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: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_pos_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: Narrative
The purpose of this activity is for students to match different diagrams and expressions representing the same product. In the previous several lessons, students have studied different ways to find products of a whole number and a fraction using arithmetic properties such as the distributive property. Earlier in the unit they learned about the connection between fractions and division. They combine these skills as the expressions and diagrams they work with incorporate both the distributive property and the interpretation of a fraction as division (MP7). Students may match diagrams to expressions differently than the ways that are listed in the sample responses. Encourage students to match the expressions and diagrams in a way that makes sense to them, as long as they can accurately explain how the expression is represented in the diagram they chose.
MLR7 Compare and Connect.
Invite students to prepare a visual display that shows their thinking about their favorite diagram and expression. Encourage students to include details that will help others understand what they see, such as using different colors, arrows, labels, or notes. If time allows, invite students time to investigate each others’ work.
Advances: Representing
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Give students a subset of options to start with and introduce the remaining numbers once students have completed their initial set of matches.
Supports accessibility for: Organization, Social-Emotional Functioning
Launch
Groups of 2
“You are going to match expressions and diagrams that show different ways to find the value of the product
\(4 \times 5 \frac{2}{3}\)
.”
Activity
5–7 minutes: independent work time
2–3 minutes: partner discussion
Student Facing
Each diagram represents a way to calculate
\(4 \times 5 \frac{2}{3}\)
. Each expression is equivalent to
\(4 \times 5 \frac{2}{3}\)
. Match the diagrams and expressions. Show or explain your reasoning.
A
[IMG]
B
[IMG]
1.
\((4 \times 5) +  \left(4 \times \frac{2}{3}\right)\)
C
[IMG]
2.
\((4 \times 6) - \left(4 \times \frac{1}{3}\right)\)
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)
3.
\(4 \times \frac{17}{3}\)
D
[IMG]
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm} \\ \hspace{2.5cm}}\)
4.
\((4 \times 17) \div 3\)
Choose your favorite diagram and expression to find the value of
\(4 \times 5 \frac{2}{3}\)
. Explain why it is your favorite.
Student Response
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Activity Synthesis
Display the diagrams B and D.
“How are the diagrams the same? How are they different?” (They both have the same shaded area and the same divisions inside. The top one shows the length of the shaded rectangle. The bottom one does not though it has enough information to find the shaded area.)
Invite students to share their favorite ways to find the product.


aligns: no