Math test 1

Discuss why teachers and students want to avoid relying on using a key words strategy.

1. sends a bad message about doing mathematics. Problems need to be analyzed using all of the words 2. key words are often misleading.

What's an example of introducing children to numbers to 100?

100's chart, 100th day.

3 types of fraction models

Area models, length models, set models

What are the structures/meanings/interpretations for addition/subtraction?

Change to join or separate, part-part whole, comparison.

how does constructivism answer the student-centered instruction?

Children's experiences help them develop connections and ideas about whatever they are learning. Actively engaged in seeking meaning during learning process

What ideas about children's learning is evident in the Promote Good Beginnings article? (Ages 3-6). How are these ideas appropriate for ages 6-8?

Collaboration, real word, child interests, process standards.

What are contextual problems?

Connected as closely as possible to children's lives rather than to school mathematics. They are designed to anticipate and to develop children's mathematical modeling of the real world.

define 1-1 correspondance

Counting objects by saying number words in a 1-1 correspondence with the objects.

What are the three levels through which children progress as they solve mathematics stories?

Direct modeling,counting strategies, and derived facts.

How do we help children learn equivalent fraction concepts?

Give emphasis on variety of meanings of fractions, incorporate models and contexts to represent fractions, emphasize fractions are numbers, spend time for children to understand, iterating and portioning must be significant aspect of fraction instruction.

Discuss how you would establish a mathematically rich environment.

I would give children a lot of experience with math and hands on manipulatives. I would use a lot of direct instruction to provide helpful lessons for students.

What is the role of choosing numbers when you and your students are working with mathematics stories (word problems)?

Increase the number depending on the child's number development.

what is denominator:

It is the number of repetitions of the unit fraction needed to create a whole.

How do the five PROCESS standards?

Problem solving, reasoning, making connections, representation, communication.

How can children's literature books help children learn mathematics?

Rich source for generating high cognitive demand tasks with multiple entry and exit points. Children can use various strategies to solve problems.

Define number sequence:

The names and the ordered list of number words

How are addition and subtraction related?

They work together, you can use both of them to solve eachother.

define cardinality

Understanding that the last number word said when counting tells us how many objects have been counted.

define array

addition situations with equal groups

benchmark numbers of 5 and 10

because the number 10 plays a large role in our numeration system and because two fives equals 10, it is useful to develop relationships between numbers 1 to 10

why are the terms part whole, equal sharing, and measurement important to be aware of?

because we can help children develop a comprehensive understanding of fractions, and it provides experience with all meanings. Describe the difference between partitioning an

How do children learn mathematics?

by doing mathematics- through personal experience, interacting with others, and reflective thought.

What does part whole mean?

commonly used meaning in fractions. Typically represented by shading part of a whole that has been broken into two parts. 1/2 , ⅓, ¾, Effective starting point for building meanings of fractions,

How can number sense ideas be related to the real world?

comparing it to realistic things like graphing snack time, riding the bus.

compare problems

comparison of 2 quantities

what is mathematics?

consists of sequences, numbers, patterns, and equations.

How are "more", "less", and "same" part of number sense (the relations core)?

contributes to children's overall understanding of number.

iterate

counting a repeated amount. ex: is 10 thirds the same as 10 fourths? how much more to get a second whole quesadilla?

What evidence will show that children have meaning with their counting?

counting at the last number

what is numerator:

counting number

what is cardinal number?

denoting quantity such as one, two, three

What are the structures for multiplication/division?

equal group and array

reasoning

explaining what they did

what are ordinal numbers?

first, second, third

what does equal sharing mean?

form of division, Can involve continuous or discrete quantities. Ex: Cutting sticks into as many equal pieces.

what does a numerator in a fraction tell us?

how many equal shares or parts we have.

What is the importance of "counting up"and "counting back" strategies

important for addition and subtraction and number sequence.

what does measurement mean?

includes time, linear measurement, Measuring a quantity that we could cut into as many equal sized pieces as we need.

problem solving

investigating, explore, experiment, discover.

what are part part whole problems

involve 2 parts that are combined as a whole.

define equal group

involve 3 quantities number of group, size of each group and total.

what is the importance of thinking about zero?

it is the most important digits in the base-ten system, and conversations about it and its position on the number line are essential. Also a required standard for kindergartners.

sociocultural with math

learner can be assisted by working with others who are more knowledgeable. Own proximal development. When teachers target students proximal development they are providing the student with the right amount of challenge.

How can manipulatives help children learn mathematics?

manipulative help children and teachers use to illustrate and explore mathematical concepts. Physical manipulative can build the foundation for understanding.

representation

manipulative, symbols, drawings

one and two more, one and two less

more than just the ability to count on two more or count back by two. for example: for 7, 1 is more than 6 and also 2 less than 9.

4 key experiences of early numerical knowledge?

number sequence, 1-1 correspondence, cardinality, subtilizing.

What are the two requirements for fractional parts?

numerator, denominator,

define derived facts

often looks for ways to decompose the numbers in a given situation to make an easier problem.

define subtilizing

quickly recognizing and naming how many objects are in a small group without counting.

making connections

real world, with other subjects

What is the importance of "counting on" strategies?

sequencing and laying a foundation for addition and subtraction. You are not starting at 1 you are counting on from any given number.

partition

splitting or cutting into equal parts ex: six brownies shared with four children, each child gets 1 and one-half brownies.

part-part whole relationships

the most important relationship that can be developed about numbers is to conceptualize a number as being composed of 2 or more

communication

verbal, writing, drawing

what does the denominator tell us in a fraction?

what size piece, or fractional part, is being counted.

what are join problems

when quantities are physically being brought together

If you were analyzing an activity with respect to early fraction ideas, what would you expect to see?

working on part whole, compare sizes, area ideas, length ideas, counter fraction parts.