Dear Family, Sincerely, Your child s teacher. Family Letter. Content Overview
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1 Family Letter Content Overview Dear Family, Your child has experience with fractions through measurements and in previous grades. Unit of Math Expressions builds on this experience. The main goals of this unit are to: understand the meaning of fractions. compare unit fractions. add and subtract fractions and mixed numbers with like denominators. multiply a fraction by a whole number. Your child will use fraction bars and fraction strips to gain a visual and conceptual understanding of fractions as parts of a whole. Later, your child will use these models to add and subtract fractions and to convert between improper fractions and mixed numbers. Examples of Fraction Bar Modeling: Fraction Comparisons Fraction Subtraction < 2-2 = In later lessons of this unit, your child will be introduced to the number line model for fractions. Students name fractions corresponding to given lengths on the number line and identify lengths corresponding to given fractions. They also see that there are many equivalent fraction names for any given length. Your child will apply this knowledge about fractions and fraction operations to solve real world problems. If you have questions or problems, please contact me. Sincerely, Your child s teacher Unit addresses the following standards from the Common Core Standards for Mathematics with California Additions:.NF.,.NF.a,.NF.b,.NF.c,.NF.d,.NF.a,.NF.b,.NF.c, and all Mathematical Practices. UNIT LESSON Understand Fractions
2 Carta a la familia Un vistazo general al contenido Estimada familia: Su niño ha usado fracciones al hacer mediciones y en los grados previos. La Unidad de Math Expressions amplía esta experiencia. Los objetivos principales de la unidad son: comprender el significado de las fracciones. comparar fracciones unitarias. sumar y restar fracciones y números mixtos con denominadores iguales. multiplicar una fracción por un número entero. Su niño usará barras y tiras de fracciones para comprender y visualizar el concepto de las fracciones como partes de un entero. Luego, usará estos modelos para sumar y restar fracciones y para convertir fracciones impropias y números mixtos. Ejemplos de modelos con barras de fracciones: Comparaciones de fracciones Resta de fracciones < 2-2 = Más adelante en esta unidad, su niño verá el modelo de la recta numérica para las fracciones. Los estudiantes nombrarán las fracciones que correspondan a determinadas longitudes en la recta numérica e identificarán longitudes que corresponden a fracciones dadas. También observarán que hay muchos nombres de fracciones equivalentes para una longitud determinada. Su niño aplicará este conocimiento de las fracciones y operaciones con fracciones para resolver problemas cotidianos. Si tiene alguna duda o algún comentario, por favor comuníquese conmigo. Atentamente, El maestro de su niño En la Unidad se aplican los siguientes estándares auxiliares, contendidos en los Estándares estatales comunes de matemáticas con adiciones para California:.NF.,.NF.a,.NF.b,.NF.c,.NF.d,.NF.a,.NF.b,.NF.c y todos los de prácticas matemáticas. UNIT LESSON Understand Fractions
3 - Class Activity Sums of Unit Fractions Shade the fraction bar to show each fraction. Then write the fraction as a sum of unit fractions and as a product of a whole number and a unit fraction. The first one is done for you.. = = = =. = = = = = =. = = UNIT LESSON Understand Fractions
4 -2 Class Activity Content Standards.NF.2,.NF.,.NF.a,.NF.b Mathematical Practices MP.2, MP., MP. Fifths that Add to One Every afternoon, student volunteers help the school librarian put returned books back on the shelves. The librarian puts the books in equal piles on a cart. One day, Jean and Maria found equal piles on the return cart. They knew there were different ways they could share the job of reshelving the books. They drew fraction bars to help them find all the possibilities.. On each fifths bar, circle two groups of fifths to show one way Jean and Maria could share the work. (Each bar should show a different possibility.) Then complete the equation next to each bar to show their shares. whole = all of the books whole Jean s Maria s share share = + = + = + = + UNIT LESSON 2 Fractions that Add to One
5 -2 Class Activity Sixths that Add to One The librarian put equal piles of returned books on the cart for Liu and Henry to reshelve. They also drew fraction bars. 2. On each sixths bar, circle two groups of sixths to show one way that Liu and Henry could share the work. (Each bar should show a different possibility.) Then complete the equation next to each bar to show their shares. whole = all of the books whole Liu s Henry s share share = + = + = + = + Find the Unknown Addend Write the fraction that will complete each equation.. = = +. = = +. = = 2 +. = = +. = = 2 +. = 0 0 = 0 + = +. = = = = + UNIT LESSON 2 Fractions that Add to One
6 - Class Activity Content Standards.NF.a,.NF.d,.MD.2 Mathematical Practices MP.2, MP., MP., MP. Add Fractions The circled parts of this fraction bar show an addition problem.. Write the numerators that will complete the addition equation. + = + = Solve each problem. Write the correct numerator to complete each equation = + =. + = + =. 2 + = + =. What happens to the numerators in each problem?. What happens to the denominators in each problem? Subtract Fractions The circled and crossed-out parts of this fraction bar show a subtraction problem.. Write the numerators that will complete the subtraction equation. - = - = UNIT LESSON Add and Subtract Fractions with Like Denominators
7 Fractions Bars one whole UNIT LESSON Add and Subtract Fractions with Like Denominators
8 0 UNIT LESSON Add and Subtract Fractions with Like Denominators
9 Understand Fractions Greater Than and Mixed Numbers whole UNIT LESSON Mixed Numbers and Fractions Greater Than
10 Understand Fractions Greater Than and Mixed Numbers (continued) whole whole whole whole whole whole whole whole whole whole whole whole whole whole whole 2 UNIT LESSON Mixed Numbers and Fractions Greater Than
11 - Class Activity Content Standards.NF.a,.NF.c Mathematical Practices MP., MP. Practice Addition and Subtraction with Fractions Greater Than Add or subtract.. + = =. 0 - =. 0 + = Add Mixed Numbers with Like Denominators Add.. - =. 0-0 = _ Subtract Mixed Numbers with Like Denominators Subtract Explain each solution. + 2 = + 2 = + 2 =. 2.. = 2 = - = - = 2 = - = UNIT LESSON Add and Subtract Mixed Numbers with Like Denominators
12 - Class Activity Make a Line Plot. Make a mark anywhere on this line segment.. Measure the distance from the left end of the segment to your mark to the nearest quarter inch.. Collect measurements from your classmates and record them in the line plot below Distance (inches). The range is the difference between the greatest value and the least value. What is the range of the data? 0. Which distance value was most common?. Describe any interesting patterns in the data values. For example, are there any large gaps? Are there clusters of values? UNIT LESSON Practice with Fractions and Mixed Numbers
13 UNIT Review/Test. Represent the shaded part of the fraction bar as the product of a whole number and a unit fraction. 2. In the morning Naomi jumps rope for hour. After lunch she jumps rope for another 2 hour. How long does Naomi jump rope? Write an equation. Then solve. Equation: Solution: hour. For numbers a d, write a fraction from the tiles to make a true equation. a. 0 0 = b. = c. 0 = d. 0 = UNIT TEST
14 UNIT Review/Test. Caesar buys dog treats and cat treats. He buys pound of dog treats. This is pound more than the weight of the cat treats he buys. How many pounds of cat treats does Caesar buy? Write an equation. Then solve. Equation: Solution: pound. A recipe calls for 2 cup of mushrooms. Dae uses times as much mushrooms. Choose the number of cups of mushrooms he uses. Mark all that apply. A cup C 2 cups B cups D cups. Complete the table to show the fraction as a product of a whole number and a unit fraction. Fraction Product 2 2. For a d, choose the operation that makes the equation true. a. b = 2 2 = 2 + c. - = d. + - = 2 UNIT TEST
15 UNIT Review/Test. Multiply the expression to complete the table. Expression 2 Written as a Fraction Written as a Mixed Number 2 2. For numbers a f, choose True or False for the equation. a. 2 + = b. - = c. + 2 = 2 d = 2 e. - = 2 f = 0 20 True True True True True True False False False False False False 0. Elias says this problem can be solved using addition. Vladmir says it can be solved using multiplication. Explain why both boys are correct. Milo practices piano hour every day. How many hours does he practice in days? UNIT TEST
16 UNIT Review/Test. For a and b, find the sum or difference. Write your answer as a mixed number or a whole number, when possible. 2 a. + 2 b On Saturday, Jesse plays basketball for 2 hour. Then he plays some more. He plays 2 hours in all. How much longer did Jesse play basketball? Part A Draw a model to represent the problem. Then solve. Explain how your model helps you solve the problem. Part B On Sunday, Jesse played basketball for 2 hours. How many total hours did he play basketball on Saturday and Sunday? Show your work. UNIT TEST
17 UNIT Review/Test. Rebecca s soup recipe calls for cup milk. She needs times as much milk to make a triple batch of soup. How many cups of milk does Rebecca need? Part A Draw a model for the problem. Part B Use your model to write two equations for the problem. Then solve.. For numbers a e, choose Yes or No to tell whether the fraction is correctly expressed as the sum of other fractions. a. = + b. = c. = + 2 d. = + + e. 0 = + Yes Yes Yes Yes Yes No No No No No UNIT TEST
18 UNIT Review/Test. The line plot shows the lengths of trails Andrea hiked last month at a state park. 2 2 Trail Lengths (miles) Andrea hiked miles last week. She could have hiked two -mile trails. Describe two other combinations 2 of trails she could have hiked.. Select the expression that is equivalent to 2 2. Mark all that apply. A B C D E F Explain how to change to a mixed number. 0 UNIT TEST
Dear Family, Sincerely, Your child s teacher. Family Letter. Content Overview
Family Letter Content Overview Dear Family, Your child has experience with fractions through measurements and in previous grades. Unit of Math Expressions builds on this experience. The main goals of this
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