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TouchMath Extend

Lesson 42: Fraction Sets

Lesson Objectives

  • Define fractions as equal parts of a whole using manipulatives and pictures 
  • Write fractions as the number of shaded parts compared to the total number of parts 
  • Label and create all fractional parts through ninths 
  • Recognize and use fourths as quarters 
  • Divide pictures of real-world objects into fractional parts 
  • See the relationship of division and fractions 


  • Extend Workbook (Page 42) 
  • Different sets of counters (e.g. different color, sizes, types of counters) 
  • Fraction manipulatives (e.g. base ten blocks, fraction strips, pizza fractions, shape fractions) 
  • Highlighters, markers, or crayons 
  • Whiteboards and dry erase markers 

Step 1: Warm Up (5 min)

Review the vocabulary for today’s lesson. Show the parts of a fraction (number above the line, number below the line, and show some actual examples) and read the fractions 3/5 is threefifths, 4/9 is fourninths) and provide a visual example of each. Next, distribute 8 counters to each pair of students. Ask how many equal parts are there in this set of counters? Yes, 8. Tell each of them to touch a counter. Tell them that you and your partner must touch the same counter. This is one-eighth of the set of eight counters. There are eight equal parts. We are talking about one of the parts. Tell them to repeat the fraction sentence after you say it: This counter is one-eighth of the set of eight counters. Tell them to touch another counter. How many counters are in this set? (8). Remind them that they are equal and the same size. Now you are talking about twoeighths of the set of counters: These two counters are two-eighths of the set of eight counters. 

Step 2: Vocab Review (5 min)

Review prior vocabulary: halves, thirds, fourths, fifths, sixths, sevenths, eighths, ninths fraction, sections, whole, parts, and shaded. Remind students that they will be learning more about fractions today, and fractions are equal parts of a whole 

Step 3: Model (5 min)

Now, move on to visual examples of fractions, showing various examples (1/4, 2/5, 3/7, 1/2). Under each fraction, write the fraction in word form (one-fourth, twofifth, threesevenths, onehalf). Shade in the fraction listed for each fraction visual. Remind students that fractions are smiliar to division: In fractions, the whole is the total number of equal parts, the bottom number. The top number is how many shaded parts we have. The parts have to be equal. For 1/4, review that there are four parts, and one is shaded. Remember, the bottom number tells the number of equal parts, and the top number tells how many are being used. Review each fraction, going over vocabulary: whole, parts, and shaded. 

Step 4: Guided Practice (5 min)

Before students practice shading in fractions, review that both the number of parts we are talking about and the total number of parts that make up the whole are the same. Write a fraction on the board, and have students write on their white boards (2/5). Tell students to draw a rectangle with four equal parts (model this). Remind students that the bottom number means the total equal parts of the fraction (5), ask what the top number means (how many parts they have), and ask how many parts should be shaded (2). Have students work in pairs, giving them fractions to work through: write the fraction, draw the fraction (give them examples for support, e.g. circle, rectangle), then shade in the correct number of parts. Next, distribute two different set of counters (e.g. 10 total counters, 6 red and 4 blue). Ask students how many total counters there are (10) and how many out of the 10 are red (6). Ask what the fraction would be (6/10) and explain that 6 out of the 10 counters are red, and 4 out of the 10 counters are blue. Continue this exercise a few times with different sets of numbers. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (42). Read the directions for each problem. Tell students they will be focusing on determining the whole/total number of equal parts/bottom number based on the total number of animals, objects, or visuals in the picture. They will be asked to find the total number cats, dogs, vegetables, fruits, and so forth, so they will need to carefully read what it is asking them to do. The first one has been done for them. Tell them a good strategy is to circle and box the different parts (circle 3 dogs, box 2 cats, and this also shows 5 total animals). Students will quickly see there are 3 dogs out of 5 pets, and 3 cats out of 5 pets. Repeat each problem, circling and boxing the two different parts, and counting the total number of objects to determine the whole. Support as needed. 

Step 6: Wrap Up (5 min)

To wrap up the lesson, review the learning objectives and core vocabulary words again and ask your students about their experience.