K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will learn that the fractions 1/2, 1/3, 1/4, 1/5, 1/6, 1/8 are part of the whole by manipulating pattern blocks and by cutting fractional parts from a whole.

Teacher planning

Time required for lesson

45 minutes

Materials/resources

  • Pattern blocks for each child or pair
  • one worksheet for each student
  • pencil
  • 5 sheets of unlined paper for folding into fractional parts
  • scissors
  • 2 index cards for words numerator and denominator
  • overhead copy of children’s worksheet and overhead pen
  • Silver-Burdett Ginn Mathematics Grade 3 book

Pre-activities

Teacher will discuss with students familiar use of fractions in everyday life as half an apple, half an hour, quarter past, etc.

Activities

  1. Introduce the topic by reviewing use of terms as 1/2 in daily life. Use other daily familiar fractional terms. (3 minutes)
  2. Distribute pattern blocks and worksheet to each child (or pairs). Teacher has overhead of worksheet and pen on overhead.
  3. Teacher has students cover figure 1 with green triangles. Teacher will ask how many spaces does the green triangles cover. Have students remove one green triangle. Tell students that the part removed is one-half of the figure 1. This is written as numerator -1 and denominator-2. The teacher writes the fraction 1/2 on the board. Teacher tells the students that the word numerator is the number part that is being talked about; denominator tells the number of parts altogether. Teacher will display word cards of numerator, denominator on the board with the word card numerator placed above word card denominator. Teacher will have students write fraction 1/2 under the figure marked number one. Teacher will write fraction 1/2 on teacher’s overhead.
  4. Teacher will have students cover figure 2 with green triangles. Teacher will ask students how many green triangles it takes to cover figure 2. Teacher will ask students to remove one green triangle. Teacher will explain that 1/3 of figure 2 has been removed. Teacher will write the term on the board using terms numerator for 1 and denominator for 3. Teacher will instruct children to write the fraction 1/3 on their paper under figure 2. Teacher will use term numerator/denominator as teacher writes fraction 1/3 on overhead under figure 2.
  5. Teacher will have students cover figure 3 with green triangles. Teacher will ask how many green triangles it takes to cover figure 3. Teacher will have students remove one green triangle. Teacher will explain that one 1/4 of figure 3 has been removed. Teacher will write term on overhead using terms numerator for 1 and denominator for 4. Teacher will instruct children to write fraction 1/4 under figure 3. Teacher will write fraction 1/4 on overhead under figure 3.
  6. Teacher will have students cover figure 4 with green triangles. Teacher will ask students how many green triangles it takes to cover figure 4. Teacher will have student remove one green triangle. Teacher will explain that 1/5 of figure 4 has been removed. Teacher will write the fraction on the board using the terms numerator for 1 and denominator for 5. Teacher will instruct children to write the fraction 1/5 on their paper under figure 4. Teacher will write fraction 1/5 under figure 4 on the overhead.
  7. Teacher will tell children to cover figure 5 with green triangles. Teacher will ask students how many green triangles it takes to cover figure 5. Teacher will explain that 1/5 of figure 5 has been removed. Teacher will write the term 1/5 on the board using terms numerator for 1 and denominator for 5. Teacher will instruct children to write fraction 1/5 on their paper under figure 5. Teacher will write term 1/5 on the overhead under figure 5.
  8. Teacher will have students cover figure 6 with blue blocks. Teacher will ask students to remove one blue block and will ask what fractional part of figure 6 is covered by one blue block. Teacher will explain that one-half of figure 6 has been removed. Teacher will instruct students to write this fraction under figure 6 as numerator/denominator. Teacher will write fraction 1/2 under figure 6 on overhead.
  9. Teacher will ask students to cover figure 7 with red blocks. Teacher will ask students to remove one red block. Teacher will explain that one-half of figure 7 has been removed. Teacher will instruct students to write this fraction under figure 7 as numerator/denominator. Teacher will write fraction 1/2 under figure 7 on the overhead.
  10. Teacher will have students place one blue block on figure 2. Teacher will ask what part is covered by the one blue block. Teacher will write this fraction 2/3 as numerator/denominator under figure 2 under the blue block.
  11. Teacher will have students cover figure 3 with one red block. Teacher will ask what factional part is covered by one red block. Teacher will tell students that 3/5 has been covered with the red block. Teacher will write this fraction 3/5 as numerator/denominator under the red block.
  12. Teacher will have students cover figure 4 with one red block. Teacher will ask students what fractional part is covered. Teacher will compare this to 1/2. Teacher will tell students that 1/2 has been covered with the red block. Teacher will write this fraction under the red block.
  13. Teacher will have students cover figure 5 with 2 red blocks. Teacher will ask what fractional part is covered. Teacher will tell that 3/5 is covered. Teacher will write this fraction under figure 5 as 3/5.(20 minutes)

Culminating Activity

(20 minutes)

  1. Teacher will distribute the five sheets of unlined paper to the students and will have students take one sheet and fold paper in half. Teacher will have students draw a line across the fold and label each part correctly using numerator/denominator.
  2. Teacher will have students fold remaining papers each for thirds, fourths, sixths, and eights. Students will draw lines on folds and label each part correctly on each sheet using numerator/denominator.
  3. Teacher will have each student cut one fractional part from each sheet.
  4. Teacher will have students arrange cut fractional parts of paper from least to greatest or greatest to least on top of desk.

Closure

(4 minutes)
Teacher will ask the following questions using fractional blocks on overhead worksheet and children are to respond using their worksheet:

  • Can you show 1/2 of figure 1?
  • Can you show 2/3 of figure 2?
  • Can you show 2/6 of figure 4?
  • Can you show 5/8 of figure 5?
  • Can you show 2 halves of figure 6?
  • Can you show 0 halves of figure 7?
  • Ask: Pizza is cut into 4 equal parts. I eat one part. What fractional part is left? Show by covering figure 3.

Assessment

  • Student performance during class discussions while manipulating pattern blocks.One point is earned for correct participation.
  • Student following directions during folding of paper to make fractional parts. One point is earned for correct participation.
  • Student labeling parts of fractions on sheet correctly. One point is earned here.
  • Student responding correctly to ordering of fractional parts from least to greatest or greatest to least. One point is earned for correct ordering according to size.
  • Student responding correctly to questions in closure. One point is earned for correct response here.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 3

        • Geometry
          • 3.G.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
        • Number & Operations—Fractions
          • 3.NOF.1Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
          • 3.NOF.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent...

North Carolina curriculum alignment

Mathematics (2004)

Grade 3

  • Goal 1: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.
    • Objective 1.05: Use area or region models and set models of fractions to explore part-whole relationships.
      • Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).
      • Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.
      • Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.
      • Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.
      • Understand and use mixed numbers and their equivalent fraction forms.