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: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Problem 1
a.   Fill in the following blanks to make true statements. Use base ten blocks to help you.
1 thousand is the same as _______ hundreds.
1 hundred is the same as _______ tens.
1 ten is the same as _______ ones.
1 one is the same as _______ tenths.
b.   Below is an area model that represents 1 one. It is partitioned into tenths. Partition it to show what you would expect the next smallest unit to look like so that it continues the pattern in Part (a).
[IMG]
c.   Use what you notice in Part (a) and (b) to write a similar sentence that starts “1 tenth is the same as…”
Problem 2
The shaded part of this diagram represents 1 hundredth. We can write this as the fraction
$$\frac{1}{100}$$
or as the decimal
0.01.
[IMG]
Fill out the following table to represent each given number.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width: 100%;"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Diagram"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Unit Form"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Fraction Form"}]}, {"_attributes": {"style": "text-align: center;"}, "strong": [{"_value": "Decimal Form"}]}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {"_attributes": {"style": "text-align: center;"}, "_value": "7 hundredths"}, {}, {}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{32}{100}$$"}]}, {}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png"}}]}]}, {}, {}, {"_attributes": {"style": "text-align: center;"}, "_value": "0.85"}]}, {"td": [{"_attributes": {"style": "text-align: center;"}, "p": [{"img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png"}}]}]}, {}, {}, {}]}]}]}]}
Problem 3
a.   Explain why
$${{1\over10}={10\over100}}$$
. Draw a picture to illustrate your explanation.
b.   Explain why
$${0.20 = 0.2}$$
. Draw a picture to illustrate your explanation.
Problem 4
Jani and Kai are representing a decimal number. Here are the area models they drew:
{"table": [{"_attributes": {"align": "center", "class": ["table"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align: center;"}, "_value": "Jani"}, {"_attributes": {"style": "text-align: center;"}, "_value": "Kai"}]}, {"td": [{"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png"}}]}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "img": [{"_attributes": {"src": "https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png"}}]}]}]}]}]}]}
a.   What value do you think Jani and Kai are trying to model? How do you know?
b.   Draw pictures to show what Kai might have drawn for each area model in Anchor Task 2.


aligns: yes