Teaching Student-Centered Mathmatics grades 3-5
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Chapters 5-8
Chapter 5 examines the development of fraction concepts. As students develop their understanding, the use of models as manipulatives is very important and should not be limited to use only in the lower grades. The models help students understand ideas that are often confusing. The author maps out three types of models, which are, region or area models, length models, and set models.
On page 138, there is an activity to help students understand if a fraction is more, less, or equal to a whole. This is an extremely difficult concept for most students to grasp, but by using pattern blocks, rods, or multiples, student can see relationships.
Chapter 6 continues the study of fractions as used in computation. It is stessed that students must have a good understanding of basic fractions before performing operations with fractions. For example, for addition and subtraction the student must understand that the numerator tells the number of parts and the denominator tells the type of part.
I was always taught and told to teach that to add and subtract fractions with unlike denominators, you must find a common denominator. The activity on page 164, shows just the opposite. By using inventive strategies students can add and subtract unlike fractions that are easily related, such as, halves, fourths, and eights.
Chapter 7 explores the use of decimals and percentages. It begins by discussing ways to help students gain a better understanding of decimals by developing a conceptual understanding between fractions and decimals.
Students should discover the relationship between decimals and fractions by reviewing the base-ten system and ultimately learning that this system can be extended to include numbers less thatn 1. By using 10x10 squares students can create fractions to represent numbers such as .65. When they color in the 65 out of 100 squares, they can then begin to see the relationship of decimals and fractions, and begin to compare the value. With questions such as is this decimal greater that 1/2?
Another activity, is to use the 10x10 grid again, but this time, dividing the grid into a fractional part. In the book they used 1/4. 25 squares are colored. Then the student changes the 25 squares into ten strips and 5 squares which represent 2/10 and 5/100, or 25/100.
Chapter 8 deals with geometric thinking and geometric concepts. Much attention is given to the Van Hiele levels which describe how we think and what types of geometric ideas we think. The chapter is logically organized to follow activities through these five levels of thinking.
Chapter 5 examines the development of fraction concepts. As students develop their understanding, the use of models as manipulatives is very important and should not be limited to use only in the lower grades. The models help students understand ideas that are often confusing. The author maps out three types of models, which are, region or area models, length models, and set models.
On page 138, there is an activity to help students understand if a fraction is more, less, or equal to a whole. This is an extremely difficult concept for most students to grasp, but by using pattern blocks, rods, or multiples, student can see relationships.
Chapter 6 continues the study of fractions as used in computation. It is stessed that students must have a good understanding of basic fractions before performing operations with fractions. For example, for addition and subtraction the student must understand that the numerator tells the number of parts and the denominator tells the type of part.
I was always taught and told to teach that to add and subtract fractions with unlike denominators, you must find a common denominator. The activity on page 164, shows just the opposite. By using inventive strategies students can add and subtract unlike fractions that are easily related, such as, halves, fourths, and eights.
Chapter 7 explores the use of decimals and percentages. It begins by discussing ways to help students gain a better understanding of decimals by developing a conceptual understanding between fractions and decimals.
Students should discover the relationship between decimals and fractions by reviewing the base-ten system and ultimately learning that this system can be extended to include numbers less thatn 1. By using 10x10 squares students can create fractions to represent numbers such as .65. When they color in the 65 out of 100 squares, they can then begin to see the relationship of decimals and fractions, and begin to compare the value. With questions such as is this decimal greater that 1/2?
Another activity, is to use the 10x10 grid again, but this time, dividing the grid into a fractional part. In the book they used 1/4. 25 squares are colored. Then the student changes the 25 squares into ten strips and 5 squares which represent 2/10 and 5/100, or 25/100.
Chapter 8 deals with geometric thinking and geometric concepts. Much attention is given to the Van Hiele levels which describe how we think and what types of geometric ideas we think. The chapter is logically organized to follow activities through these five levels of thinking.
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