few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Visualize relationships between two-dimensional and three-dimensional objects.

Prove theorems involving similarity.

Reason with shapes and their attributes.

Understand similarity in terms of similarity transformations.

Translate between the geometric description and the equation for a conic section.

Understand and apply the Pythagorean Theorem.

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Find arc lengths and areas of sectors of circles.

Explain volume formulas and use them to solve problems.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Apply geometric concepts in modeling situations.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Prove geometric theorems.

Make geometric constructions.

Classify two-dimensional figures into categories based on their properties.

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Solve real-world and mathematical problems involving area, surface area, and volume.
problem_activity: Problem 1
Your group should have a few copies of
Handout #2
and a set of cards from
Handout #1
.
Draw three cards and place them in the appropriate places on the Handout #2 form. This represents three conditions about a triangle. Once you’ve placed them on the form, do not change the order.
Determine if the set of conditions will make one unique triangle, more than one triangle, or no triangle.
If you can make one unique triangle, draw and label the triangle.
If more than one or no triangle can be made, be prepared to explain your reasoning.
Choose another three cards and repeat the activity.
Problem 2
Two triangles are described below. Determine if each description results in one unique triangle, more than one triangle, or no triangle. Explain your reasoning or draw images to support your conclusion.
a.   Triangle
$${EFG}$$
is an isosceles triangle with two angles measuring 35°. Side length
$${EG}$$
measures 10 cm.
b.   Triangle
$${{PQ}R}$$
is an isosceles triangle with
$${\angle P}$$
and
$${\angle Q}$$
measuring 22°. Side length
$${PQ}$$
measures 8 cm.


correct_option_index: 14