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: 
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_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
problem_activity: Activity
Students solved equations of the form
\(x+p = q\)
and
\(px=q\)
in grade 6, but the equations only involved positive values. This activity bridges their understanding of a solution to an equation as a value that makes the equation true with their understanding of operations involving negative numbers from this unit. This activity builds on the work students have done in this lesson evaluating expressions at different values.
Monitor for students who:
take an arithmetic approach by substituting in values and evaluating. (Does
\(\text-2 \boldcdot (\text-4.5) = \text-9\)
?)
take an algebraic approach by writing an equivalent equation using an inverse operation (If
\(\text-2 \boldcdot x=\text-9\)
, then
\(x=\text-9 \div \text-2\)
.)
Digital
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to a value that makes it true by dragging the answer to the corresponding equation. Be prepared to explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Allow students 5 minutes quiet work time followed by whole class discussion.
The digital version has an applet that allows students to see how many correct answers they have at any time.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Check to make sure students matched the correct solution to the first equation and can explain their reasoning with an arithmetic or algebraic approach.
Supports accessibility for: Memory; Organization
Student Facing
Match each equation to its solution.
\(\frac12 x=\text-5\)
\(\text-2x=\text-9\)
\(\text-\frac12 x=\frac14\)
\(\text-2x=7\)
\(x+\text-2 = \text-6.5\)
\(\text-2+x=\frac12\)
\(x = \text-4.5\)
\(x = \text-\frac12\)
\(x = \text-10\)
\(x = 4.5\)
\(x = 2 \frac12\)
\(x=\text-3.5\)
Be prepared to explain your reasoning.
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
Select an equation for which there is a student who took an arithmetic approach and a student who took an algebraic approach. Ask students to share their reasoning for why a solution is correct. Sequence arithmetic approaches before algebraic approaches. An example of an arithmetic approach: “I know that -3.5 is the solution to
\(\text-2x=7\)
, because I know that
\(\text-2 \boldcdot (\text-3.5)=7\)
. An example of an algebraic approach: “If
\(\text-2x=7\)
, then I know that
\(x=7 \div \text-2\)
.) Record their work, side by side, for all to see. If there are no equations for which students took both approaches, present both approaches anyway. Tell students that either approach is valid, but that in the next unit they will see some more complicated equations for which one approach might be simpler than the other.
Representing, Conversing, Listening: MLR7 Compare and Connect.
Use this routine to support whole-class discussion. Ask students, “What is the same and what is different?” about how they matched the expressions. Connect strategies by showing the different ways operations are used in each approach (e.g., arithmetic method by substituting in values and evaluating; algebraic method by using an inverse operation). Use gestures, and color on the display to highlight these connections. This helps students use mathematical language as they reason about their strategies to evaluate equivalent equations.
Design Principle(s): Maximize meta-awareness; Support sense-making


aligns: no