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Lesson plan Grade 3 Math

Cobblewell Creek Staff Gauge: A Grade 3 Unit Fraction Lesson

A 45-minute grade 3 lesson where students partition a creek staff gauge board into equal parts and name unit fractions and their multiples at a fictional gauging station.

Objectives

  1. Students will partition a whole into equal parts and name one part as a unit fraction.
  2. Students will name a quantity made of several equal parts as a fraction with a numerator greater than one.
  3. Students will explain why more equal parts in the same whole means each part is smaller.

Vocabulary

Key words: staff gauge, equal parts, unit fraction, whole, creek

Teacher overview

A staff gauge is a painted board fixed upright in a stream so that anyone standing on the bank can read how high the water is. Cobblewell Creek in this lesson is fictional, and the three gauge boards described here were designed for the lesson rather than copied from a real gauging station. Students fold and mark paper strips into equal parts, name one part as a unit fraction, and then name the part of a board the water covers. The misconception this lesson corrects is the belief that one-sixth is larger than one-fourth because six is larger than four, an error that becomes visible as soon as students lay one folded strip directly on top of the other.

Procedure

Hook (5 min): Hold up two paper strips of the same length. Fold one into 4 equal parts and the other into 6 equal parts in front of the class. Ask which strip has the larger parts and record the votes on the board without comment.

Direct instruction (12 min): Introduce the setting: a staff gauge at Cobblewell Creek is a board of one fixed height, painted into equal bands so a reader can tell at a glance how high the water is. Draw a board split into 4 equal parts and shade one band. Name it one-fourth, and write that the whole board is 4 parts of size one-fourth. Shade a second and third band and name three-fourths, saying aloud that three-fourths is three parts each the size of one-fourth. Repeat the same routine on a board split into 6 equal parts so students hear the same sentence structure with a different denominator.

Guided practice (12 min): Students fold their own strips into 4 equal parts and then into 6 equal parts, label one band on each, and complete handout items 1 and 2 with a partner. Then hold up the two folded strips side by side and return to the hook question. This is the formative check: ask for a thumbs up from every student who now says the 4-part board has the larger bands, and if fewer than four out of five agree, refold both strips together and lay one directly on top of the other.

Independent practice (11 min): Students complete handout items 3 through 6 alone, using their folded strips as a reference. Watch for students who count the shaded bands but write the total number of bands as the numerator.

Closure (5 min): Students hold up their strips and say one sentence to a partner in the form "One part of this board is one-___, because the board has ___ equal parts." Collect the handouts on the way out.

Cobblewell Creek Staff Gauge: A Grade 3 Unit Fraction Lesson — Grade 3 Math
Name: ____________________________ Date: ______________

Student Handout

A staff gauge is a board in a creek. It is painted into equal parts so you can read how high the water is.

  1. The first gauge board at Cobblewell Creek is painted into 4 equal parts. What fraction of the whole board is 1 part?
  2. The second gauge board is painted into 6 equal parts. What fraction of the whole board is 1 part?
  3. On the first board, the water covers 3 of the 4 equal parts. What fraction of that board does the water cover?
  4. On the second board, the water covers 5 of the 6 equal parts. What fraction of that board does the water cover?
  5. Both boards are the same height. Which board has larger equal parts, the 4-part board or the 6-part board? Tell how you know.
  6. A third gauge board is painted into 8 equal parts. The water covers 1 part. What fraction of that board does the water cover?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 1/4 of the board.
    The board is one whole split into 4 equal parts, so each single part is one-fourth.
  2. Answer: 1/6 of the board.
    The board is one whole split into 6 equal parts, so each single part is one-sixth.
  3. Answer: 3/4 of the board.
    Three parts, each of size one-fourth, make three-fourths of the whole board.
  4. Answer: 5/6 of the board.
    Five parts, each of size one-sixth, make five-sixths of the whole board.
  5. Answer: The 4-part board.
    The two boards are the same height, so splitting one of them into more parts makes every part smaller. Four parts means each band is one-fourth, and six parts means each band is only one-sixth, which is smaller.
  6. Answer: 1/8 of the board.
    The board is one whole split into 8 equal parts, so one covered part is one-eighth.

Differentiation

Support

Pre-fold the paper strips so students receive one strip already creased into 4 parts and one already creased into 6 parts, and let them trace the creases with a marker rather than folding. Provide a matching card set that pairs a shaded picture with its written fraction for one-fourth, three-fourths, one-sixth, and five-sixths. Allow students to answer item 5 by laying one strip on the other and pointing.

Extension

Ask students to design a fourth gauge board whose bands are smaller than one-eighth, state how many equal parts it has, and explain what happens to the size of a band as the number of parts keeps growing. Have them shade a board so that the water covers exactly half of it in two different ways, once on a 4-part board and once on a 6-part board, and explain how the same amount of water can be named by two different fractions.

ELL supports

Pre-teach "creek," "board," "equal parts," and "covers" with a simple sketch of a marked board standing in shallow water. Provide the sentence frame "The board has ___ equal parts, so one part is one-___." Let students point to their folded strip while answering aloud before they write, and accept a labeled drawing for item 5.