Complete this statement, “Number sense is linked to a complete understanding of..”.
Problem solving.
Place-value.
Base-ten models.
Basic Facts.
What statement below would represent a child that has yet grasped the knowledge of recognizing groups of ten?
Counts out sixteen objects and can tell you how many by counting each piece.
Counts out sixteen and puts the 10 in one pile and 6 in another and tells you there are sixteen.
Counts out sixteen and makes two piles of eight and tells you there are sixteen.
Counts out sixteen and places 6 aside and tells you 10 and 6 are sixteen.
All the examples below are examples of proportional base-ten models EXCEPT:
Counters and cups.
Cubes.
Strips and squares.
Money.
What does the relational understanding of place value needs to begin with?
Counting by ones and saying and writing the numeral.
Counting by ones, making a model and saying and writing the numeral.
Counting by tens and ones and saying and writing the numeral.
Counting by tens and ones, making the model, saying and writing the numeral.
What would be a strong indication that students are ready to begin place-value grouping activities?
Students understand counting by ones.
Students have had time to experiment with showing amounts in groups of twos, fives and agree that ten is a useful-sized group to use.
Students have only worked with small items that can easily be bundled together.
Students are able to verbalize the amounts they are grouping.
Base ten riddles engage students in what type of mathematical demonstration?
Part-part-whole representation.
Commutative representation.
Equivalent representation.
Nonproportional representation.
All of the activities below would provide opportunities for students to connect the baseten concepts with the oral number names EXCEPT:
Using arrays to cover up rows and columns and ask students to identify the number name.
Lie out base-ten models and ask students to tell you how many tens and ones.
A chain of paper links is shown and students are asked to estimate how many tens and ones.
Students need to show with fingers how to construct a named number.
What is the major challenge for students when learning about three-digit numbers?
Students are not clear on reading a number with an internal zero in place.
A different process is used than how students learned with two-digit numbers.
Students are not competent with two-digit number names.
An instructional process that values quick recall and response.
Place-value mats provide a method for organizing base-ten materials. What would be the purpose of using two ten-frames in the ones place?
Show the left-to-right order of numbers.
Show how numbers are built.
Show that there is no need for regrouping.
Show that there is no need for repeated counting.
What mathematical representation would help students identify patterns and number relationships?
Blank number line.
Hundreds chart.
Place value chart.
10 x 10 Multiplication Array.
What is the valuable feature of what hundred charts and ten-frame cards demonstrate?
The meaning behind the individual digits.
The identity of the digit in the ones place and in the tens place.
The distance to the next multiple of ten.
The importance of place-value.
The multiplicative structure of a number would help students in acquiring skill in all of the following EXCEPT:
Writing numbers greater than 100.
Reading large numbers.
Knowing ten in any position means a single thing.
Generalizing structure of number system.
The ideas below would give students opportunities to see and make connections to numbers in the real world. The statements below identify examples that would engage students with large benchmark numbers EXCEPT:
Measurements and numbers discovered on a field trip.
Number of milk cartons sold in a week at an elementary school.
Number of seconds in a month.
Measurement of students’ height in second grade.
The mathematical language we use when introducing base-ten words is important to the development of the ideas. Identify the statement that consistently connects to the standard approach.
Sixty-nine.
Nine ones and 6 tens
6 tens and 9.
6 tens and 9 ones.
The statement below are all helpful when guiding students to conceptualize numbers with 4 or more digits EXCEPT;
Students should be able to generalize the idea that 10 in any one position of the number result in one single thing in the next bigger place.
Because these numbers are so large, teachers should just use the examples provided in the mathematics textbook.
Models of the unit cubes can still be used.
Students should be given the opportunity to work with hands-on, real-life examples of them.
What is the primary reason for delaying the use of nonproportional models when introducing place-value concepts?
Models do not physically represent 10 times larger than the one.
Models like abacus are hard to learn how to use.
Models like money provide more conceptual than procedural knowledge.
Models do not engage the students as much as the proportional models.
As students become more confident with the use of place value models they can represent them with a semi-concrete notations like square-line-dot. What number would be represented by 16 lines, 11 dots and 5 squares?
16115
5,171
671
32
Three section place-value mats can help students see the left to right order of the pieces. What statement below would correctly depict 705?
7 hundred blocks and 5 tens.
7 hundred blocks and 0 tens.
7 hundred blocks and 0 units.
7 hundred blocks and 5 units.
A calculator activity that is good assessment to see whether students really understand the value of digits is titled “Digit Change”. Students must change one number without putting in the new number. What place value would a student need to know in order to change 315 to 295?
Ones.
Tens.
Hundreds.
Tens and ones.
The statements below are true of patterns and relationships on a hundreds chart EXCEPT:
Count by tens going down the far-right hand column.
Starting at 11 and moving down diagonally you can find the same number in the ones and tens place.
Starting at the 10 and moving down diagonally the numbers increase by ten.
In a column the first number (tens digit) counts or goes up by ones as you move down.
Modern technology has made computation easier. Identify the true statement below
But mental computation strategies can be faster than using technology.
And recent studies have found that a very low percentage of adults use mental math computation in everyday life.
And mental computation contributes to diminished number sense.
So the ability to compute fluently without technology is no longer needed for most people.
All of the following provide an example of a method used for computation EXCEPT:
Standard algorithms.
Student-invented strategies.
Discourse modeling.
Computational estimation.
One of the statements below would NOT be considered a benefit of invented strategies.
They require one specific set of steps to use them, which makes them easier to memorize.
They help reduce the amount of needed re-teaching.
Students develop stronger number sense.
They are frequently more efficient than standard algorithms
Which of the following is a true statement about standard algorithms?
Students will frequently invent them on their own if they are given the time to experiment.
They cannot be taught in a way that would help students understand the meaning behind the steps.
In order to use them, students should be required to understand why they work and explain their steps
There are no differences between various cultures.
Complete the statement, “When creating a classroom environment appropriate for inventing strategies..”.
The teacher should immediately confirm that a student’s answer is correct, in order to build his/her confidence.
The teacher should attempt to move unsophisticated ideas to more sophisticated thinking through coaching and questioning.
The teacher should discourage student-to-student conversations in order to provide students with a quiet environment to think.
The teacher should encourage the use of naked numbers as a starting point.
Cultural differences are evident in algorithms. What reason below supports teaching formathematics?
Notational algorithms.
Customary algorithms.
Mental algorithms.
Invented algorithms.
The models listed below are used to support the development of invented strategies EXCEPT:
Jump strategy.
Split strategy
Take-away strategy
Shortcut strategy
An open number can be used effectively for thinking about addition and subtraction. All of the reasons below support the use of an open number line EXCEPT:
Is less flexible than a numbered line.
Eliminates confusion with hash marks and spaces.
Less prone to computational errors.
Helps with modeling student thinking.
The ten-structure of the number system is important to extend students thinking beyond counting. All of the activities below reference a strategy for calculation EXCEPT:
Using decade number.
Odd or even.
Up over 10.
Add on to get to 10.
All of the following could be examples of invented strategies for obtaining the sum of two-digit numbers EXCEPT:
Adding on tens and then ones (For example, to solve 24 + 35, think 24 + 30 = 54 and 5 more makes 59.)
Using nicer numbers to estimate (For example, to solve 24 + 47, think 24 is close to 25 and 47 is closer to 45 so 24 + 47 = 25 + 45 = 70.)
Moving some to make 10 (For example, to solve 24 + 35, move 6 from 35 to make 24 + 6 and then add 30 to the remaining 29.)
Adding tens and adding ones then combining (For example, to solve 24 + 35, think 20 + 30 = 50 and 4 + 5 = 9 so 50 + 9 = 59.)
Students who have learned this strategy for their “basic facts” can use it effectively with solving problems with multidigit numbers.
Shortcut strategy.
Think addition strategy.
Split strategy.
When a problem has a number that is a multiple of ___ or close to ___it is an example of a problem that you leave one number intact and subtract from it.
85 – 35
85 – 64
85 – 29
85 - 56
There are important things to remember when teaching the standard algorithm. Identify the statement that does not belong.
Good choice in some situations.
Require written record first.
Require concrete models first.
Explicit connections are made between concept and procedure.
The general approach for teaching the subtraction standard algorithm is the same as addition. What statement below would not be a problem when using the standard algorithm for addition?
Develop the written record.
Begin with models.
Trades made after the column in the left has been done.
Exercises with zeros.
The following statements are true regarding computational estimation EXCEPT:
Use the language of estimation- about, close, just about.
Focus on flexible methods.
Focus on answers.
Accept a range of estimates.
What strategy for computational estimation after adding or subtracting do you adjust to correct for digits or numbers that were ignored?
Front-end.
Rounding
Compatible numbers.
Over and under.
Complete the statement, “A mental computation strategy is a simple..”.
Left-handed method.
Invented strategy.
Standard algorithm.
One right way.
Often siblings and family members are pushing the use of the standard algorithm while students are learning invented strategies. What is the course of action for a teacher?
Insist on invented strategies.
Require students demonstrate both standard and invented strategies.
Expect them to be responsible for the explanation of why any strategy works.
Memorize the steps
All of the statements below represent the differences between invented strategies and standard algorithms EXCEPT:
A range of flexible options.
Left-handed rather than right-handed.
Number oriented rather than digit oriented.
Basis for mental computation and estimation.
The Common Core State Standards states that student should learn a variety of strategies. These strategies should be based on all of the following EXCEPT:
Place value.
Sophisticated thinking.
Properties of operations.
Prior to the standard algorithm.
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.
5 groups of 30 lines and 5 groups of 7 dots.
5 circles with 37 items in each.
37 + 37 + 37 + 37 + 37 + 37 + 37.
What invented strategy is represented by a student multiplying 58 x 6 by adding 58 + 58 to get 116 and then adding another 116 to get 232 and then adding another 116 to find the product of 348.
Partitioning.
Clusters.
Complete number.
Compensation.
What invented strategy is just like the standard algorithm except that students always begin with the largest values?
What compensation strategy works when you are multiplying with 5 or 50?
Partitioning the multiplier.
Array.
Half-then-double.
What statement below describes the cluster problem approach for multidigit multiplication?
Encourages the use of known facts and combinations.
Encourages the manipulation of only one of the factors.
Encourages the use of an open array.
Encourages the use of fair sharing.
This model uses and a structure that automatically organizes proportionate equal groups and offers a visual demonstration of the commutative and distributive properties.
Missing Factor.
Area.
Open array.
When developing the written record for multiplication computation it is helpful to encourage students to follow these suggestions EXCEPT:
Use sheets with base-ten columns.
Record partial products
Record the combined product on one line
Mark the subdivisions of the factors.
Division may be easier for students if they are familiar with the concepts. All of the statements below are related to division of whole numbers EXCEPT:
Partitioning
Fair sharing.
Compensating.
Repeated subtracting.
Cluster problems are an approach to developing the missing-factor strategy and capitalize on the inverse relationship between multiplication and division. All of equations below represent clusters that would help solve 381 divided by 72 EXCEPT:
81 x 70
10 x 72
5 x 70
4 x 72
Which of the following is a strategy that is more applicable for multiplying single digits than multidigits?
Compatible numbers
Doubling
Which is an example of the compensation strategy?
63 × 5 = 63 + 63 + 63 + 63 + 63 = 315
27 × 4 = 20 × 4 + 7 × 4 = 80 + 28 = 108
46 × 3 = 46 × 2 (double) + 46 = 92 + 46 = 138
27 × 4 is about 30 (27 + 3) × 4 = 120; then subtract out the extra 3 × 4, so 120 –12 = 108
Identify the statement that represents what might be voiced when using the missing-factor strategy.
When no more tens can be distributed a ten is traded for ten ones.
Seven goes into three hundred forty-five how many times?
What number times seven will be close to three hundred forty-five with less than seven remaining?
Split three hundred forty-five into 3 hundred, four tens and five ones.
Developing the standard algorithm for division teachers should used all of the following guides EXCEPT:
Partial quotients with a visual model.
Partition or fair share model.
Explicit trade method.
Area model.
An intuitive idea about long division with two digit divisors is to round up the divisor. All of examples below support this idea EXCEPT:
Think about sharing base-ten pieces.
Underestimate how many can be shared.
Pretend there are fewer sets to share than there really are
Multiples of 10 are easier to compare.
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 it more or less that 1000?
Is it between $400 and $700?
Is one of these right?
Is your estimate about how much?
What is the purpose of using a side bar chart in multidigit division?
Easier to come up with the actual answer.
Uses a doubling strategy for considering the reasonableness of an answer
Increases the mental computation needed to find the answer.
Uses the explicit trade notation.
What is the reason why mental calculations estimates are more complex?
They require a deep knowledge of how numbers work.
They require a solid knowledge of division procedures.
They require a deep knowledge of partitioning.
They require a solid knowledge of multiplication procedures.
A number line can be helpful with teaching this estimation strategy.
Front end.
Compatible
Rounding.
Mental computation.
