Task Name Task Type Grouping Strategy Content Addressed Standard(s) Description Scaffolding Task Individual/Small Group Task Naming fractional pieces, length model MGSE3.NF.1 In this lesson students will use strips of paper to create fraction bar models that they can refer back to and utilize throughout the unit Constructing Task Partner/Small Group Task Naming the value of a fraction of a set MGSE3.NF.1 In this lesson students will find the value of fractions of sets. Scaffolding Task Individual/Small Group Task Naming fractional pieces, exploring inequalities, length model MGSE3.NF.3 Students will create models of fractions that they can manipulate to find equivalent fractions. Scaffolding Task Individual/Small Group Task Naming fractional pieces, exploring inequalities, length model MGSE3.NF.3 Students will use their fraction bars from the previous lesson to find inequalities and express those inequalities as number sentences. 3-Act Task Whole Group Divide and label fractional parts MGSE3.NF.1 MGSE3.NF.3 In this task, students will watch a Vimeo and tell what they noticed. Next, they will be asked to discuss what they wonder about or are curious about. Students will then use mathematics to answer their own questions. Constructing Task Individual/Small Group Task Create a number line, explore fractions between 0 – 1, length model MGSE3.NF.2 Students create fraction number lines using strips of paper and use the number lines to find equalities and inequalities.
ACT 2 What information would you like to know or need to solve the MAIN question? Record the given information (measurements, materials, etc…) Act 2 (con’t) If possible, give a better estimation with this information: _______________________________ Use this area for your work, tables, calculations, sketches, and final solution.
c. “Explore” b’s relationship to division with remainders. Throughout this unit, students have justified their understanding of how unit fractions make a whole. Just like counting whole numbers, the counting of unit fractions is called iterating. Like partitioning, iterating is an important part of being able to understand and use fractions. Understanding that ¾ can be thought of as a count of three parts called fourths is an important idea for students to develop (Van de Walle). COMMON MISCONCEPTIONS Many students do not see unit fractions as the basic building block of fractions, in the same sense that the number 1 is the basic building block of the whole numbers. Just as every whole number is obtained by combining sufficient number of 1s, every fraction is obtained by combining a sufficient number of unit fractions (Kentucky DOE FALs document). ESSENTIAL QUESTIONS What is the relationship between a unit fraction and a unit of 1? How is the odd and even pattern with unit fractions on a number line similar to units of 1 on a number line? Why is the denominator important to the unit fractions? How does the numerator impact the denominator on the number line? MATERIALS Sidewalk chalk GROUPING Partners/Small Group NUMBER TALKS By now number talks should be incorporated into the daily math routine. Continue utilizing the different strategies in number talks and revisiting them based on the needs of your students. TASK DESCRIPTION, DEVELOPMENT AND DISCUSSION Part I It is imperative that the teacher conducts the following discussion using the below mentioned questions before the task since they will serve as a bridge for conceptual understanding.
I would like to order a pizza that is ¼ cheese, ¼ black olives, ¼ pepperoni, and ¼ green peppers. CONSTRUCTING TASK: GRAPHING FRACTIONS From NCTM Illuminations APPROXIMATE TIME: 2 class periods Students will draw a picture graph of their classmates’ favorite pets, a bar graph of their classmates’ favorite sports, and a graph of their choice of a bag of colored candies. Students will identify the fractional representation of each bar of data and create questions that could be answered using the data in their graphs. CONTENT STANDARDS MGSE3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. MGSE3.NF.1 Understand a fraction as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction as the quantity formed by a parts of size . For example, means there are three parts, so = + + . STANDARDS FOR MATHEMATICAL PRACTICE 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Children need to understand the meaning of fractions based on repeated hands-on activities. They need a general rule for explaining the numerator and denominator of a fraction.