This is a prerequisite for performing fraction operations.
300
What can fractions be great substitutions for?
What is they can be great substitutes for percentages.
300
What are some ways to help students make a connection between fractions and decimals?
What is the use familiar fraction concepts and models to explore rational numbers that are easily represented by decimals: tenths, hundredths, thousandths, base 10 system can be extended to include numbers less than 1 as well as large numbers, and the use models to make meaningful transitions between fractions and decimals.
300
Convert 45% into a fraction.
What is 45/100 or 9/20
400
What do students see the equal sign as, and how should they see the equal sign as instead?
What is students see the equal sign as signifying the answer. Instead they should see the equal sign as an indicator of equivalence.
400
What does iteration mean?
What is iteration is the counting or repeating of a piece. This concept is most clear when students know that the top number counts (numerator), and the bottom number tells what is being counted (denominator).
400
Contextual problems are usually a mix of what?
What is they use a mix of area and linear models, whole numbers, mixed numbers and fractions, a variety of contexts, and include both addition and subtraction situations.
400
What are some ways to teach students about percentages?
Limit the percents to familiar fractions (halve, thirds, fourths, fifths) or easy percents (1/10, 1/100) and use numbers compatible with those fractions. Do not suggest any rules or procedures for different types of problems. Do use terms part, whole and percent (or fraction). Percent and fraction are interchangeable. Require students to use models or drawings to explain their solutions. Encourage mental computation.
400
Convert 3/8 into a percentage.
What is 37.5%.
500
How can mathematical modeling link the classroom to mathematics?
What is by giving math context it allows students to apply it to everyday situations making the mathematical concept gain a deeper understanding.
500
What are two ways you can support a students' development of estimating fractions?
What is through the use of number lines is a great way for students to develop an understanding of the relative size for a fraction. Another way for students to develop an understanding of estimating fractions teachers should provide students with opportunities to estimate. For example, during everyday discussion ask questions like "About what fraction of your class are wearing sweaters?" This provides students with visual activities of estimating fractions.
500
Why should estimation be an integral part of computation development?
What is this should be an integral part of computation development because it keeps student's attention on the meaning of the operations and the expected sizes of the results.
500
How do you convert percents to decimals?
What is converting from a percent to a decimal is done by dividing the percentage value by 100.
500
Convert 115.9% into a decimal?
What is 1.159