Study Guide

Elementary Education Multi-Content: Mathematics and ScienceSample Questions

Competency 0002Apply knowledge of relationships and algebraic thinking.

1. A student performs addition of the numbers a and b as follows:

a + b
a + (b + c) − c

Which of the following arithmetic strategies is the student implementing by introducing the number c into the expression as shown?

1. counting on
2. compensation
3. counting back
4. constant differences
Correct Response: B. This is the addition strategy of compensation. The expressions a + b and a + (b + c) − c are equivalent. The difference is that a is added to (b + c) first and then this sum is reduced by c. For example, 17 + 19 may be changed to 17 + 20 − 1 without affecting the sum.

Competency 0003Apply knowledge of geometry and measurement.

2. Fifth-grade students will explore volume by stacking small cubes inside of several different square prisms. Which of the following mathematical concepts would best prepare students to understand the relationship between the volume of the prism and the number of small cubes it contains?

1. describing measurements with units
2. using exponents to simplify repeated multiplication
3. substituting variables in equations
4. evaluating multiplication expressions
Correct Response: A. When the students completely fill the prism with smaller cubes, they can describe the volume of the prism by the number of small cubes within it. The volume of each individual cube becomes a unit of measurement. Students who are comfortable with the concept of measurement being iterations of a particular unit should be comfortable exploring volume in this activity.

Competency 0004Apply knowledge of data analysis, statistics, and probability.

3. Use the information below to answer the question that follows.

Choice Frequency
First Week 20
Second Week 30
Third Week 50
Fourth Week 100

A group of students then attempted to represent this information by creating the following pie chart.

A pie chart is shown with four sectors with the following angle measures: 10 degrees, 15 degrees, 25 degrees, and 50 degrees.

The students may fix the error in each angle measure by multiplying the values by which of the following amounts and then adjusting the size of each sector accordingly?

1. 1.5
2. 1.8
3. 3.0
4. 3.6
Correct Response: D. The frequency of each choice in the table and the angle of its corresponding sector in the pie chart follows a 2:1 ratio. Additionally, the sum of the angles for each sector is 100°, which could indicate a misconception with the magnitude of a circle's central angle. The circle will be completely covered, and each sector will be the proper size, when each angle shown is multiplied by 3.6.

Competency 0005Apply knowledge of physical science.

4. Which of the following student statements is an example of a misconception about physical science?

1. When a ball is at rest, there are no forces acting upon it.
2. Gravity continues to act on a dropped ball once it hits the ground.
3. In order to change the motion of a ball, a force needs to be applied to it.
4. A ball released by an astronaut on the moon will fall to the surface of the moon.
Correct Response: A. When a ball is a rest, this means that the forces acting on the ball are in equilibrium and not that there are no forces acting upon it. There will be a gravitational force, as well as a normal force that is pushing back perpendicular to the surface the ball is resting on, such as the ground. There may even be a frictional force or other balanced forces acting upon the ball in addition.

Competency 0006Apply knowledge of life science.

5. Fifth-grade students are using mealworms as part of a life science investigation about behaviors that help organisms maintain homeostasis. Students place 20 mealworms on a piece of paper in the center of a box, and half of the paper is dampened with water. The number of mealworms in each half of the box is recorded every minute for 10 minutes. This investigation addresses which of the following student hypotheses?

1. Mealworms prefer to inhabit a moist environment.
2. Mealworms use visual cues to respond to stimuli.
3. Mealworms learn to respond to environmental changes.
4. Mealworms show similar behaviors to earthworms.
Correct Response: A. A hypothesis is an educated guess that is used as the starting point for an investigation. The investigation must have a control and a test section. In this case, examining whether mealworms prefer a moist environment will rely on having the control dry side of the box and the tested wet side of the box. The way that the experiment is set up will allow the mealworms to move freely between the dry and wet sides of the box. By recording the position of the mealworms, the students can see what environment is preferred over time.

Competency 0007Apply knowledge of Earth and space science.

6. Which of the following examples represents an interaction between the biosphere and the atmosphere?

1. Carbon dioxide is produced as a result of the eruption of a volcano.
2. Remains of plants form coal after being subjected to heat and pressure over time.
3. Animals produce moisture as they undergo the process of respiration.
4. Warm air temperatures increase the rate of evaporation from bodies of water.
Correct Response: C. Many elements and compounds move between the biosphere and the atmosphere, with some of the reservoirs that move in this way being water, oxygen, and carbon dioxide. In particular, respiration produces water and carbon dioxide, which enter the atmosphere and continue in their respective cycles.

Multiple Competencies

Use the information below to answer the questions that follow.

A particular section of a field receives 4.7 K W H per M squared of sunlight a day. This energy is converted directly into sugars and plant biomass by the first trophic level. However, when those plants are consumed, only 10 percent of their energy will move into the next trophic level. Successively, organisms that consume them will only gain about 10 percent of the last trophic level's energy. This is known as the 10 percent Rule in ecology and is true with every increasing trophic level.

Competency 0007Apply knowledge of Earth and space science.

7. A teacher uses a thousands cube manipulative to represent the amount of energy received by the section of the field described. Which of the following representations best describes the amount of energy that will reach two trophic levels beyond the first trophic level?

1. Two ten-rods
2. One ten-rod
3. Two unit cubes
4. One unit cube
Correct Response: B. If a thousands cube represents the amount of energy entering the first trophic level, then 10%, or a hundreds flat, would be used to represent the next level. Of that energy, 10 percent, or 1 ten-rod, would represent the portion of the energy available for the third trophic level.

Competency 0006Apply knowledge of life science.

8. Which of the following types of organisms is most likely to have eaten their meal to gain 10 percent of the energy from the sun?

1. primary producers
2. detritivores
3. secondary consumers
4. herbivores