D700 Early Mathematics Methods and
Interventions Final Exam Study QUESTIONS
SOLVED 100% CORRECT!!! 2025
Lucis is working on a division problem and needs a step-by-step approach to solve it
step-by-step graphic organizer
Eva needs to understand how numbers are related and practice counting by using a visual
representation
number lines graphic organizer
Oliver wants to practice and compare different arithmetic operations like addition,
subtraction, multiplication, and division
four operations graphic organizer
Fatima is learning about shapes and needs to define, list properties, and provide examples
and non-examples of a square
frayer model graphic organizer
Sara needs to break down a multi-step word problem to understand what to do first, second,
and third
word problem graphic organizer
Benefits of Graphic Organizers
visual learning support, enhanced problem solving skills, improved organization and structure,
supports different learning styles, encourages critical thinking
word problem graphic organizer
use to break down complex word problem
Step-by-step graphic organizer
,use to solve multi-step division problem
Four operations graphic organizer
2nd grade - compare and solve addition and subtraction problems
Pre-K real-life math example
count how many blocks they can stack before they tumble down
Kindergarten real-life math example
measuring how tall they are compared to their friends
1st grade real-life math example
sharing snacks equally among friends
2nd grade real-life math example
comparing weights of objects using a balance scale
3rd grade real-life math example
reading and understanding large numbers on a scoreboard during a game
Culturally responsive teaching
key to promoting equity in math education because it acknowledges and incorporates students'
diverse cultural backgrounds, enhancing their engagement and learning outcomes
Understanding the rationale behind the scientific study of mathematics
helps teachers apply evidence-based strategies that improve how students grasp and retain
mathematical concepts
primary goal of the science of math in education
to enhance educational practices by identifying evidence-based approaches that promote deep
mathematical understanding and proficiency
,Five Strands of Mathematical Proficiency #1 (of 5)
Conceptual Understanding
Five Strands of Mathematical Proficiency #2 (of 5)
Procedural Fluency
Five Strands of Mathematical Proficiency #3 (of 5)
Strategic Competence
Five Strands of Mathematical Proficiency #4 (of 5)
Adaptive Reasoning
Five Strands of Mathematical Proficiency #5 (of 5)
Productive Disposition
Conceptual Understanding EXAMPLE
grasping the concept of place value and how it related to addition and subtraction
Procedural Fluency EXAMPLE
quickly recalling multiplicationfacts up to 10x10
Strategic Competence EXAMPLE
choosing appropriate problem-solving strategies for different types of math problems
Adaptive Reasoning EXAMPLE
explaining why a certain mathematical strategy works and applying it to new situations
Producative Disposition EXAMPLE
maintaining positive attitude towards math challenges and persisting in problem-solving tasks
Active engagement
, develop deeper understanding of mathematical concepts, foster critical thinking and problem-
solving skills
Key Aspects of doing math #1 (of 4)
Representing and connection - drawing, symbols, graphs, objects to make abstract concepts
concrete
Key Aspects of doing math #2 (of 4)
Explaining and justifying - students explain their thought process and justify solutions
Key Aspects of doing math #3 (of 4)
Contextualizing and decontextualizing - relate math concepts to real-world situations
Key Aspects of doing math #4 (of 4)
Noticing and using mathematical structures - recognize and use patterns and structures in math
to deepen understanding and solve math problems more effectively
Representing and Connecting EXAMPLE
Jan explained how she used colored markers on a chart to show the different combinations of
red and blue buttons
Explaining and Justifying EXAMPLE
Joe used counters to model different combinations of red and blue buttons and explained his
strategy to the class
Contextualizing and Decontextualizing EXAMPLE
Mrs. Naylor told the class that Sam had ten buttons and asked if they knew how many were red
or blue. She asked, "What do we know? What can we figure out? Discuss with your partner."
Noticing and Using Mathematical Structures EXAMPLE
Interventions Final Exam Study QUESTIONS
SOLVED 100% CORRECT!!! 2025
Lucis is working on a division problem and needs a step-by-step approach to solve it
step-by-step graphic organizer
Eva needs to understand how numbers are related and practice counting by using a visual
representation
number lines graphic organizer
Oliver wants to practice and compare different arithmetic operations like addition,
subtraction, multiplication, and division
four operations graphic organizer
Fatima is learning about shapes and needs to define, list properties, and provide examples
and non-examples of a square
frayer model graphic organizer
Sara needs to break down a multi-step word problem to understand what to do first, second,
and third
word problem graphic organizer
Benefits of Graphic Organizers
visual learning support, enhanced problem solving skills, improved organization and structure,
supports different learning styles, encourages critical thinking
word problem graphic organizer
use to break down complex word problem
Step-by-step graphic organizer
,use to solve multi-step division problem
Four operations graphic organizer
2nd grade - compare and solve addition and subtraction problems
Pre-K real-life math example
count how many blocks they can stack before they tumble down
Kindergarten real-life math example
measuring how tall they are compared to their friends
1st grade real-life math example
sharing snacks equally among friends
2nd grade real-life math example
comparing weights of objects using a balance scale
3rd grade real-life math example
reading and understanding large numbers on a scoreboard during a game
Culturally responsive teaching
key to promoting equity in math education because it acknowledges and incorporates students'
diverse cultural backgrounds, enhancing their engagement and learning outcomes
Understanding the rationale behind the scientific study of mathematics
helps teachers apply evidence-based strategies that improve how students grasp and retain
mathematical concepts
primary goal of the science of math in education
to enhance educational practices by identifying evidence-based approaches that promote deep
mathematical understanding and proficiency
,Five Strands of Mathematical Proficiency #1 (of 5)
Conceptual Understanding
Five Strands of Mathematical Proficiency #2 (of 5)
Procedural Fluency
Five Strands of Mathematical Proficiency #3 (of 5)
Strategic Competence
Five Strands of Mathematical Proficiency #4 (of 5)
Adaptive Reasoning
Five Strands of Mathematical Proficiency #5 (of 5)
Productive Disposition
Conceptual Understanding EXAMPLE
grasping the concept of place value and how it related to addition and subtraction
Procedural Fluency EXAMPLE
quickly recalling multiplicationfacts up to 10x10
Strategic Competence EXAMPLE
choosing appropriate problem-solving strategies for different types of math problems
Adaptive Reasoning EXAMPLE
explaining why a certain mathematical strategy works and applying it to new situations
Producative Disposition EXAMPLE
maintaining positive attitude towards math challenges and persisting in problem-solving tasks
Active engagement
, develop deeper understanding of mathematical concepts, foster critical thinking and problem-
solving skills
Key Aspects of doing math #1 (of 4)
Representing and connection - drawing, symbols, graphs, objects to make abstract concepts
concrete
Key Aspects of doing math #2 (of 4)
Explaining and justifying - students explain their thought process and justify solutions
Key Aspects of doing math #3 (of 4)
Contextualizing and decontextualizing - relate math concepts to real-world situations
Key Aspects of doing math #4 (of 4)
Noticing and using mathematical structures - recognize and use patterns and structures in math
to deepen understanding and solve math problems more effectively
Representing and Connecting EXAMPLE
Jan explained how she used colored markers on a chart to show the different combinations of
red and blue buttons
Explaining and Justifying EXAMPLE
Joe used counters to model different combinations of red and blue buttons and explained his
strategy to the class
Contextualizing and Decontextualizing EXAMPLE
Mrs. Naylor told the class that Sam had ten buttons and asked if they knew how many were red
or blue. She asked, "What do we know? What can we figure out? Discuss with your partner."
Noticing and Using Mathematical Structures EXAMPLE
