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How Much: Total, More, Of, Equal Portions?

Learn how to model situations involving fractions, recognize appropriate operations, write mathematical statements, and fluently multiply or divide fractions.

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How Much: Total, More, Of, Equal Portions?

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  1. How Much: Total, More, Of, Equal Portions? Created by Sara De Voogd Objectives The learner will be able to: • Model situations involving fractions • Recognize when addition, subtraction, multiplication, or division is the appropriate operation to solve a problem • Write a mathematical statement to represent a given applied situation involving multiplying or dividing fractions • Multiply or divide any two fractions including mixed numbers fluently • Contextualize and explain the meaning of a problem's solution Begin

  2. Welcome! This activity is structured in a KWL format. K: What students expected to know at beginning of task W: What students will be investigating L: Opportunity to demonstrate learning Letters like the ones to the right will assist in navigating through the activity. Click on them to return to a specific section or advance through the activity. Please do not use the space bar. Be sure to investigate all links and buttons prior to advancing. Continue K W L

  3. K: What you should knowTerms and Concepts Vocabulary Click each category below before advancing using the “W” Addition & Subtraction Multiplication & Division W Click “W” to continue

  4. VocabularyPlease click the following links to clarify terms before moving on. Denominator Common Denominator Least Common Denominator Improper Fraction Mixed Fraction Addition Subtraction Multiplication Division Fraction Numerator K

  5. Addition and Subtraction of fractions Adding/Subtracting Fractions Adding Fractions with Unlike Denominators Subtracting Fractions with Unlike Denominators Matha Mia Adding Fractions Song K

  6. Multiplication and Divisionof fractions Multiplying & Dividing Fractions How to Multiply Fractions Division of Fractions Song I Can Divide fractions song K

  7. W: What you want to know Fractions: Modeling and solving real-world problems SOLVE Addition/Subtraction Multiplication/Division Dinner Party Click to continue

  8. Steps to SOLVE word problems Study the problem; identify the question Organize the facts; highlight key information Line up a plan; select a strategy to solve Verify chosen plan with computation Examine and explain solution W

  9. Addition & Subtraction W of fractions Key words to indicate addition or subtraction: Addition • Sum • Total • Altogether • Increased by • More than • Combined • In addition to Subtraction • Difference • Minus • Less • Less than • Fewer than • Decreased by • How much more

  10. Multiplication & Division W of fractions Key words to indicate multiplication or division: Multiplication • Product • Of • Multiplied by • Increased by a factor of • Times Division • Per • Out of • How many equal groups • Ratio of • Quotient of

  11. W: The Dinner Party Miss De Voogd decided to host a dinner party. She sent out invitations and selected the menu for the event. As the date quickly approached, Miss D realized her work was far from finished. Consider Miss D's current dilemmas: W Dilemma I Dilemma III Dilemma II Dilemma IV L Click each Dilemma below before advancing using the “L”

  12. W: Dilemma I Miss D looked at the ingredients for the recipe and wanted to know the total amount of spices included in the recipe. Menu Baked Ziti Salad Breadsticks Baked Ziti Remember to SOLVE! ¾ teaspoon dried oregano 1/2 teaspoon salt 1/8 teaspoon pepper ¼ teaspoon dried thyme 1/3 teaspoon dried rosemary S

  13. S: Dilemma I What is the total amount of spices included in the recipe? Study the problem; identify the question O

  14. O: Dilemma I Organize the facts; highlight key information ¾ teaspoon dried oregano 1/2 teaspoon salt 1/8 teaspoon pepper ¼ teaspoon dried thyme 1/3 teaspoon dried rosemary Key Information L

  15. L: Dilemma I Line up a plan; select a strategy to solve What is the total amount of spices included in the recipe? Plan: Addition of fractions V

  16. V: Dilemma I Verify chosen plan with computation 1. Strategy: Addition 2. Common Denominators 3. Multiply 4. Simplify E

  17. E: Dilemma I Examine and explain solution Solution Explanation Miss D needs a total of teaspoons of spices for her recipe. Dinner Party

  18. W: Dilemma II Miss D mixed together all the spices in one container. As she measured the total amount, she found she had teaspoons of spices.How much more spice does she have than she needs? Menu Baked Ziti Salad Breadsticks Baked Ziti Remember to SOLVE! ¾ teaspoon dried oregano 1/2 teaspoon salt 1/8 teaspoon pepper ¼ teaspoon dried thyme 1/3 teaspoon dried rosemary S

  19. S: Dilemma II How much more spice does she have than she needs? Study the problem; identify the question O

  20. O: Dilemma II Organize the facts; highlight key information Amount of Spice Needs Has L

  21. L: Dilemma II Line up a plan; select a strategy to solve How much more spice does she have than she needs? Plan: Subtraction of fractions V

  22. V: Dilemma II Verify chosen plan with computation 1. Strategy: Subtraction 2. Convert to Improper Fractions 3. Common Denominators 4. Multiply 5. Simplify E

  23. E: Dilemma II Examine and explain solution Solution Explanation Miss D has more teaspoons of spices than she needs Dinner Party

  24. W: Dilemma III Miss D received word that additional guests were attending the dinner. She quickly repeated the steps resulting in trays of baked ziti. The recipe states the serving size is of the tray. Miss D wants to ensure everyone is well fed and decides to plate one and a half times the serving size. What is the amount guests are served? S

  25. S: Dilemma III What is the amount guests are served? Study the problem; identify the question O

  26. O: Dilemma III Organize the facts; highlight key information Serving Size Servings per person L

  27. L: Dilemma III Line up a plan; select a strategy to solve Miss D wants to ensure everyone is well fed and decides to plate one and a half times the serving size V Plan: Multiplication of fractions

  28. V: Dilemma III Verify chosen plan with computation 1. Strategy: Multiplication 2. Rewrite 3. Simplify E

  29. E: Dilemma III Examine and explain solution Solution Explanation Each guest would receive of a tray. Dinner Party

  30. W: Dilemma IV Miss D looked around the kitchen at all the food. She knew 14 people would arrive for dinner soon, but wondered the maximum number of people the food would serve. How many servings can be plated out of trays? S

  31. S: Dilemma IV How many servings can be plated out of trays? Study the problem; identify the question O

  32. O: Dilemma IV Organize the facts; highlight key information Total Amount Serving Size L

  33. L: Dilemma IV How many servingscan be plated out of trays? Line up a plan; select a strategy to solve V Plan: Division of fractions

  34. V: Dilemma IV Verify chosen plan with computation 1. Strategy: Division 2. Multiply by the reciprocal 3. Simplify E

  35. E: Dilemma IV Examine and explain solution Solution Explanation Miss D has enough food for people. Dinner Party

  36. L: What you learnedDetermining operation and contextualizing solutions Race Training Click on key words and all four scenarios before advancing using “The End” 1 3 2 4 Key Words Operations The End

  37. L: Key Words Math Operations Key Word Sort Click the link above Read the directions Click “start” L

  38. L: Race Training 1 One week during training for her race, Miss D ran the following number of miles each day: Monday Tuesday Wednesday Thursday Friday Saturday How many miles did Miss D run altogether during the week? miles miles

  39. Correct! S: How many miles did Miss D run altogether during the week? O: L: Addition of fractions V: E: Miss D ran miles in a week. L

  40. Think about the following and try again! S: How many miles did Miss D run altogether during the week? O: L: Addition of fractions V: E: Miss D ran ? miles in a week. Adding Fractions with Unlike Denominators Race Training 1

  41. L: Race Training 2 During her second week of training, Miss D had a mileage goal of miles. How many miles does Miss D have left to run to meet her goal? By Thursday, Miss D recorded running miles. miles miles

  42. Correct! S: How many miles does Miss D have left to run to meet her goal? O: L: Subtraction of fractions V: E: Miss D needs to run more miles this week. L

  43. Think about the following and try again! S: How many miles does Miss D have left to run to meet her goal? O: L: Subtraction of fractions V: E: Miss D needs to run ? more miles this week. Subtracting Fractions with Unlike Denominators Race Training 2

  44. L: Race Training 3 During another week of training, Miss D determined she completed of her mile run. How much of her run has Miss D completed? miles miles

  45. Correct! S: How much of her run has Miss D completed? O: L: Multiplication of fractions V: E: Miss D completed miles of her run. L

  46. Think about the following and try again! S: How much of her run has Miss D completed? O: L: Multiplication of fractions V: E: Miss D completed ? miles of her run. How to Multiply Fractions Race Training 3

  47. L: Race Training 4 Due to the weather, Miss D needed to complete her run on an indoor track which is of a mile. Miss D needs to run of a mile today. How many equal laps must Miss D run? laps laps

  48. Correct! S: How many equal laps must Miss D run? O: L: Division of fractions V: E: Miss D must run equal laps. L

  49. Think about the following and try again! S: How man equal laps must Miss D run? O: L: Division of fractions V: E: Miss D must run ? equal laps. Division of Fractions Song Race Training 4

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