PECT module 3

An understanding of which of the following mathematical concepts is most helpful when working with probabilities?

ratios and proportions

A Venn diagram would be most appropriate for visually representing which of the following problems?

What are the common multiples of 2, 3, and 5 that are less than 40?

A teacher wants to help students develop their understanding of the relative magnitude of numbers. Which of the following types of mathematics learning materials would be most effective for the teacher to use for this purpose?

number lines

Which of the following strategies is most appropriate for solving the problem?

working backward

To correctly use the ordinal numbers first through fifth with a group of five objects placed in a row, a young child first must be able to:

recognize that the last number counted is the number of objects in the group

A preschool child measures the length of a long rectangular block by lining up several smaller blocks along the length of the longer block. This demonstrates that the child has an understanding of which of the following measurement concepts?

unit iteration

With respect to mathematics instruction, a standardized development screening test would be most appropriate for helping a second-grade teacher:

identify whether any student is at risk of a possible learning problem in mathematics

A kindergarten teacher wants to promote students’ ability to interpret data. The teacher provides stickers of various colors and asks students to select the sticker that best matches the color of the shirts they are wearing. The students then place the stickers in columns based on color on a large sheet of paper. To meet the objective of the lesson, the most appropriate step for the teacher to take next would be to:

ask students to identify which columns have more stickers and which have fewer

A second-grade teacher is having students work on adding double-digit numbers. The teacher writes a problem on the board, asks students to estimate the answer and then asks them to explain how they arrived at their answers. As students listen to their peers’ explanations, some students are able to revise their answers correctly while others are not. Which of the following follow-up activities would be most appropriate?

working with students in small groups to help students at different ability levels construct their understanding of the concept of addition

Which of the following mathematics activities would be most appropriate for promoting preschool students’ skills in measurement?

sequencing three different events that occur in the daily classroom routine

A third-grade teacher is developing a criterion-reference test for a mathematics unit on multiplication. During the unit, students use arrays to solve multiplication problems involving one and two digit numbers. To produce a valid criterion-referenced test for this unit, the teacher must:

include test questions that allow students to solve multiplication problems using arrays as they did during the unit

A preschool teacher wants to promote children’s skills related to counting and comparing numbers. Which of the following activities is most appropriate to use for this purpose?

letting the class vote on which book the teacher should read next and then asking the class which book won based on the votes

A third-grade student is having difficulty solving word problems in mathematics. Which of the following strategies would be most helpful for the teacher to suggest the student use first?

restating the problem in his or her own words

A teacher provides mathematics instruction using manipulatives, worksheets, games, and class discussion. The primary bene fit of providing instruction in multiple formats is that it:

addresses a variety of learning styles

A teacher gives groups of students a number of triangles, squares, and semicircles and asks the students to combine these shapes to make as many different figures as they can. This activity will help build a foundation for students’ future development of which of the following skills?

determining the area of irregular shapes

During group time, a preschool teacher uses shapes made out of felt to create a circle-circle-square, circle-circle-square pattern. The teacher asks children which shape should come next to continue the pattern. Some of the children say a circle and some say a square. Which of the following teacher strategies will best help the children construct their own understanding of the concept?

having children say the pattern out loud as a group and again asking which shape should come next

A student incorrectly solves the multiplication problems. Based on this work, the best strategy would be to provide the student with additional instruction in:

working with carried digits

A third-grader teacher asks teams of students to develop a scientific way for determining what types of materials can become charged with static electricity when rubbed again another material. To produce scientifically valid results from their investigations, it is most important that student teams:

develop a system for recording how strong a static charge develops on each material

A second-grade class is beginning a unit on weather. Which of the following activities associated with this unit would be most effective for helping the students develop an understanding of the foundations of scientific inquiry?

the teacher sets up a simple weather station and has the class keep regular rainfall and temperature records

Which of the following provides the best inquiry based learning activity for a third-grade class studying rocks and minerals?

performing simple tests on a set of minerals and then using a key to identify them

To present the concept of the conservation of mass to children in a prekindergarten class, it would be most appropriate for the teacher to ask the children to:

roll out balls of clay into flat pancake shapes and then discuss the concepts of shape and weight

A teacher is planning an activity to introduce the concept of density to first graders. The teacher would like to get students interested in the topic by using a discrepant event that surprises them with a result they do not expect. Which of the following activities would be most effective for stimulating students’ interests in this topic?

after filling one glass with a saturated sal solution and one glass with tap water, the teacher asks students to predict what will happen when an egg is placed in each of the two glasses

A first-grader is planning a science unit on insects with the goal of motivating students to be good scientific observers of the natural world. The most effective way to achieve this goal would be to have the students:

make drawings of ants from memory to share with the class and then observe real ants and draw them again

A third grade teacher is planning a science unit on human body systems, a topic that ha quite a bit of specialized scientific terminology associated with it. In presenting information during the unit, it is most advisable for the teacher to:

use the appropriate scientific terminology

A fourth-grade teacher wants to integrate the arts into the science curriculum. Which of the following student activities would be most appropriate for this age group?

researching an animal’s habitat and creating a diorama

A teacher wants to introduce a kindergarten class to the concept of structure and function in living systems. Which of the following activities would provide the most appropriate introduction to the biological concept of structure and function for this age group?

comparing what different insects look like with how they move

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