Who Wants Pizza? (Teachers' Page)

 
Level of activities:
2nd -7th grade

Materials:
Computers with Internet access, square grid paper

Strategies:
The "Want Some Pizza?" activities are designed to introduce fractions in a concept-building way. The activities can be done on computers with Internet access with square grid paper printed out and used along with the electronic images. On the "More Practice" pages, students color online on a square grid. An effective model is for pairs of students to work together at the computer talking to each other about the activities and drawing the fractions on the grid paper. One advantage of using grid paper over other fraction modeling manipulatives (fraction bars or pattern blocks, etc.) is that any denominator can be easily modeled with grid paper.

Assessment:
Exercises are checked on-line, which teachers can record. Some answers are hidden under a tab so that students can easily check their answers.

Standards:
Notice what the NCTM Principles and Standards of School Mathematics says about fractions.

A significant amount of instructional time should be devoted to rational numbers in grades 3 to 5. The focus should be on developing students' conceptual understanding of fractions and decimals -- what they are, how they are represented, and how they are related to whole numbers -- rather than on developing computational fluency with rational numbers. Fluency in rational-number computation will be a major focus of grades 6 to 8.
The Standards go on to specify students in grades 3 to 5 should
  • develop meaning for fractions as parts of a unit whole, as a part of a collection, as numbers, and as a division of whole numbers;
  • read and write fractions and decimals and relate the notation to the meaning of these numbers;
  • develop strategies for judging the size of fractions and decimals and for comparing them using a variety of models and of benchmarks (such as 1/2 or .5);
  • recognize and use common fraction, decimal, and percent equivalents;
In Grades 6-8, they should
  • understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
  • use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals;
  • understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems;
  • select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods;

The Texas Essential Knowledge and Skills indicates the following skills at the specified grade level:

Grade 2 --

    The student uses fraction words to name parts of whole objects or sets of objects. The student is expected to:
  • name fractional parts of a whole object (not to exceed twelfths) when given a concrete representation; and
  • name fractional parts of a set of objects (not to exceed twelfths) when given a concrete representation.
Grade 3 --
    The student uses fraction names and symbols to describe fractional parts of whole objects or sets of objects. The student is expected to:
  • construct concrete models of fractions;
  • compare fractional parts of whole objects or sets of objects in a problem situation using concrete models;
  • use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 12 or less; and
  • construct concrete models of equivalent fractions for fractional parts of whole objects.
Grade 4 --
    The student describes and compares fractional parts of whole objects or sets of objects. The student is expected to:
  • generate equivalent fractions using concrete and pictorial models;
  • model fraction quantities greater than one using concrete materials and pictures;
  • compare and order fractions using concrete and pictorial models; and
Grade 5 --
    The student uses fractions in problem-solving situations. The student is expected to:
  • compare two fractional quantities in problem-solving situations using a variety of methods, including common denominators;
  • model and record addition and subtraction of fractions with like denominators in problem-solving situations.
Grade 6 --
    The student uses fractions in problem-solving situations. The student is expected to:
  • model addition and subtraction situations involving fractions with objects, pictures, words, and numbers;
  • use addition and subtraction to solve problems involving fractions and decimals;
Grade 7 --
    The student adds, subtracts, multiplies, or divides to solve problems and justify solutions. The student is expected to:
  • represent multiplication and division situations involving fractions and decimals with concrete models, pictures, words, and numbers;
  • use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals;

Resources:


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URL http://math.rice.edu/~lanius/fractions/fractea.html