5.1 math standards to be continued in January

STANDARDS FOR MATHEMATICAL CONTENT 

MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators.

MGSE5.NF.2 Solve word problems involving addition and subtraction of fractions, including cases of unlike denominators (e.g., by using visual fraction models or equations to represent the problem). Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7, by observing that 3/7 < ½.

MGSE5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Example: 3 5 can be interpreted as “3 divided by 5 and as 3 shared by 5”.

MGSE5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a.Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: 𝑎 𝑏 ×𝑞 as 𝑎 𝑏 × 𝑞 1 and 𝑎 𝑏 × 𝑐 𝑑 = 𝑎𝑐 𝑏𝑑
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

MGSE5.NF.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Example 4 x 10 is twice as large as 2 x 10. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

MGSE5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

MGSE5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share ½ lb of chocolate equally? How many 1/3-cup servings are 2 cups of raisins 1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

MGSE5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were

COMMON MISCONCEPTIONS MGSE5.NF.1, MGSE5.NF.2 – Students often mix up models when adding, subtracting or comparing fractions. Students will use a circle for thirds and a rectangle for fourths when comparing fractions with thirds and fourths. Remind students that the representations need to be from the same whole models with the same shape and size.

BIG IDEAS 

• A fraction is another representation for division.
• Fractions are relations – the size or amount of the whole matters.
• Fractions may represent division with a quotient less than one.
• Equivalent fractions represent the same value.
• With unit fractions, the greater the denominator, the smaller the equal share.
• Shares don’t have to be congruent to be equivalent.
• Fractions and decimals are different representations for the same amounts and can be used interchangeably.

ESSENTIAL QUESTIONS

• How are equivalent fractions helpful when solving problems?
• How can a fraction be greater than 1?
• How can a fraction model help us make sense of a problem?
• How can comparing factor size to 1 help us predict what will happen to the product?
• How can decomposing fractions or mixed numbers help us model fraction multiplication?
• How can decomposing fractions or mixed numbers help us multiply fractions?
• How can fractions be used to describe fair shares?
• How can fractions with different denominators be added together?
• How can looking at patterns help us find equivalent fractions?
• How can making equivalent fractions and using models help us solve problems?
• How can modeling an area help us with multiplying fractions?
• How can we describe how much someone gets in a fair-share situation if the fair share is less than 1?
• How can we describe how much someone gets in a fair-share situation if the fair share is between two whole numbers? • How can we model an area with fractional pieces?
• How can we model dividing a unit fraction by a whole number with manipulatives and diagrams?
• How can we tell if a fraction is greater than, less than, or equal to one whole?
• How does the size of the whole determine the size of the fraction?
• What connections can we make between the models and equations with fractions?
• What do equivalent fractions have to do with adding and subtracting fractions?
• What does dividing a unit fraction by a whole number look like?
• What does dividing a whole number by a unit fraction look like?
• What does it mean to decompose fractions or mixed numbers?
• What models can we use to help us add and subtract fractions with different denominators?
• What strategies can we use for adding and subtracting fractions with different denominators?
• When should we use models to solve problems with fractions?
• How can I use a number line to compare relative sizes of fractions?
• How can I use a line plot to compare fractions?