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 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: 
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_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
problem_activity: Activity
In this activity, students get a chance to practice solving equations with a single variable. The equations resemble the types of equations students see in the associated Algebra 1 lesson after they substitute for a variable. Students will work in pairs and each partner is responsible for answering the questions in either column A or column B. Although each row has two different problems, they share the same answer. Ensure that students work their problems out independently and collaborate with one another when they do not arrive to the same answers. Students construct viable arguments and critique the reasoning of others (MP3) when they resolve errors by critiquing their partner's work or explaining their reasoning.
Launch
Arrange students in groups of 2.
Student Facing
Solve each equation.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "row"}, {"_attributes": {"scope": "col"}, "_value": "column A"}, {"_attributes": {"scope": "col"}, "_value": "column B"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "1"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28834"}, "_value": "\\(4(2x+8)-10 = 14\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28861"}, "_value": "\\(4 + 2(\\text-3x+5)=20\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "2"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28897"}, "_value": "\\(3(x-4)+6 = 60\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28936"}, "_value": "\\(3(\\frac12x + 9)-5=55\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "3"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "28976"}, "_value": "\\(4(\\frac{x+3}{2})-5 = 10\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29019"}, "_value": "\\(7-2(6x+1)=\\text-49\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "4"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29065"}, "_value": "\\(2x+(5-3x) = 14\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29114"}, "_value": "\\(1=5x+10-4x\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "5"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29167"}, "_value": "\\(4x + 2(3-x)=16\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29213"}, "_value": "\\(x+2(x-4)+5=12\\)"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "6"}], "td": [{"p": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29263"}, "_value": "\\(2x - 2(3x-1) = 8\\)"}]}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29314"}, "_value": "\\(\\text-6x+2(4x+5)=7\\)"}]}]}]}]}]}
​​
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
The purpose of the discussion is to recall strategies for solving equations with one variable. Select students to share their solutions including their reasoning for the steps they take.
Some questions for discussion:
"When there is a variable inside parentheses, how did you approach the problem?" (I distributed the value multiplying the parentheses to remove the parentheses then solved the equation as usual.)
"How could you check that your answer works using the original equation?" (I could substitute the value for
\(x\)
into the original equation and determine if the equation is true.)


aligns: no