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:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
problem_activity: Narrative
This optional activity gives students additional opportunities to compare multi-digit numbers by reasoning about the value of the digits in different places. It also prompts students to generalize the relative size of two numbers based on their understanding of place value. Students practice constructing logical arguments (MP3) as they explain whether it is possible for
\(4 \underline{\phantom{5}},\!300\)
to be less than
\(3 \underline{\phantom{5}},\!400\)
, or for
\( \underline{\phantom{5}}4,\!300\)
to be less than
\( \underline{\phantom{5}}3,\!400\)
.
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group of 2 needs a set of cards from the previous activity.
Launch
Groups of 2
Give each group a card with a digit between 0 and 9 for each group
Activity
“Use the digit on the card to complete the comparison statements in the first problem and decide if they are true.”
4–5 minutes: group work time
Pause to collect responses from all the groups.
“Is the first comparison statement true for all digits?” (Yes, because if the digits are the same, we can just compare 999 to 500.)
Repeat the question with all statements. Record responses in a chart such as shown:
{"table": [{"_attributes": {"border": "1", "class": ["c-table-spread"]}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "statement"}, {"_attributes": {"scope": "col"}, "_value": "true"}, {"_attributes": {"scope": "col"}, "_value": "false"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\( \\underline{\\phantom{00}} \\ , 999 > \\underline{\\phantom{00}} \\ , 500\\)"}]}, {"_value": "all digits"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(15,2 \\underline{\\phantom{00}}0 > 15, \\underline{\\phantom{00}}02\\)"}]}, {"_value": "0, 1, 2"}, {"br": [{}], "_values": ["3, 4, 5, 6,", "7, 8, 9"]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(4 \\underline{\\phantom{00}},700 < 7 \\underline{\\phantom{00}} ,400 \\)"}]}, {"_value": "all digits"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(1 \\underline{\\phantom{00}}5,000 > 5 \\underline{\\phantom{00}}1,000\\)"}]}, {}, {"_value": "all digits"}]}]}]}]}
“Why are the statements in parts a and c true no matter what digit is used?” (Sample response:
In part a, both numbers are missing the first digit, in the thousands place. Since the missing digit is the same, we’re comparing the hundreds, and 999 is always greater than 500.
In part c, the missing digit is in the thousands place of both numbers, but the digits in the ten-thousands place need to be compared first, and 4 ten-thousand is always less than 7 ten-thousand.)
“Why is the statement in part d false no matter what digit is used?” (Ten-thousand is never greater than 50 thousand.)
“Take a few quiet minutes to work on the last two problems independently.”
5 minutes: independent work time
Student Facing
Each of the following pairs of numbers is missing the same digit but in different places.
Your teacher will assign a digit to you. Use it as the missing digit and decide if each comparison statement is true.
\(\large \boxed{\phantom{0}} \ , \boxed{9} \ \boxed{9} \ \boxed{9} > \boxed{\phantom{0}} \ , \boxed{5} \ \boxed{0} \ \boxed{0}\)
\(\large \boxed{1} \ \boxed{5} \ , \boxed{2} \ \boxed{\phantom{0}} \ \boxed{0} > \boxed{1} \ \boxed{5} \ , \boxed{\phantom{0}} \ \boxed{0} \ \boxed{2}\)
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{7} \ \boxed{0} \ \boxed{0} < \boxed{7} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
\(\large \boxed{1} \ \boxed{\phantom{0}} \ \boxed{5} \ , \boxed{0} \ \boxed{0} \ \boxed{0} > \boxed{5} \ \boxed{\phantom{0}} \ \boxed{1} \ , \boxed{0} \ \boxed{0} \ \boxed{0}\)
Here are two numbers, each with the same missing digit.
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{3} \ \boxed{0} \ \boxed{0} \qquad \qquad \boxed{3} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
Choose a digit to complete the numbers and show where they would be on the number line.
[IMG]
Is it possible to fill in the two blanks with the same digit to make each statement true? If you think so, give at least one example of what the digits could be. If not, explain why it is not possible.
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{3} \ \boxed{0} \ \boxed{0}\)
is less than
\(\large {\boxed{3}} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
.
\(\large \boxed{\phantom{0}} \ \boxed{4} \ , \boxed{3} \ \boxed{0} \ \boxed{0}\)
is less than
\(\large \boxed{\phantom{0}} \ \boxed{3} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
.
Student Response
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Activity Synthesis
Select students to share their responses to the last two problems.
Highlight explanations that make it clear that:
\(4 \underline{\phantom{5}},\!300\)
will always be greater than
\(3 \underline{\phantom{5}},\!400\)
because 4 ten-thousand is always greater than 3 ten-thousands.
\( \underline{\phantom{5}}4,\!300\)
will always be greater than
\( \underline{\phantom{5}}3,\!400\)
because, given the first digit is the same, the digits to compare are the thousands, and 4 thousands is always greater than 3 thousands.


aligns: no