Primary Math Test 2

Number Lines

Number Lines

Put Numbers in Order

A number line is…

• A spatial, or graphic, arrangement of counting numbers.

• It introduces the idea of counting up by walking forward, walking backwards, or turning around.

• Counting up with objects or on the *blank* connects counting to addition and subtraction.

How do manipulatives fit into the CRA model?

It helps students move from concrete to abstract.

Four Step Problem Solving

1. Identify the problem or question

2. Propose a solution

3. Carry out the plan

4. Look back or evaluate the solution

Four Step Problem Solving Step 1:

Identify the Problem or Question

Four Step Problem Solving Step 2:

Propose a Solution

Four Step Problem Solving Step 3:

Carry Out the Plan

Four Step Problem Solving Step 4:

Look Back or Evaluate the Solution

Ordinal Numbers

• Designate location is a sequence.

• Occur in many situations that teachers and students can discuss and label.

• Discussing sequence in stories, in the days of the week or month, or in each day’s events.

  EX:

• Evan is first in line; Kelly is last.

• Tuesday is the seventh day of school.

• Who was second in line today?

Cardinal Numbers

• Counting numbers because they tell how many objects are in a set.

• Stress the last or *blank* of a set as objects are counted.

  EX:

• Shelby has 1 dog. Ashley has 2 cats. Rachael has 3 goldfish.

Nominal Numbers

• A number that is used to identify or name, although it may code other information.

  EX:

• A jersey number represents a player.

• The are code “405” represents the area where we live.

Take-Away

Removing part of a set.

EX:

• Take away 5 from 9, how many are left?

• Sara had 36 cookies. She gave two cookies each to 12 friends.

Whole-Part-Part

• Separating a set into subsets.

  EX:

• The whole class has 25 children. 14 are girls. How many are boys?

• Jace has 17 stuffed animals. 14 are bears.

Comparison Subtraction

• Showing the difference between two sets.

  EX:

• On Friday, $10 was collected. On Saturday, $7 was collected. How much more was collected on Friday?

• The circus put on two performances. The matinee was attended by 100 people, and in the evening performance attracted 213 people.

Completion Subtraction

• Finding the missing part needed to finish a set.

  EX:

• “How much more is needed?” She has $9. The pizza cost $16. How many more dollars does she need?

• Faith is collecting state quarters. She already has 34.

Commutative Property

The order of addends does not affect the sum.

• (EX. 2+3=3+2 and a+4=4+a)

Associative Property

• Applies to three or more addends.

• If the problem shows the *blank*, the order in which the pairs of addends are added does not change the sum.

• (EX: 8+(2+3)=(8+2)+3 and a+(b+c)=(a+b)+c)

Identity Property

Adding or subtracting “0” to a number does not change the sum and results in that same number.

• (Ex. 6 - 0 = 6 and a+0=a)

Partition

To cut or divide.

Importance of Number Formation:

• Crucial for expressing math understanding.

• If a student can’t write the numbers, they can’t do the math.

• If a student can’t write the numbers, they can’t read them.

Hundreds Chart Benefits

• Skip counting and seeing patterns in numbers.

• Illustrates for children the pattern of tens and ones that structures the base-10 numeration system.

Inverse of Addition

Subtraction

Benefits of Skip Counting

• Encourages faster and flexible counting and is connected to multiplication and division.

• Should be done with manipulatives.

• First experience in counting is one-to-one correspondence between objects and natural numbers.

  EX:

• How many eyes are in our room? Count by two.

How can word problems enhance children’s understanding of mathematical operations and problem solving? 

• Stories in *blank* help students understand how addition and subtraction work.

• Helps them think critically.

• Students can find reasoning for their answer.

What is the importance of understanding number operations in early childhood mathematics?

• Understanding numbers and their relationships helps children grasp more complex mathematical concepts later on.

• This includes addition, subtraction, multiplication, division, fractions, and algebra.

• Early numeracy skills, such as counting and recognizing numbers, set the stage for success in these more advanced areas.

Number Operation Phases

1. Exploring concepts and number combinations through various experiences. 

2. Learning strategies and properties of each operation.

3. Developing accuracy and speed.

4. Maintenance of conceptual understanding. 

5. Extending concepts and skills. 

1. Number Operation Phase

Exploring concepts and number combinations through various experiences. 

PSS: Find and Use a Pattern

Students identify a pattern and extend the pattern to solve the problem.

2. Number Operation Phase

Learning strategies and properties of each operation.

3. Number Operation Phase

Developing accuracy and speed.

4. Number Operation Phase

Maintenance of conceptual understanding. 

5. Number Operation Phase

Extending concepts and skills. 

PSS: Act It Out

By acting out a problem situation, students understand the problem and devise a solution plan.

PSS: Build a Model

Students use objects to represent the situation.

PSS: Make a Table and/or a Graph

Students organize and record their data in a table, chart, or graph. Students are more likely to find a pattern or see a relationship when it is shown visually.

PSS: Draw a Picture or Diagram

Student show what is happening in the problem with a picture or a diagram.

EX:

• Venn diagram

PSS: Write a Mathematical Sentence

If the problem involves numbers or number operations, strategies often lead to a mathematical sentence or expression of a relationship with numbers or symbols.

PSS: Guess and Check, or Trail and Error

By exploring a variety of possible solutions, students discover what works and what doesn’t. Even if a potential solution does not work, it may give clues to other possibilities or help the student to understand the problem.

PSS: Account for All Possibilities

Students systematically generate many solutions and find the ones that meet the requirements of the problem solution.

PSS: Break Down the Problem or Solve a Simpler Problem

If a problem is too large or complicated to attack, students can reduce the size of the problem or break it into parts to make it more manageable.

PSS: Work Backward

Considering the goal first can make some problems easier. Starting with the end in mind helps students develop a strategy that leads to the solution by backing through the process.

EX:

• 7 pets = 5 dogs + ______ cats

PSS: Dimensional Analysis

This approach uses the measurement units in the problem to formulate a solution design.

PSS: Change Point of View or Solving Method

When a strategy is not working, students need flexibility and in their thinking. They may need to discard what they are doing and try something else or think about the problem in a different way.

Abstraction Principle

 any collection of real or imagined objects can be counted

Stable-Order Principle

counting numbers are arranged in a sequence that does not change

One-to-One Principle

principle requires taking off the items in a set so that one and only one number is used for each item counted

Order-Irrelevance Principle

The order in which items are counted is irrelevant. The number stays the same regardless of the order.

Cardinal Principle

Gives special significance to the last number counted because it is not only associated with the last item but also represents the total number of items in the set. Tells how many are in the set.