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Final edci 350 Shepard
Terms in this set (75)
The front end estimation strategy involves changing the number(s) to one(s) that would make the problem easier to compute mentally i.e. 413 x 24 use 400 x 25.
Teachers should never say "0" is a placeholder in multi-digit multiplication because it gives students the impression that zero has no numerical value
Third graders are expected to interpret the product of 5 x 7 as the total number of objects in 5 groups of 7 objects each.
In division, both the dividend and divisor can be decomposed to find the correct quotient
Flexible methods of computation in multiplication and divisiom involve decomposing and composing numbers in a variety of ways.
In multiplication, there is a direct relationship between the area of any given rectangle and the product of its dimensions.
In division, the divisor can be subtracted from the dividend in groups of any amount
Effective teaching single digit multiplication or division does not require teachers to teach for conceptual understanding.
In equal group structured problems, when either group size or number of groups is unknown the problem is division
The rounding estimation strategy focuses on the leading or left most digit in number i.e. 480 x 7 becomes 400 x 7.
Place value and the properties of operations are fun in the early grades but do not support the learning of a variety of computational strategies in multiplication.
Fifth graders are expected to fluently multiply multi-digit whole numbers and find whole number quotients with up to four-digit dividends and two-digit divisors
Representing a product of two factors may depend on the methods student experienced. What representation of 37 x 5 below would indicate that the student had worked with base-ten?
an array with 5 x 30 and 5 x 7
Identify the statement that represents what might be voiced when using the missing-factor strategy for 98 divided by 7.
what number times seven will be close to 98?
One strategy for teaching computational estimation is to ask for information, but no answer. Which statement below would be an example of NOT gathering information?
Is one of these right?
Which problem is an example of the equal groups, measurement structure?
Ed saved $24 total, and he saved $6 each month. For how many months had he been saving?
Which problem is an example of the comparison, product unknown (multiplication) structure?
This month, Khalid saved 8 times as much as last month. Last month, he saved $3. How much did Khalid save this month?
Which of the following statements is not aligned to teachers supporting children's conceptual understanding of division involving zero?
"Just memorize that you can't divide by 0"
Despite the fact that many learners in the past learned basic facts from memorization, there is strong evidence that this may not be the most effective strategy for all of the following reasons EXCEPT:
Students are motivated when they are assessed with timed tests
Supporting older students who still struggle with basic facts can be done through the following steps EXCEPT:
Drill to strengthen memory and retrieval capabilities
The statements below would assist students in thinking about how to solve 42= 7 EXCEPT:
7 + 7 + 7 + 7 + 7 + 7 + 7
The following statements below are effective for teaching the basic facts EXCEPT:
practice in longer time frames
Which of the following students is mathematically correct in her view division?
Tabitha: "Two hundred sixteen divided by three is 72, because 210 divided by three is 70 and 6 divided by three is 2, so I just added those two quotients together"
When developing the standard algorithm for division, teachers should
Utilize the process of recording explicit trades because it is more mathematically meaningful than the more common "bringing down"
When developing a written record for modeling division it is important to:
use place value columns to help ensure that quotients are accurate
Brittany solved 16 x 12 this way: 16 x 12 =16(10 + 2) = 160 + 32 = 192. What property is illustrated by her work?
The following personifies which interpretation of remainders: Rio's soccer league for children had thirty-seven children try out for three teams. If 11 players are allowed on each team, how many players will not be on a team?
leftover- the remainder itself is the appropriate answer
Which interpretation of remainders is personified in the question that follows: Sarah has 6 nephews. For Christmas, she plans to spend the same amount on a gift for each nephew. If she spends $81 total, how much will she spend for each gift?
exact- the problem requires an exact quotient in the form of a decimal
If Taylee thinks of 455 x 8 as being more than 3200 but less than 4000 because 400 x 8 is 3200 the student is:
using front end estimation to estimate the product
When teaching basic facts, your text recommends that teachers
(all are correct)
-ask students to self monitor
-focus on self-improvement
-limit practice to short time segments
Which structure of multiplication is personified in the following problem: Ashley has four bags of apples. There are six apples in each bag. How many apples does Ashley have altogether?
When teaching the basic facts teachers should...
work on multiplication facts over time
Which structure of division is personified in the following question: Danielle, Caitlin, and Abby shared 39 Barbie dolls. How many Barbie Dolls did each person get?
In an effort to increase her third grade students' conceptual understanding of division, Lily should:
(all are correct)
-begin teaching division with concrete or pictorial models
-create logical links between mult & division
-utilize estimation as means of solving problems, checking answers, and/or detecting errors
Which of the following should Hailey, a 3rd grade teacher, avoid when teaching multiplication and/or division?
use public comparisons of mastery of facts
Which of the following future teachers is correct in explaining shortcomings of using timed tests?
(all are correct)
-nicole, who thinks timed tests do not assess the four elements of fluency
-stephanie, who thinks timed tests negatively affect students' number sense and recall of facts
-amanda, who says timed tests take up time that could be used in more meaningful learning experiences
When multiplying mixed numbers by fractions you will always get a product that is larger than your original mixed number.
Which subtraction structure below is epitomized in the following scenario: Tayle wanted to go on a ice cream binge for her birthday while watching netflix. Her goal was to eat 2 quarts of ice cream by the end of the day. If she ate 1/2 quart of ice cream for breakfast, how much more ice cream does she have to eat to meet her goal?
this is a subtraction problem. more specifically, it models the part-part whole/completion/additive/take apart structure
Which of the following creates a fraction in any given figure?
A figures whose parts have the same size but different shape
Which of the following standards are required for fifth grade students?
(all are correct)
-Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. -interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, create a story context for (1/3) divided by 4 and use a visual fraction model to show the quotient. - interpret divisions of a whole number by a unit fraction, and compute such quotients. for example, create a story context for 4 divided by (1/5) and use visual fraction model to show the quotients
The division problem 1/2 divided by 3 can be interpreted as
one-half is what part of three?
When comparing fractions....
If the numerators are the same, the fraction with the largest equal sized-pieces is the larger fraction.
One of Kassidy's third grade students thinks that one-fifth of a whole is less than one-tenth of the same whole. What could she do to help the student address this common misconception?
(all of the above) -Use context and explain how the context relates to comparing those fractions - use visuals including fraction strips, or circles to visualize the approximate size of each fraction - teach estimation and benchmark strategies fro comparing fractions
A student in Lily's fourth grade classroom computed the following: 5 1/8 - 2 3/8 = 3 8/8 or 4. Which of the following is an appropriate next course of action?
Show the student that/he she is incorrect. Have the student use equal additions and add 5/8 to both fractions to obtain the correct answer and see that his answer is incorrect.
How many sets of 3/4 can be made from 2 1/2?
Three full sets of 3/4 and 1/3 of another set of 3/4, so 3 1/3 sets
If three acres of land are shared among five children, how many acres will each child get?
Each child will receive three-fifths of an acre.
Which of the following is considered a fraction construct?
(All are correct) - ratio: for example, the fraction 3/4 could represent three out of every four girls at the school participating in extra-curricular activities. Measurement: identifying a length, then using that length as a measurement unit to determine the length of an object. & Operator: this "construct" builds on the concept of seeing a fraction as a multiple of a unit fraction.
Iterating, counting fraction parts, helps students understand the relationship between the parts and the whole and understand the fraction as a number.
Which of the following descirbes the type of contextual problem written here: Hailey has an exercise regimen that totals three miles. So far, she has run 1 1/4 miles. She plans to speed walk for half of her remaining regiment. What fraction of her exercise regimen is speed walking?
If you divide two fractions that are less than one (1), it is possible that the resulting quotient could be two (2).
Research-based recommendations for teaching fractions include:
(All are correct) -providing a variety of models and context to represent fractions. - linking fractions to key benchmarks and encouraging estimation. - emphasizing that fractions are numbers
Abby provides her students with the following subtraction problem: 1 1/4- 3/4Caitlin, a student in the class, solves the problem by using fraction strips. She starts with a model of 1 1/4 and physically removes 3/4 from the 1 1/4. She says her answer is 1/2. Which visual model for subtraction did Caitlin demonstrate?
She modeled the take away/separate structure for subtraction.
Nicole's Boutique typically stocks 15 styles of peacoats during the Fall season. In the winter she stocks five-thirds of what she stocks in the Fall. How many styles of peacoats does she stock in the winter?
She stocks twenty-five styles in the winter.
Unifex cubes can be used to model how mixed numbers can be decomposed into fractions greater than one.
If 28 counters are a whole set, how many counters are in 11/7 (eleven-sevenths) of a set?
According to your textbook, one of the most significant ideas for students to develop about fractions is the sense that fractions are quantities that have values.
When teaching fractions teachers should
(All are correct) - give greater emphasis on the meaning of fractions rather than role procedures for manipulating them. - spend a significant amount of time understanding equivalence through concrete and symbolic representations. - provide a variety of models and contexts to represent fractions
It is important for students to recognize that, regardless of the whole, 1/2 is always bigger than 1/3
The process of sectioning a shape into equal-sized parts is called
Danielle believes that there are fractions between 3/5 (three-fifths) and 4/5 (four-fifths). In fact, she says 3/4 is one of those fractions. Ashley disagrees and states that no fractions exist between the two given fractions. Who is correct?
Danielle is correct in fact there are an infinite number of fractions between three-fifths and four-fifths and 3/4 is one of those fractions.
Which of the following "big ideas" should Amanda, a third grade teacher, consider when teaching fractions
(All are correct) - students need a conceptual understanding of equivalent fractions, - students must experiences fractions across many constructs, including part of whole, ratio, and division. - students need many experiences estimating with fractions
If Maranda has 24 counters that represent six-fourths of a set, how many counters are in one whole set?
Sixteen counters represent one whole set.
Any given fraction can be interpreted as a unit fraction or the sum of unit fractions if the numerator and/or denominator is greater than zero.
Complete the statement, "Developing the algorithm for adding and subtracting fractions should..."
Be done side by side with visuals and situations.
While working at Pear Inc, Taylee noticed that the price the company sells its EYE-phones for is 7/3 of the price it takes them to make the phone. If the phone sells for $1260 how much does it cost the company to create the phone?
While co-teaching in her third grade classroom, Rio overhears a student say, "The only way to add or subtract fractions is to find common denominators." Is this statement true?
No. Finding common denominators is the most popular way to add or subtract fractions but it is not the only way. Number lines can be used to solve addition and subtraction problems without finding common denominators.
(All are correct)-are representations for the same number or quantity. - can be used to assist students in adding, subtracting, or dividing fractions with unlike denominators. - can be modeled using fraction strips, cuisinaire rods, or drawing
Monica's plans was to serve 8 1/4 pounds of crawfish for her friends and family from Wisconsin when they visit for her Spring graduation. If each person, were to receive 3/4 pounds of crawfish, how many people could be served?
Which of the following students best described the meaning of 2 1/2 x 1 1/4?
Tabitha who stated, it can be interpreted as: two full groups of one and one-fourth plus an additional half-group of one and one- fourth.
Which of the following is among the four common errors students make in working with number lines?
(All are correct) - students count on the tick marks rather than the spaces between the marks. - students use incorrect notation on the number line. - students change the unit (whole) on the number line
One of the most common errors Amandas students make when adding fractions is adding the numerators for the numerators answer and denominator for denominators answer. What should she do to correct a student who computes 3/5 + 1/3 = 4/8
Begin by showing him why his answer is incorrect by asking him to demonstrate the problem using physical models (rods, fraction strips, number lines, balance)
In addition, subtraction, and division of fractions you can use a common denominator algorithm to find the correct answer.
According to your textbook, the term improper fraction is used to describe fractions greater than one. Identify the statement that is true about the term improper fraction.
Should be introduced to students in a relevant context.
When changing mixed numbers to fractions greater than one (and vice versa), it is important to use physical models (like unifex cubes) so that students can make sense of the relationship between the two representations.
Which of the following statements is always true regarding fractions?
A fraction a/b can be modeled using equal sized-segments modeled on a number line (assuming a or b are non-zero whole numbers)
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