TEACHING PRIORITY CONCEPTS IN MATH GRADE 6 KIM LOUTTIT SEPTEMBER 26, 2013.

TEACHIN

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CONCEPTS IN

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GRADE 6

K I M L

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S E P T E MB

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UPDATES

• Annotated 2013 assessment questions• Modules•As per a phone call, Ken Slentz said that a quarter to half of the modules will be out by the end of this month…

http://www.engageny.org/sites/default/files/resource/attachments/grade_6_math_released_questions.pdf

http://www.engageny.org/resource/grade-6-mathematics

CONTENT EMPHASIS BY CLUSTER

LET’S DO SOME MATH!!

• Go to www.infuselearning.com

• Choose STUDENT LOGIN

• Enter Room ID: 69506

• Enter your first name

• Click Submit

WEBSITES

• Learnzillion.com• http://learnzillion.com/lessons/1181-

divide-a-whole-number-by-a-unit-fraction

http://learnzillion.com/lessons/1181-divide-a-whole-number-by-a-unit-fraction



TAPE DIAGRAMS

• If you have any tape diagramming experience, try to solve this problem using tape diagrams. If not, solve it algebraically.

Two pears and a pineapple cost $2. Two pears and three pineapples cost $4.50. Find the cost of a pineapple.

USING TAPE DIAGRAMS

• Promote perseverance in reasoning through problems.

• Develop students’ independence in asking themselves: “Can I draw something?” “What can I label?” “What do I see?” “What can I learn from my drawing?”

FORMS OF THE TAPE DIAGRAM

Part-Whole Model

Comparison Model

FOUNDATIONS FOR TAPE DIAGRAMS IN PK-1• Sara has 2 apples. Jon has 5 apples. How many

apples do they have altogether? How many more apples does Jon have than Sara?

TAPE DIAGRAM PROBLEMS

Example 1: Sara has 5 stamps. Mark brings her 4 more stamps. How many stamps does Sara have now?


Example 2: Sara has 16 stamps. Mark brings her 4 more stamps. How many stamps doesSara have now?


Example 3: Sara brought 4 apples to school. After Mark brings her some more apples, she has 9 apples altogether. How many apples did Mark bring her?


Example 4: Matteo has 5 toy cars. Josiah has 2 more than Matteo. How many toy cars do Matteo and Josiah have altogether?


Example 5: Jasmine had 328 gumballs. Then, she gave 132 gumballs to her friend. How many gumballs does Jasmine have now?


Example 6: Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips does Harry have?


Example 7: Jose has 4 paper clips. Harry has twice as many paper clips as Jose. How many paper clips do they have altogether?


Example 8: William’s weight is 40 kg. He is 4 times as heavy as his youngest brother Sean. What is Sean’s weight?


Example 9: Jamal has 8 more marbles than Thomas. They have 20 marbles altogether. How many marbles does Thomas have?


Example 10: The total weight of a football and 10 tennis balls is 1 kg. If the weight of each tennis ball is 60 g, find the weight of the football.


Example 11: David spent 2/5 of his money on a storybook. The storybook cost $20 how much did he have at first?


Example 12: Alex bought some chairs. One third of them were red and one fourth of them were blue. The remaining chairs were yellow. What fraction of the chairs were yellow?


Example 13: Jim had 360 stamps. He sold 1/3 of them on Monday and ¼ of the remainder on Tuesday. How many stamps did he sell on Tuesday?


Example 14: Max spent 3/5 of his money in a shop and ¼ of the remainder in another shop. What fraction of his money was left? If he had $90 left, how much did he have at first?


Example 15: Henry bought 280 blue and red paper cups. He used 1/3 of the blue ones and 1/2 of the red ones at a party. If he had an equal number of blue cups and red cups left, how many cups did he use altogether?


Example 16: A club had 600 members. 60% of them were males. When 200 new members joined the club, the percentage of male members was reduced to 50%. How many of the new members were males?


Example 17: Meagan had $1780 and Lisa had $1910. Lisa gave some money to Meagan. In the end Meagan had twice as much money as Lisa. How much money did Lisa give to Meagan?


Example 18: The ratio of the length of Tom’s rope to the length of Jan’s rope was 3:1. The ratio of the length of Maxwell’s rope to the length of Jan’s rope was 4:1. If Tom, Maxwell and Jan have 80 feet of rope altogether, how many feet of rope does Tom have?


Example 19: Lena finds two boxes of printer paper in the teacher supply room. The ratio of the packs of paper in Box A to the packs of paper in Box B is 4:3. If half of the paper in Box A is moved to Box B, what is the new ratio of packs of paper in Box A to Box B?


Example 20: Sana and Amy collect bottle caps. The ratio of the number of bottle caps Sana has to the number Amy has is 2:3. The ratio became 5:6 when Sana added 8 more bottle caps to her collection. How many bottle caps does Amy have?


Example 21: The ratio of songs on Jessa’s phone to songs on Tessie’s phone is 2 to 3. Tessie deletes half of her songs and now has 60 fewer songs than Jessa. How many songs does Jessa have?


Example 22: Of the kids taking swimming lessons at City Pool this summer, 36 of them, or 45%, are girls. How many kids are taking swimming lessons?


Example 23: A digital picture frame was on sale at Circuit City for $78. If this reflects a discount of 35%, what was the original price of the picture frame?

KEY POINTS

• When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time.

• Develop habits of mind in students to reflect on the size of bars relative to one another.

• Part-whole models are more helpful when modeling situations where:_____________________________

• Compare to models are best when: ____________________________________

RATIO TABLES & DOUBLE NUMBER LINES

RATIO TABLES & EQUATIONS

COORDINATE PLANE

DIVIDING FRACTIONS (BEGINS IN GRADE 5)

DIVIDING FRACTIONS

WHAT DOES DIVISION MEAN?

• Interpret quotients of whole numbers as the number of objects in each share when _____ objects are partitioned into equal shares of _____ objects each

• ½ ÷ 3 means what?• 3 ÷ ½ means what?

DIVIDING FRACTIONS

Maura cuts a piece of rectangular clay in half. She then divides one half into 3 equal parts. What fraction of the whole piece of clay is each of the 3 parts?

DIVIDING FRACTIONS

A roll of wire 3/5 long is cut into 6 equal pieces. How long is each piece?

DIVIDING FRACTIONS

A 4/5 pound cantaloupe is cut into 2 equal pieces. What is the weight of each piece of cantaloupe?

DIVIDING FRACTIONS

Mia walks a 2 mile trail. She stops to exercise every 1/5 mile. How many times does Mia stop to exercise?

DIVIDING FRACTIONS

The serving size for a toddler’s daily vitamin C is ¾ cup of orange juice. If there are 2 cups of orange juice, how many servings of vitamin C are there for a toddler?

DIVIDING FRACTIONS

What is ?

Create a model to support your answer.

DIVIDING FRACTIONS

How many cup servings are in cup of yogurt?

RELATIONSHIP BETWEEN FRACTION MODELS AND EQUATIONS

14÷23

RELATIONSHIP BETWEEN FRACTION MODELS AND EQUATIONS

23÷34

DIVIDING WITH FRACTIONS

Why do we multiply by the reciprocal when dividing fractions?• If you were to divide 2 by 3…• Is that the same as 2 × 1/3?• When you are dividing number (whole

and fractions) you can always write the fraction as a product of two numbers.

DIVIDING WITH FRACTIONS

Why do we use models????• Helps students to understand what

division of fractions actually looks like!

• A picture is worth 1000 words!!!!

DEVELOP LESSONS

• www.kltp.weebly.com• Choose “Grade 6 Lessons”• Click on “Lesson Plan Template”

• Equivalent Ratios

• Percent of a Quantity

• Find the Whole Given a Part and a Percent

• Division of a Fraction by a Whole Number

• Division of a Whole Number by a Fraction

• Division of a Fraction by a Fraction

http://www.kltp.weebly.com/

TEACHING PRIORITY CONCEPTS IN MATH GRADE 6 KIM LOUTTIT SEPTEMBER 26, 2013.

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