Day 2 – Fractions as Quotients and Equivalence

Problem to Solve

Margie is biking around Lake Harriet. She stops and notices that she has biked for two miles and has made it three-fourths around the lake. Determine the distance around Lake Harriet.

Which thing does not belong?

Equal Sharing Problems

Solve each of the problems below by drawing pictures to show solution.

A. Kyle and Derek have 23 cookies. If they share the cookies evenly, how many cookies will each person get?
B. There is one and three-fourths cups of lime-aid in the refrigerator. Mike and Karla want to share the lime-aid equally. How much lime-aid will each person get?
C. Brooke purchased 11 burritos at Chipotle. She and her three brothers plan to eat them all and share them equally. How much will each person get?
D. Three people share two apple pies equally. How much pie will each person receive?
E. There are 17 pounds of birdseed in a large can. Rimma wants to put the birdseed into 3 containers with the same amount in each container. How many pounds of birdseed will be in each container?

Multiplication and Division (Draw a picture)

A.
B.
C.
Problem Type / # of groups / amount in each group / total / equation
A. Multiplication
Marlo gives five pieces of candy to each of her three friends. How much candy does she give away?
B. Measurement Division
(repeated subtraction)
Jay has 15 cups of flour. Each batch of pancakes he makes requires three cups of flour. How many batches can he make?
C. Partitive Division
(fair sharing)
Lizzy and her two friends want to share 15 grapes evenly. How many grapes will each friend receive?

Write your own partitive division (fair sharing) problem for

Analyzing Student Work

Problem: Six children share four candy bars evenly. How much candy bar can each child have?

A
/ B

C
/ D

E
/ F

Writing your own problems and predicting student responses

Problem 1 (2 sharing 7):
predicted student response A / predicted student response B
Problem 2 (5 sharing 3):
predicted student response A / predicted student response B

Equivalent Fractions – NAEP Question

What percent of kids at the 8th grade level got this question correct on NAEP?

Write three fractions that are equivalent to

Two fractions are equivalent if …

Equivalence Using Fraction Circles and Equivalence Chart

red / / / / / / / / / / / /
white
gray
pink
blue
brown
yellow

Two fractions are equivalent if …

Equivalence Using Paper Strips

A. Fold and shade in six-eighths of a paper-strip. Use the space below to show your work.

B. Use the same paper strip to show that six-eighths is equivalent to twelve-sixteenths.

C. Make a new paper strip folded into six-eighths. Use this paper strip to show that six-eighths is equivalent to three-fourths.

Two fractions are equivalent if …

Equivalence Using Chips

A. Use the chips on your table to show that three-fourths is equivalent to six-eighths. Shade in the circles below to match your work.

unit: 8 chips / unit: 4 chips

B. Use the chips to show that two-thirds, four-sixths, and eight-twelfths are equivalent.

unit: 12 chips / unit: 12 chips / unit: 12 chips

Two fractions are equivalent if …

Equivalence Using the Number Line

A. Use the number line below to show that is equivalent to .

B. Use the number line below to show that is equivalent to .

C. Use the number line below to show that is equivalent to .

Two fractions are equivalent if …

Equivalence Using Equal Sharing

Ms. Elwood brought 6 cakes to share evenly among her 9 students. How much of a cake can each student have?

Strategy A:

Strategy B:

Strategy C:

Two fractions are equivalent if …

Why?

Conjecture 1:

Conjecture 2:

Conjecture 3:

Equivalence Using Open Number Sentences

Day 2 – Fractions as Quotients and Equivalence page 15