BP Pak final
Select all you think are the roles of the constructivist teacher:
1. Asking questions that would require students to explain and justify: why, what does that tell you? or why not? 2. Focusing on children's thinking rather than on their writing correct answers. 3. Encouraging children to discuss among themselves rather than concentrate on getting right answers and correcting wrong answers.
Mark all that are basic facts.
14-8=6 6*0=0 3+9=12
Many beginning teachers believe that children will automatically memorize basic facts if they just get enough practice. One very effective strategy to help children learn basic facts is the three-step approach. The first step is [ ] . The second step is [ ] . The third step is[].
Answer 1: Understanding the meaning of the operations Answer 2:Using thinking strategies to retrieve facts. Answer 3:Using consolidating activities for drill and practice.
What do we call our system? This ]is the number of objects use in the grouping process. Our system is a [ ] system. Wherever we have 10 or more objects, they may be regrouped to make one group of the next larger place value. there is n one numeral for ten, rather, the number 10 is expressed as 1 ten and 0 ones, or 10. There are ten digits in the [ ] system: 0 through 9.
Base ten system
Kindergarten Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the [ ] of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. Fourth grade KCC 4: Understand the relationship between numbers and quantities; connect counting to [ ].
Cardinality
Megan has 3 stickers. Randy has 8 stickers. How many more stickers does Randy have than Megan? Which structure of addition and subtraction could explain this problem the most?
Compare- difference unknown
True or False:The estimation is not necessarily a legitimate mathematical tool
False
This strategy involves beginning with one addend and counting on the number of the second addend. For example, to solve the problem 6+3, ah child could start with 6 and count forward three times, saying seven, eight, nine.
Counting on
Mark all reasons that children should explore different algorithms.
Different algorithms provide variety in the math class. Different algorithms may help children develop more flexible mathematical thinking and number sense. Awareness of different algorithms demonstrates the fact that algorithms are inventions and can change Different algorithms may serve reinforcement, enrichment, and remedial objectives
[ ] refers to the process in which children use concrete materials to exactly represent the problem as it is written.
Direct modeling
T/F: The belief that mathematics needs to be meaningful and the idea that children construct their own math knowledge does rule out the need for practice.
False
T/F: The number line is not a difficult model for children to understand and should be the first model to represent an operation.
False
What do we call this transitional step below when solving an addition problem, 28+34? 2 tens and 8 ones + 3 tens and 4 ones ------------------------------------ 5 tens and 12 ones or 6 tens and 2 ones or 62 This is called [ ]
Expanded notation
T/F: Children will replace 10 unit blocks with a "rod" to represent a two-digit number, a place-value mat (with headings) should be used rather than an organization mat (without column headings).
F
T/F: The fact that two objects that are the same may have different values is not difficult for children to understand.
F
T/F According to CCSSM, to add and subtract within 20, you may use several strategies. One strategy is decomposing a number leading to a ten. Its example is "8+6 = 8+2+4 =10+4 = 14."
False
T/F: In learning problem-solving strategies, children should first be received to have enough time to practice problem-solving strategies given by teachers.
False
T/F: Poly's (1957) phases of problem solving consists of 1) understanding the problem, 2) devising a plan to solve the problem, 3) reflecting on the problem, and 4) implementing the solution plan.
False
Megan has 15 cookies. She puts 3 cookies in each bag. How many bags can she fill?
Measurement division
Which statement explains tasks and materials appropriate for problem solving? (Mark all that apply.)
Involve children in activities that promote communication and math thinking. Be motivating and culturally relevant Sometimes contain missing or contradictory information. Engage children in activities that use diverse problem-solving strategies.
Chuck had 3 peanuts. Clara gave him some more peanuts.Now Chuck has 8 peanuts. How many peanuts did Claragive him? Which structure of addition and subtraction could explain this problem the most?
Join- change unknown
Deborah had some books. She went to the library and got 3 more books. Now she has 8 books altogether. How many books did she have to start with? Which structure of addition and subtraction could explain this problem the most?
Join- start unknown
Ellen had 3 tomatoes. She picked 5 more tomatoes. How many tomatoes does Ellen have now? Which structure of addition and subtraction could explain this problem the most?
Join-result unknown
Estimation strategy Front-end strategy
Leftmost or highest place value
Estimation strategy- Special number strategy
Looking for numbers that are close to special numbers and easier to work with
Megan has 5 bags of cookies. There are 3 cookies in each bag. How many cookies does Megan have all together?
Multiplication
Remainder
Number of objects unable to be shared equally
Children can be given a set of miniature dolls, a set of cars, or other small objects and asked to record in some way (tallies or circles, for example) "how many" object they have. There should be one tally or mark per object. Children should be aware that their recording shows how many objects there are in the set.
One to one correspondence
Mark all that can be considered to be components that are important to keep in mind when teaching computational procedures to children.
Pose story problems set in real-world contexts. Use estimation and mental computation. Use models for computation
Mark all activities proper to consolidate basic facts.
Puzzles Using computer software Games
Select all that belong to ways to assess children's place-value understanding.
Regrouping with tens and ones Understanding tens and ones Using manipulatives to represent numbers
[ ] is simply saying the numbers in order, usually starting with one, e.g. 1,2,3,4,5 etc. It does not mean counting objects, or counting actions, although it is connected to these skills. It just means saying the numbers in order not connected to anything.
Rote counting
What do we call an instructional approach consistent with vygotsky's ideas for guiding children's learning in mathematics, an approach where the teacher gradually releases the learning responsibility to the children?
Scaffolding
John had some cookies. He gave 7 cookies to Amit. Now John has 4 cookies. How many cookies did John have to start with? Which structure of addition and subtraction could explain this problem the most?
Separate- Start unknown
Read a description about what a teacher is teaching her students. Have your students stand in a circle. Decide what number you're starting with and what number you're going to skip by. Go around the circle with one student at a time saying a number. Try counting forward and backward, starting and different numbers, and making different size skips Choose what kinds of counting skill can be developed by this teaching practice.
Skip counting
There are factors contributing to children's difficulties in problem-solving. Which factor does the statement explain? -Statement- Children's out-of-school experiences are varied; therefore, children develop various problem-solving strategies.
Sociocultural factors
Select statements that are not ideal as the teacher's role in problem-solving instruction.
Teach children how to prevent them from making mistakes.Expect specific responses from students.
If students think that there is no relationship between the value of each place,
Then have students describe value of adjacent place values
If students think that numbers with the same digits have the same value (For example, 23 and 32 or 15 and 150)
Then have students model the values with manipulatives then discuss why they have the same numbers in different place values
T/F: When solving division problems such as 56 divided by 5, the phrase "5 goes into 56" should not be used because it has no mathematical meaning.
True
You might ask a child who has displayed five fingers whether she or he could show the same number in another way, such as by drawing a picture of five objects or picking up a group of five blocks. This is called [ ].`
Translation
Translation problems process problems puzzles application problems
Translation problems- An auditorium can seat 648 people in 18 equal rows. How many seats are in each row? process problems- At an air show, 8 skydivers were released from an airplane. Each skydiver was connected to each other skydiver by a piece of ribbon. How many pieces of ribbon were there in total? puzzles- Can you join all 9 dots using 4 straight lines without lifting your pencil? application problems- How much does the school board pay for the electricity in the school each year?
T/F: To solve addition and subtraction problems using the base ten blocks, children exchange or trade a rod for ten units rather than "take apart" a rod.
True
T/F:There was an addition problem: Ray has 6 goldfish. But he wants 13. How many more does he need to buy? Corey solved this problem. He said, "Six plus six is twelve, and one plus is seven is thirteen." We can say that he was using derived facts.
True
Estimation strategy- Clustering strategy
When a set of numbers are close in value
Vygotsky describes children's learning as "cultural" where they interact with others, objects, and events in the classroom environment. He adds to this notion that children's ability to solve a problem is affected by a window of opportunity that he labeled as the [ ] or ZPD. The lower limit (A in the diagram below) begins the children's prior knowledge, concepts, and skills and the upper limit (B in the diagram below) is determined by the tasks that can be successfully completed only with step-by-step instruction.
Zone of Proximal Development
divisor
number in each group
Estimation strategy- Compatible number strategy
adjusting to easier numbers
The [ ] strategy involves increasing one addend while decreasing the other by the same amount.
compensation
To examine whether a child has this ability, have the child count two sets of the same objects, such as Unifix cubes. One set of, say, 32 cubes is left spread out on the table, while the other set is placed in small transparent plastic glasses in groups of 10. The child is then asked to compare the sets. Children who realizes that both sets have the same number, regardless of their arrangement, are said to be able to have this ability.
conservation of number
One of the most useful strategies for computing a multiplication exercise mentally is to employ the [ ]. For example, 5××76 can be computed as (5××70) + (5××6).
distributive property
If students think that number that look different must have different values (for example, 23 and 1 ten and 13 ones),
have student model two such numbers with manipulatives then discuss why they have the same value but look different.
Select all items that belong to number relationships
order relations Part-part-whole relationships One greater than, one less than more than, fewer than
Megan has 15 cookies. She puts the cookies into 5 bags with the same number of cookies in each bag. How many cookies are in each bag?
partitive division
Mark all that can be included in the blank. children should know to fluently add and subtract within 1000 using strategies and algorithms based on [ ].
properties of operation the relationship between addition and subtraction place vlaue
Product
the multiple of each factor
multiplicand
the number in each group
Multiplier
the number of groups
dividend
the number/amount that is being divided
quotient
the resulting number of groups
T/F: A problem like "a gardener has 60 feet of fence to keep animals out of the garden. What is the largest area of garden that this fence will enclose?" may be effective to develop Constructing a Table or Chart.
true
T/F: To help students make better sense of representing numbers, many researchers and teachers have recommended teaching children by beginning from concrete models, pictorial and graphic representation of numbers, and symbolic representation of numbers.
true
T/F: US students exhibit this misconception much more often than students in other countries. It has to do with thinking of the = sign as an operator (the operational view ). Kind of like thinking that = means "to do" the operation. For example, a student with this operational view of the equal sign tends to solve the problem, 7 + 6 = _13_ + 2 True
true
T/F: When children first decode numbers, they are not likely to use the multiplicative term times; rather, they talk about groups. For example, the 2 in 28 is explained as two groups of ten or two tens.
true
Once children have developed computational procedures, they need many activities that will help to consolidate their understanding and to develop proficiency in terms of accuracy and speed. Mark all activities that consolidate and enrich children's understanding.
using riddles using games using puzzles using computer softwares
Mark all of what to do when teaching basic facts.
work on facts over time. focus on self-improvement mark drill enjoyable.