Measure Treasures Lesson 1

Objectives Create graph models for fractions less than or equal to one whole Use graphed models to find equivalent names for fractions Estimate the size of fractions Compare the relative size of fractions less than 1 Apply the concept of identity for multiplication to renaming equivalent fractions

Materials Math notebook ½ inch graph paper Rulers Homework

Mathematical Language Take notes in your notebook Denominator-- the number below the line in a fraction  It tells the total amount or size of parts that the numerator counts In the fractions ¾ and 5 ¼, 4 is the denominator Equivalent fractions– fractions that have equal value or the same decimal form Numerator– the number above the line in a fraction.  It tells how many parts of the total, indicated by the denominator, are being counted. In the fractions ½ and 4 ½, the 1 is the numerator. Identity Property of Multiplication– states that a number multiplied by 1 (including other representations of 1, such as 3/3) results in a product identical to the given number.  For example 5x1=5 and 1x2=2 Unit Fraction– a fraction with 1 in the numerator and a counting number in the denominator, such as 1/8.

Establishing Equivalence The size of the whole is constant but the size of the parts varies, depending on the fraction being explored. All of the parts that the whole is dived into are equal More than one name can be used to name a fraction The numerator names how many equal- sized parts are being considered or counted and the denominator names the size or equal parts the numerator counts

The Story Tori and Jordan were visiting their grandmother. It was a rainy day, Grandmother knew the children were bored, and she decided to take them into the attic on a treasure hunt. She invited them to investigate the treasures stored inside an old trunk– items that had been used at the Rabbit Hutch General Store that her own grandparents had operated early in the twentieth century. While Grandmother sat in a rocking chair enjoying their excitement, Tori and Jordan first found 10 lengths of fabric, each a different color, with some markings on them. They asked their grandmother about their discovery. Tori and Jordan learned that the lengths of cloth had been used to measure fabric in their great-great-grandparents' general store. As their grandmother reminisced about stories that her grandparents had told her and looked at the strips of cloth, she noticed that some of the measures had worn off because they had been used so often. Tori and Jordan decided to see if they could identify the missing numbers. They decided to make similar strips to represent halves, thirds, fourths, fifths, sixths, eights, ninths, tenths, twelfths, fifteenths, and sixteenths to help solve the mystery

Fraction number line 1 Use a piece of graph paper, turned horizontally, and a ruler to complete the following steps: 1. Mark a space eight inches apart. Label the mark on the left 0/1 and the mark on the right 1/1 2. Mark half of the total length and label this as ½. 3. Divide the total length into fourths and mark each of these distances, labeling them ¼, 2/4, ¾, 4/4 4. Divide the total lengths into eights and mark each of these with its fractional part. 1. The denominator should always be 8 5. Repeat dividing and marking the total length using 16 as the equal parts the numerator counts Answer in your notebook: These are multiples of _____

Fraction number line 2 Use a piece of graph paper, turned horizontally, and a ruler to complete the following steps: 1. Mark a space six inches apart. Label the mark on the left 0/1 and the mark on the right 1/1 2. Mark half of the total length and label this as ½. 3. Divide the total length into thirds and mark each of these distances, labeling them 1/3, 2/3, 3/3. 4. Repeat dividing and marking the total length using 9, and 12 as the equal parts the numerator counts Answer in your notebook: These are multiples of _____

Fraction number line 3 Use a piece of graph paper, turned horizontally, and a ruler to complete the following steps: 1. Mark a space seven and a half inches apart. Label the mark on the left 0/1 and the mark on the right 1/1 2. Mark half of the total length and label this as ½. 3. Divide the total length into fifths and mark and label each of these distances. 4. Repeat dividing and marking the total length using 15 as the equal parts the numerator counts Answer in your notebook: These are multiples of _____

Math Journal (notebook) The next three slide will provide you with information regarding how you should complete your math journal and the expectations for complete answers to questions

Math Journal (notebook) Expectations: Concepts 3 Overall, student demonstrates a strong understanding of concepts and, if applicable, uses appropriate and efficient strategy to solve problem correctly. The student answers all parts of the question/prompt. 2Overall, student demonstrates a good understanding of concepts and, if applicable, uses appropriate and efficient strategy but with minor errors or incomplete understanding. The student answers all parts of the question/prompt. 1Overall, student demonstrates partial understanding of concepts and, if applicable, uses appropriate strategy but may have major errors. The student answers all parts of the question/prompt. 0Overall, student demonstrates a lack of understanding of concepts and, if applicable, does not use appropriate strategy. The student may not have answered all question/prompt.

Math Journal (notebook) Expectations: Communication 3 Student states ideas/generalizations that are well developed and reasoning is supported with clear details, perhaps using a variety of representations such as examples, charts, graphs, models, and words. 2 Student states adequately developed ideas/generalizations and reasoning is supported with some details. When appropriate, representations may be limited 1 Student states partially developed ideas/generalizations and reasoning is incomplete 0 Student does not state ideas/generalizations correctly and reasoning is unclear with little or no support

Math Journal (notebook) Expectations: Vocabulary 3Student uses all mathematical vocabulary appropriately, including mathematical vocabulary related to the major math concept(s) from the unit. 2Student uses most mathematical vocabulary appropriately or may have minor misunderstanding. Student may have misused or omitted an appropriate vocabulary term. 1Student uses some mathematical vocabulary or may have a major misunderstanding. Student may have misused or omitted several appropriate vocabulary terms or a key vocabulary term related to the major math concept(s) from the unit. 0Student does not use any mathematical vocabulary.

Equivalent Fractions Answer the following question in your notebook: What are some fractions from different number lines that are equivalent? Explain why/how this works mathematically.

Application of concepts Choose a fraction number line to divide into six equal parts and add the fractional parts to the number line.  Answer in your journal: Which fraction number line did you choose? Explain why that line was your choice and use mathematical vocabulary to support your decision.

Application of concepts Choose a fraction number line to divide into six equal parts and add the fractional parts to the number line.  Answer in your journal: Which fraction number line did you choose? Explain why that line was your choice and use mathematical vocabulary to support your decision.

Think Deeply What are equivalent fractions? Use numbers, pictures and words to explain. Do not use ½ as one of your fractions.