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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
problem_activity: Narrative
The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression
\(4\times6\)
. Feel free to adjust this expression to better fit the number of students in your class.
Launch
Groups of 2
Display
\(4\times6\)
“Work together as a class to use your bodies to create an array for this multiplication expression.”
If the number of students does not exactly match the product, ask extra students to monitor the array and be prepared to explain where they see parts of the expression in the array.
3–5 minutes: whole-class work time
Activity
“Work with your partner to draw an array for each multiplication expression. Be ready to share connections you notice between the multiplication expressions and arrays.”
2–3 minutes: partner work time
Student Facing
Draw an array for each multiplication expression. Be prepared to share your reasoning.
\(2\times3\)
\(5\times2\)
\(4\times4\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students draw equal groups that are not arrays, consider asking:
“How did you use the expression to create your drawing?”
“How could we rearrange your drawing into an array?”
Activity Synthesis
Share an array or two for each expression.
“What connections did you and your partner see between the multiplication expressions and arrays?” (The factors tell us how many things are in each row and column. For
\(2\times3\)
, we drew an array with 2 columns that have 3 things in each column. For
\(2\times3\)
, we drew an array with 2 rows that have 3 things in each row.)


aligns: no