Session 240 Hillen, Olanoff, & Welder, Moving beyond common ...
1. Identify some fractions that would fit in the following buckets1:
2. For each set of fractions below, circle the fraction that is greater (or if the fractions are equivalent, write “=” in between them), and provide a “sense-making” explanation for how you know2. a.
1 2
!
! 13 f. 15
!
! 2 k. 7
!
!
17 31
2 17
2 19
17 ! 19
! 15 g. 17
19 18
!
!
! 25 l. 12
31 15
!
!
!
3 8
b.
c.
!
4 7
! 7 h. 10
! 11 m. 20
!
9 14
3 7
6 11
8 ! 9
! 1 i. 4
! 25 99
! 24 j. 7
34 15
19! 36
! 2 n. 9
3! 8
! 18 !" 25
16 # 27
d.
!
!
!
e.
8 9
12 13
!
1 2
Adapted from Sowder, Sowder, & Nickerson (2010), pp. 119-120 Taken from Thanheiser, E., et al. (in press)
Amy Hillen, Dana Olanoff, and Rachael M. Welder (in collaboration with Ziv Feldman, Jennifer Tobias, and Eva Thanheiser) [email protected] Moving beyond common denominators: Comparing fractions using reasoning and sense-making (Session 240) 2015 NCTM Annual Meeting and Exposition
3. Arrange the following in order from smallest to largest:
! !
1 200
1 99
12 11
1 4
4 3
10 5
5 2
24 24
5 4
3 4
1
0
! !
! !
! !
!
!
!
!
Amy Hillen, Dana Olanoff, and Rachael M. Welder (in collaboration with Ziv Feldman, Jennifer Tobias, and Eva Thanheiser) [email protected] Moving beyond common denominators: Comparing fractions using reasoning and sense-making (Session 240) 2015 NCTM Annual Meeting and Exposition
2. For each set of fractions below, circle the fraction that is greater (or if the fractions are equivalent, write “=” in between them), and provide a “sense-making” explanation for how you know2. a.
1 2
!
! 13 f. 15
!
! 2 k. 7
!
!
17 31
2 17
2 19
17 ! 19
! 15 g. 17
19 18
!
!
! 25 l. 12
31 15
!
!
!
3 8
b.
c.
!
4 7
! 7 h. 10
! 11 m. 20
!
9 14
3 7
6 11
8 ! 9
! 1 i. 4
! 25 99
! 24 j. 7
34 15
19! 36
! 2 n. 9
3! 8
! 18 !" 25
16 # 27
d.
!
!
!
e.
8 9
12 13
!
1 2
Adapted from Sowder, Sowder, & Nickerson (2010), pp. 119-120 Taken from Thanheiser, E., et al. (in press)
Amy Hillen, Dana Olanoff, and Rachael M. Welder (in collaboration with Ziv Feldman, Jennifer Tobias, and Eva Thanheiser) [email protected] Moving beyond common denominators: Comparing fractions using reasoning and sense-making (Session 240) 2015 NCTM Annual Meeting and Exposition
3. Arrange the following in order from smallest to largest:
! !
1 200
1 99
12 11
1 4
4 3
10 5
5 2
24 24
5 4
3 4
1
0
! !
! !
! !
!
!
!
!
Amy Hillen, Dana Olanoff, and Rachael M. Welder (in collaboration with Ziv Feldman, Jennifer Tobias, and Eva Thanheiser) [email protected] Moving beyond common denominators: Comparing fractions using reasoning and sense-making (Session 240) 2015 NCTM Annual Meeting and Exposition
