distribution of the distributive property your mobile devices ready!standards involving the...
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Have your mobile devices ready! Standards involving the distributive property and sample tasks References
Distribution of the Distributive Property
Dr. Roger FischerEMAT Project FacilitatorMontana State University
June 2016
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
OVERVIEW
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Standards involving the distributive property and sample tasks
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
AUDIENCE POLLING
https://www.polleverywhere.com/my/polls
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
MULTIPLICATION FACTS
Grade 3: 3.OA.5Apply properties of operations as strategies tomultiply.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASK
from Kling and Bay-Williams (2015)
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
AREA MODELS
Grade 3: 3.MD.7CUse area models to represent the distributive propertyin mathematical reasoning.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASKFrom Illustrative Mathematics (2016d)
1. How many circles are there in all? Write down a numbersentence that shows how you might have thought about it.
2. Alonso said he figured out how many shaded circles therewere first and then how many unshaded circles there weresecond. Once he knew how many of each, he added themtogether to find the total. Write a number sentence Alonsocould have used that shows his reasoning.
3. Jennifer said “I just saw 3 rows of 8 circles.” Write anumber sentence that Jennifer could have used that showsher reasoning.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASKFrom Illustrative Mathematics (2016d)
1. How many circles are there in all? Write down a numbersentence that shows how you might have thought about it.
2. Alonso said he figured out how many shaded circles therewere first and then how many unshaded circles there weresecond. Once he knew how many of each, he added themtogether to find the total. Write a number sentence Alonsocould have used that shows his reasoning.
3. Jennifer said “I just saw 3 rows of 8 circles.” Write anumber sentence that Jennifer could have used that showsher reasoning.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASKFrom Illustrative Mathematics (2016d)
1. How many circles are there in all? Write down a numbersentence that shows how you might have thought about it.
2. Alonso said he figured out how many shaded circles therewere first and then how many unshaded circles there weresecond. Once he knew how many of each, he added themtogether to find the total. Write a number sentence Alonsocould have used that shows his reasoning.
3. Jennifer said “I just saw 3 rows of 8 circles.” Write anumber sentence that Jennifer could have used that showsher reasoning.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
MENTAL DIVISION
Grade 4: 4.NBT.6Find whole-number quotients and remainders withup to four-digit dividends and one-digit divisors,using strategies based on place value, the propertiesof operations, and/or the relationship betweenmultiplication and division. Illustrate and explain thecalculation by using equations, rectangular arrays,and/or area models.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASK
From Illustrative Mathematics (2016a)
Jillian says “I know that 20 times 7 is 140 and if I take away 2sevens that leaves 126. So 126 ÷ 7 = 18.
1. Is Jillian’s calculation correct? Explain.2. Draw a picture showing Jillian’s reasoning.3. Use Jillian’s method to find 222 ÷ 6.
SOLUTION:https://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
NUMBER THEORY
Grade 6: 6.NS.4Use the distributive property to express a sum of twowhole numbers 1-100 with a common factor as amultiple of a sum of two whole numbers with nocommon factor.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASK
From Illustrative Mathematics (2016b)
Nina was finding multiples of 6. She said, “18 and 42 are bothmultiples of 6, and when I add them, I also get a multiple of 6.
18 + 42 = 60
Explain to Nina why adding two multiples of 6 will alwaysresult in a multiple of 6.
SOLUTION:https://www.illustrativemathematics.org/content-standards/tasks/257
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
MORE NUMBER THEORY
Grade 6: 6.EE.3Apply the. . . distributive property to the expression3(2 + x) to produce the equivalent expression 6 + 3x;apply the distributive property to the expression24x + 18y to produce the equivalent expression6(4x + 3y).
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
MORE NUMBER THEORY
Grade 6: 6.EE.3Apply the. . . distributive property to the expression3(2 + x) to produce the equivalent expression 6 + 3x;apply the distributive property to the expression24x + 18y to produce the equivalent expression6(4x + 3y).
‘I Discuss with your peers any possible connections between
this standard and the last sample task.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
“TWO NEGATIVES MAKE A POSITIVE”
Grade 7: 7.NS.2aUnderstand that multiplication is extended fromfractions to rational numbers by requiring thatoperations continue to satisfy the properties ofoperations, particularly the distributive property,leading to products such as (−1)(−1) = 1 and therules for multiplying signed numbers.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASK
From Illustrative Mathematics (2016c)
5 × 5 5 × 4 5 × 3 5 × 2 5 × 1 5 × 0 5×(−1) 5×(−2) 5×(−3)25 20 15 10 5 0 -5 -10 -15
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
SAMPLE TASK
From Illustrative Mathematics (2016c)
5 × 5 5 × 4 5 × 3 5 × 2 5 × 15 × (5 − 0) 5 × (5 − 1) 5 × (5 − 2) 5 × (5 − 3) 5 × (5 − 4)5 × 5 − 5 × 0 5 × 5 − 5 × 1 5 × 5 − 5 × 2 5 × 5 − 5 × 3 5 × 5 − 5 × 4
5 × 0 5 × (−1) 5 × (−2) 5 × (−3) 5 × (−4)5 × (5 − 5) 55 × (5 − 6) 5 × (5 − 7) 5 × (5 − 8)5 × 5 − 5 × 5 5 × 5 − 5 × (−1) 5 × 5 − 5 × (−2) 5 × 5 − 5 × (−3) 5 × 5 − 5 × −4
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
LOOK FOR AND MAKE USE OF STRUCTURE
Grade 8: 8.EE.7bSolve linear equations with rational numbercoefficients, including equations whose solutionsrequire expanding expressions using the distributiveproperty and collecting like terms.
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
LOOK FOR AND MAKE USE OF STRUCTURE
1. Solve the equation 9x + 9 = 180 for x.2. Solve the equation 7y + 7 = 140 for y3. Solve the equation 12z + 12 = 240 for z
Find a way to solve each of these equations using thedistributive property. How are these equations similar toNina’s question about multiples of 6?
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
THANKS FOR COMING!
Dr. Roger FischerMathematics InstructorGallatin College – Montana State University201 Hamilton HallBozeman, MT [email protected]
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
REFERENCES I
Illustrative Mathematics. (2016a, June). 4.NBT: Mental divisionstrategy. Retrieved June 9, fromhttps://www.illustrativemathematics.org/content-standards/4/NBT/B/6/tasks/1774
Illustrative Mathematics. (2016b, June). 6.NS: Adding multiples.Retrieved June 9, fromhttps://www.illustrativemathematics.org/content-standards/tasks/257
Illustrative Mathematics. (2016c, June). 6.NS: Why is a negativetimes a negative always a positive? Retrieved June 9, fromhttps://www.illustrativemathematics.org/content-standards/7/NS/A/2/tasks/1667
Have your mobile devices ready! Standards involving the distributive property and sample tasks References
REFERENCES II
Illustrative Mathematics. (2016d, June). 6.RP: Unit conversions.Retrieved June 10, 2016, fromhttps://www.illustrativemathematics.org/content-standards/tasks/1992
Kling, G., & Bay-Williams, J. (2015). Three steps to masteringmultiplication facts. Teaching Children Mathematics, 21(9),548–559.