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### Big Ideas

### Grandes idées

Fractions and decimals are types of numbers that can represent quantities.

numbers

- Number: Number represents and describes quantity.
*Sample questions to support inquiry with students:*- What is the relationship between fractions and decimals?
- How are these fractions (e.g., 1/2 and 7/8) alike and different?
- How do we use fractions and decimals in our daily life?
- What stories live in numbers?
- How do numbers help us communicate and think about place?
- How do numbers help us communicate and think about ourselves?

Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.

fluency

- Computational Fluency: Computational fluency develops from a strong sense of number.
*Sample questions to support inquiry with students:*- What is the relationship between multiplication and division?
- What patterns in our number system connect to our understanding of multiplication?
- How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex multiplication facts?

Regular changes in patterns can be identified and represented using tools and tables.

patterns

- Patterning: We use patterns to represent identified regularities and to make generalizations.
- Sample questions to support inquiry with students:
- What regularities can you identify in these patterns?
- Where do we see patterns in the world around us?
- How can we represent increasing and decreasing regularities that we see in number patterns?
- How do tables and charts help us understand number patterns?

Polygons are closed shapes with similar attributes that can be described, measured, and compared.

attributes

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
*Sample questions to support inquiry with students:*- How are these polygons alike and different?
- How can we measure polygons?
- How do the properties of shapes contribute to buildings and design?

Analyzing and interpreting experiments in data probability develops an understanding of chance.

data

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
*Sample questions to support inquiry with students:*- How is the probability of an event determined and described?
- What events in our lives are left to chance?
- How do probability experiments help us understand chance?

Numbers represent quantities that can be decomposed into smaller parts.

Numbers

- Number: Number represents and describes quantity.
- Sample questions to support inquiry with students:
- How do these materials help us think about numbers and parts of numbers?
- Which numbers of counters/dots are easy to recognize and why?
- In how many ways can you decompose ____?
- What stories live in numbers?
- How do numbers help us communicate and think about place?
- How do numbers help us communicate and think about ourselves?

- Sample questions to support inquiry with students:

One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.

fluency

- Computational Fluency: Computational fluency develops from a strong sense of number.
- Sample questions to support inquiry with students:
- If you know that 4 and 6 make 10, how does that help you understand other ways to make 10?
- How does understanding 5 help us decompose and compose numbers to 10?
- What parts make up the whole?

- Sample questions to support inquiry with students:

Repeating elements in patterns can be identified.

patterns

- Patterning: We use patterns to represent identified regularities and to make generalizations.
- Sample questions to support inquiry with students:
- What makes a pattern a pattern?
- How are these patterns alike and different?
- Do all patterns repeat?

- Sample questions to support inquiry with students:

Objects have attributes that can be described, measured, and compared.

attributes

- Geometry and Measurement: We can describe, measure, and compare spatial relationships.
- Sample questions to support inquiry with students:
- What do you notice about these shapes?
- How are these shapes alike and different?

- Sample questions to support inquiry with students:

Familiar events can be described as likely or unlikely and compared.

Familiar events

- Data and Probability: Analyzing data and chance enables us to compare and interpret.
- Sample questions to support inquiry with students:
- When might we use words like unlikely and likely?
- How does data/information help us predict the likeliness of an event (e.g., weather)?
- What stories can data tell us?

- Sample questions to support inquiry with students:

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