Richland Parish School Board



Grade 3

Mathematics

Unit 5: Division and Fractions

Time Frame: Approximately six weeks

Unit Description

The focus of this unit is the development of the concept of division in terms of equal shares (size of group unknown) and repeated subtraction (number of groups unknown). It furthers understanding of how all of the concepts relate to one another through modeling, drawing, using number sentences, and additional strategies. The unit also focuses on fractions looking at different representations, equivalency, and comparison.

Student Understandings

Students make sense of division and fraction situations. Students understand that multiplication and division are inter-related and are inverse operations. Students use different representations to model fractions, to find equivalent fraction, and to compare fractions.

Guiding Questions

1. Can students represent and solve a division problem?

2. Can students describe how multiplication and division are related?

3. Can students apply their knowledge of fact families to solve real-life problems?

4. Can students model basic fractions through tenths in different ways?

5. Can students find equivalent fractions?

6. Can students compare fractions?

Grade 3 Grade-Level Expectations (GLEs) and Common Core State Standards (CCSS)

|Grade-Level Expectations |

|GLE # |GLE Text and Benchmarks |

|Number and Number Relations |

|6. |Recognize and model division as separating quantities into equal subsets (fair shares) or as repeated subtraction (N-4-E)|

| |(N-7-E) |

|7. |Recognize and apply multiplication and division as inverse operations (N-4-E) |

|8. |Recognize, select, connect, and use operations, operational words, and symbols (i.e., +, (, x, () to solve real-life |

| |situations (N-5-E) (N-6-E) (N-9-E) |

|9. |Know basic multiplication and division facts [0s, 1s, 2s, 5s, 9s, and turn-arounds (commutative facts), including |

| |multiplying by 10s] (N-6-E) (N-4-E) |

|15. |Use objects, pictures, numbers, symbols, and words to represent multiplication and division problem situations (A-1-E) |

|16. |Use number sentences to represent real-life problems involving multiplication and division (A-1-E) (N-4-E) |

|18. |Use letters as variables in mathematical statements that represent real-life problems (e.g., [pic]) (A-2-E) |

|23. |Find the area in square units of a given rectangle (including squares) drawn on a grid or by covering the region with |

| |square tiles (M-1-E) |

|47. |Find patterns to complete tables, state the rule governing the shift between successive terms, and continue the pattern |

| |(including growing patterns) (P-1-E) (P-2-E) |

|CCSS for Mathematical Content |

|CCSS # |Core Curriculum State Standards |

|Operations and Algebraic Thinking |

|3.OA.3 |Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and |

| |measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the |

| |problem. |

|Numbers and Operations-Fractions |

|3.NF.1 |Understand a fraction 1/b as the quantity formed by 1 part when a whole is |

| |partitioned into b equal parts; understand a fraction a/b as the quantity formed |

| |by a parts of size 1/b. |

|3.NF.2 |Understand a fraction as a number on the number line; represent fractions on a |

| |number line diagram. |

| |Represent a fraction 1/b on a number line diagram by defining the interval from 0 to1 as the whole and partitioning it into|

| |b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b |

| |on the number line. |

| |Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting |

| |interval has size a/b and that its endpoint locates the number a/b on the number line. |

|3.NF.3 |Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. |

| |Understand two fractions are equivalent (equal) if they are the same size, or the same point on a number line. |

| |Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, |

| |e.g., by using a visual fraction model. |

| |Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in |

| |the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. |

| |Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that |

| |comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the |

| |symbols >, =, , [pic]of a small pizza

[pic]of a small coke < [pic]of a large coke

[pic]of a medium cup of ice cream = [pic]of a medium cup of ice cream

When finished, have students share their statements with the class.

Show students a piece of paper. Cut the paper into fourths. Ask students to write a sentence telling which is greater, [pic] or [pic] of the paper ([pic] is more). Have students read their responses and discuss them. Since the denominator is the same, the pieces are the same size. Because the numerator is larger in [pic] than in [pic], [pic] is greater. They have more of the same size pieces.

Have students use their fraction circles or strips.

Ask them to show [pic]and [pic]and ask which fraction is greater ([pic]).

Have them show [pic]and [pic]and ask which fraction is greater ([pic]).

Have them show [pic] and [pic] and ask which fraction is greater ([pic]).

Have them show [pic]and [pic]and ask which fraction is greater. Ask students what is similar about the pairs of fractions. (The numerators are the same but the denominators are different in each pair of fractions.)

Have students make a generalization comparing fractions. (If the numerators are the same, the fraction with the smaller denominator is larger.) Relate this to a pizza. The more slices that the pizza is divided into, the smaller the slice. So 3 pieces of a pizza cut into [pic]ths will be more than 3 pieces of a pizza cut into[pic]ths. Have students complete the Ordering Fractions BLM. Collect students’ work and review it to determine their progress in understanding equivalent fractions and comparing fractions.

Sample Assessments

General Guidelines

Students need to be observed both as individuals and in groups. Continue to assess students by listening to them during whole class and partner discussions.

General Assessments

• Include in the portfolio assessment the following:

✓ Anecdotal notes from teacher observation

✓ Student explanations from specific activities

✓ Learning entries, using specific topics such as:

▪ What is division? (Given at the beginning of the unit and again at the end)

▪ What is 16 ( 2? What does each part of 16 ( 2 mean?

▪ How would you explain 16 ( 2 to someone who doesn’t know about division?

▪ How would you share $25 among five friends if they all must get the same amount?

• While students are working in groups, ask probing questions such as:

✓ How would you prove that?

✓ Do you understand what ____ is saying?

✓ Is the solution reasonable?

✓ What would happen if?

• Provide sharing time for group work, asking questions such as:

✓ Can you convince everyone that your answer makes sense?

✓ Does anyone have another way to explain that?

✓ What do you think about that?

• Have students write their own division story problems and show their solutions. Monitor to see if the students’ problems illustrate division as fair shares and as repeated subtraction.

• Have students illustrate solutions to given problems by drawing pictures.

• Have students write their own division fact riddles and share them with the class. Students will be able to provide the answers to their riddles. Observe students to see if they are using the correct terminology and symbols.

• Bring in items (e.g., cookies) for students and have them determine the number each student in their group will receive. Have students draw models for the problems and write the division problems as number sentences.

• Set up performance tasks. Use real object sets (e.g. six packs of soda, pack of gum, etc.) around the room for students to demonstrate an understanding of fractions. Have students complete the activity and write about what they did.

• Give students pictures of circular and rectangular pizzas and have them color in[pic], 2/3, 5/6, 3/8, etc., of the pizza and label the fractional part colored or not colored. Have students explain their thinking and how they decided what to shade or what to leave unshaded.

Activity-Specific Assessments:

• Activity 4: Have students answer the question for this situation. Someone told Kevin that division and multiplication are alike. Someone else told him that division and multiplication aren’t alike. What would you tell Kevin?

• Activity 7: Have students explain how to divide 12 by three different numbers. Have students fold paper into 3 sections. In each section, have the student write one of the following: How would you share 12 balloons among 4 people? How would you share $12.00 among 6 people? How would you share 12 brownies among 2 people? Have students explain each situation using pictures, words, and numbers.

• Activity 12: Have students represent the fractions[pic][pic], [pic], and[pic] by drawing pictures of each.

• Activity 15: Have students compare the pairs of fractions[pic]and [pic], [pic] and [pic], and [pic]and [pic]. Have them explain how they know which fraction in each pair is the greater fraction.

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