few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

Answer: 
Yes. This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
problem_activity: Narrative
The purpose of this activity is for students to apply what they have learned in this section to compare a number to the product of that number with a fraction. There are two cases where the fraction has a value of 1. Students may identify that the value of the fraction is 1 and use what they know about multiplying a number by 1. They may also use their knowledge of how to multiply fractions and the calculations for these products have been made simpler so that students can find the product to make the comparison. For the other problems, the numbers are sufficiently complex that the most efficient way to compare is to think about the size of the factors.
MLR1 Stronger and Clearer Each Time.
Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to whether the expressions are
\(<\)
,
\(>\)
, or
\(=\)
. Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.
Advances: Writing, Speaking, Listening
Launch
Groups of 2
Activity
1–2 minutes: quiet think time
10–12 minutes: partner work time
For the expressions
\(\frac{1}{4} \times \frac{5}{5}\)
and
\(\frac{10}{10} \times \frac{1}{2}\)
monitor for students who calculate the products and for students who reason about the size of the factors.
Student Facing
Write
\(<\)
,
\(>\)
, or
\(=\)
in each blank to make true statements.
Choose one problem and explain or show your reasoning.
\(567 \, \underline{\hspace{0.7cm}} \,345 \times 567\)
\(\frac{4}{5} \times 851 \, \underline{\hspace{0.7cm}} \, 851\)
\(\frac{1}{4} \, \underline{\hspace{0.7cm}} \, \frac{5}{5} \times \frac{1}{4}\)
\(\frac{103}{104} \, \underline{\hspace{0.7cm}} \, \frac{103}{104} \times \frac{103}{104}\)
\(\frac{99}{8} \times \frac{23}{22} \, \underline{\hspace{0.7cm}} \, \frac{99}{8}\)
\(\frac{10}{10} \times \frac{1}{2} \, \underline{\hspace{0.7cm}} \, \frac{1}{2}\)
\(\frac{100}{7} \times \frac{9}{13} \, \underline{\hspace{0.7cm}} \, \frac{9}{13}\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share their solution for comparing
\(\frac{10}{10} \times \frac{1}{2}\)
and
\(\frac{1}{2}\)
.
“How do you know that
\(\frac{10}{20} = \frac{1}{2}\)
?” (If you cut the half into 10 equal pieces then you get 10 pieces and there are 20 in the whole.)
“Can you use the equation
\(\frac{10}{10} = 1\)
to see that
\(\frac{10}{10} \times \frac{1}{2} = \frac{1}{2}\)
?” (Yes, because 1 times any number is that same number.)
Invite students to share their solution for comparing
\(\frac{103}{104}\)
and
\(\frac{103}{104} \times \frac{103}{104}\)
.
“Did you find the product to compare?” (No, the numbers are big so it would have taken a long time.)
“What did you do to compare the numbers?” (I know that
\(\frac{103}{104}\)
is less than 1, it’s
\(1 - \frac{1}{104}\)
. So when I multiply it by any number I get less than that number.)


aligns: no