MTTC Test (Lower Elementary Test #119)
1. A kindergarten teacher observes as a small institution of students practice evaluating
numbers and portions using manipulatives. Each student has four counters. One pupil's
counters are spaced farther apart than the alternative college students' counters, and numerous
contributors of the organization claim that scholar has greater counters than absolutely
everyone else. The instructor can build on the students' information of counting and cardinality
by using:
A. Encouraging the only student to count their counters for the institution.
B. Identifying the mistake and moving the one student's counters closer together.
C. Asking probing questions on the total range of counters every pupil has.
D. Prompting the institution to combine their counters and matter how many they have in all. -
ANS-A. Having one pupil count number their own set of counters aloud does not deal with the
misconception that the range of counters in a set depends on how they are arranged.
B. This way of addressing the misconception does no longer always construct upon the
students' expertise because the instructor did now not take a look at whether or not they
grasped the explanation or offer them with possibilities to provide an explanation for of their very
own phrases why the overall range of items in each group is the same.
C. CORRECT. By asking probing questions on the whole range of counters each pupil has, the
trainer can assist students move beyond a naïve idea that bigger equals more and deepen their
conceptual knowledge of counting and cardinality.
D. The affordances created by using combining the counters right into a large group do no
longer offer those college students more considerable insights into information counting and
cardinality standards than the affordances created by means of the use of smaller corporations
of counters.
10. During a lesson on subtraction inside 20, first-grade college students engage with a series
of phrase problems about lost gadgets (e.G., books, toys, mittens). Some students have trouble
fixing the subtraction troubles with out drawing out the whole situation. The teacher can aid
those college students as they consider subtraction via:
A. Encouraging the scholars to try a matter-lower back or a matter-up approach.
B. Explaining the way to use context to determine which operation to use.
,C. Reminding the scholars of their earlier learning regarding operations.
D. Explaining how addition and subtraction are associated operations. - ANS-A. CORRECT.
Students who continuously resolve subtraction troubles by drawing (i.E., through growing strains
or snap shots to symbolize items after which crossing them out) should be endorsed to exercise
other subtraction techniques, such as counting-returned or counting-up, to promote their
conceptual and procedural expertise.
B. The college students demonstrate that they understand to use subtraction, so an explanation
approximately figuring out an operation from a situational context isn't vital.
C. This response does now not specifically target college students' established need to practice
subtraction techniques that do not involve drawing them out.
D. An explanation of ways subtraction and addition are associated operations (e.G., by means
of explaining how the equations a − c = b and a + b = c are associated) does no longer directly
guide the students to apply subtraction strategies that do not require drawing.
Eleven. First-grade college students play with tiles. One desk institution counts their tiles and
unearths there are 24. The teacher asks the scholars if they could institution the tiles to be able
to identify the entire variety easily. A pupil creates the subsequent representation:
A diagram of an association of 24 squares is shown. The squares are located in rows. There are
10 squares in every of the first two rows and 4 squares within the 1/3 row.
Presenting this representation to the elegance demonstrates the usage of manipulatives to:
A. Critique the reasoning of others.
B. Guide reasoning with evidence.
C. Create a foundation for the concept of grouping.
D. Expand expertise of the base-ten gadget. - ANS-A. Opportunities for the magnificence to
interact inside the positive grievance of a scholar's reasoning, together with via collaborating in
a discussion about the student's idea processes or suggesting viable refinements to their
illustration, have no longer taken location at this factor inside the learning activity.
B. The scholar's reasons for grouping the tiles as shown have now not yet been shared with the
magnificence.
C. The ones unit is the most effective unit represented inside the representation (i.E., each tile
represents 1), and the basis of grouping, wherein a set of 10 ones may be interchanged with a
unmarried unit of ten, is not illustrated right here.
,D. CORRECT. The pupil arranged their illustration for clean counting by means of forming rows
of 10 and one row of 4, and presenting this to the magnificence facilitates them increase their
knowledge of the base-ten machine.
12. First-grade students explore representations of two-digit numbers the use of base-ten
blocks. The instructor asks one scholar to expose the quantity 33. The scholar provides the
subsequent association.
The variety 33 is proven represented with base-ten blocks. There are three ten-rods and three
unit squares in this diagram.
When asked to give an explanation for their solution, the scholar says, "I understand I want 3 of
both due to the fact that it's 3 and 3." Which of the following questions should the trainer ask to
facilitate a clearer information of composing numbers extra than 10?
A. "How would you provide an explanation for the distinction among a rod and a block?"
B. "How would you display a variety of like forty four with rods and blocks?"
C. "How can you use tally marks to represent the quantity 33?"
D. "How are you able to give an explanation for the function of three in 333?" - ANS-A.
CORRECT. This question allows to make clear whether or not the pupil translates rods and
blocks to symbolize one-of-a-kind positions in the variety (i.E., the left 3 manner the range of
rods and the proper three means the number of blocks) or exclusive devices (i.E., the left 3
means 30, which is represented by means of 3 rods, and the right three method 3, which is
represented by means of three blocks).
B. The scholar could possibly answer this query with the aid of announcing, "I recognise I want
4 of both in view that it is four and four," which would not offer any deeper insight into the
scholar's questioning than the original answer.
C. The student demonstrates as a minimum a partial expertise of the way to represent 33 with
base-ten blocks, and the instructor have to try to construct upon the scholar's response in
preference to transfer to a distinctive illustration—specially whilst the opportunity representation
does not exhibit location-cost principles effectively.
D. Expanding the number of location price positions is unlikely to assist the scholar explain what
fee every digit of 3 represents.
14. A third-grade teacher asks students how they could determine which fraction is more when
the fractions have the same numerator and a special denominator, like the fractions 232 thirds
and 262 sixths, initiating the following conversation:
, Student A: If you rating dreams out of 3 tries in soccer, it is higher than out of six. So 232 thirds
is more than 262 sixths.
Student B: But you still only scored two desires.
Student A: Yeah, however you scored extra of the desires you tried.
Which of the subsequent interpretations exceptional compares each students' reasons?
A. Student A explains that a fragment is greater if the numerator is closer to the denominator,
even as Student B interprets simplest the denominator.
B. Student A compares the fractions the usage of a not unusual wide variety of tries, at the
same time as Student B compares handiest the number of goals scored.
C. Student A makes use of equivalent fractions to examine magnitudes, wh - ANS-A. Student B
does now not do not forget the denominator after they interpret the fractions.
B. Student A does no longer try and examine the 2 fractions via representing them with a
commonplace denominator.
C. Student A does not use the concept of equal fractions within the discussion.
D. CORRECT. Student A refers to the entire for each fraction while they say "3 tries" and "out of
six," and Student B handiest compares the numerators while they say "handiest scored
desires."
15. After a lesson on the progression of fractions from 0 to one the usage of fourths, a trainer
presents this problem to the elegance.
A question is shown. It reads, "What is the unknown cost within the bottom variety line?"Below
this question, a diagram of 3 range traces is proven. The first wide variety line displays the
numbers 0, one-fourth, two-fourths, 3-fourths, 1, and one and one-fourth.The second variety line
suggests 0, one-third, -thirds, 1, and one and one-1/3.The 1/3 number line indicates zero, 1 and
a question mark. The first tick mark is classified 0, the 5th tick mark is categorized 1, and the
sixth tick mark is classified with a question mark.
One pupil responds, "The query mark is after the 1, so the answer is 1 12and 1 half of".
Which of the following teacher responses could excellent prompt a discussion about unit
fractions and generation?
A. "Which styles do you notice among zero and 1 in the first two range lines?"
B. - ANS-A. CORRECT. This question encourages the student to make connections between
the number of tick marks among zero and 1 and the denominators of the fractions on the variety
line.
