Fractions and decimals are types of numbers <ul><li>Number: Number represents and describes quantity.</li><li><em>Sample questions to support inquiry with students:</em><ul><li>What is the relationship between fractions and decimals?</li><li>How are these fractions (e.g., 1/2 and 7/8) alike and different?</li><li>How do we use fractions and decimals in our daily life?</li><li>What stories live in numbers?</li><li>How do numbers help us communicate and think about place?</li><li>How do numbers help us communicate and think about ourselves?</li></ul></li></ul> that can represent quantities.
Development of computational fluency <ul><li>Computational Fluency: Computational fluency develops from a strong sense of number.</li><li><em>Sample questions to support inquiry with students:</em><ul><li>What is the relationship between multiplication and division?</li><li>What patterns in our number system connect to our understanding of multiplication?</li><li>How does fluency with basic multiplication facts (e.g., 2x, 3x, 5x) help us compute more complex multiplication facts?</li></ul></li></ul> and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Regular changes in patterns <ul><li>Patterning: We use patterns to represent identified regularities and to make generalizations.</li><li>Sample questions to support inquiry with students:<ul><li>What regularities can you identify in these patterns?</li><li>Where do we see patterns in the world around us?</li><li>How can we represent increasing and decreasing regularities that we see in number patterns?</li><li>How do tables and charts help us understand number patterns?</li></ul></li></ul> can be identified and represented using tools and tables.
Polygons are closed shapes with similar attributes <ul><li>Geometry and Measurement: We can describe, measure, and compare spatial relationships.</li><li><em>Sample questions to support inquiry with students:</em><ul><li>How are these polygons alike and different?</li><li>How can we measure polygons?</li><li>How do the properties of shapes contribute to buildings and design?</li></ul></li></ul> that can be described, measured, and compared.
Analyzing and interpreting experiments in data <ul><li>Data and Probability: Analyzing data and chance enables us to compare and interpret.</li><li><em>Sample questions to support inquiry with students:</em><ul><li>How is the probability of an event determined and described?</li><li>What events in our lives are left to chance?</li><li>How do probability experiments help us understand chance?</li></ul></li></ul> probability develops an understanding of chance.
Numbers <ul><li>Number: Number represents and describes quantity.<ul><li>Sample questions to support inquiry with students:<ul><li>How do these materials help us think about numbers and parts of numbers?</li><li>Which numbers of counters/dots are easy to recognize and why?</li><li>In how many ways can you decompose ____?</li><li>What stories live in numbers?</li><li>How do numbers help us communicate and think about place?</li><li>How do numbers help us communicate and think about ourselves?</li></ul></li></ul></li></ul> represent quantities that can be decomposed into smaller parts.
One-to-one correspondence and a sense of 5 and 10 are essential for fluency <ul><li>Computational Fluency: Computational fluency develops from a strong sense of number.<ul><li>Sample questions to support inquiry with students:<ul><li>If you know that 4 and 6 make 10, how does that help you understand other ways to make 10?</li><li>How does understanding 5 help us decompose and compose numbers to 10?</li><li>What parts make up the whole?</li></ul></li></ul></li></ul> with numbers.
Repeating elements in patterns <ul><li>Patterning: We use patterns to represent identified regularities and to make generalizations.<ul><li>Sample questions to support inquiry with students:<ul><li>What makes a pattern a pattern?</li><li>How are these patterns alike and different?</li><li>Do all patterns repeat?</li></ul></li></ul></li></ul> can be identified.
Objects have attributes <ul><li>Geometry and Measurement: We can describe, measure, and compare spatial relationships.<ul><li>Sample questions to support inquiry with students:<ul><li>What do you notice about these shapes?</li><li>How are these shapes alike and different?</li></ul></li></ul></li></ul> that can be described, measured, and compared.
Familiar events <ul><li>Data and Probability: Analyzing data and chance enables us to compare and interpret.<ul><li>Sample questions to support inquiry with students:<ul><li>When might we use words like unlikely and likely?</li><li>How does data/information help us predict the likeliness of an event (e.g., weather)?</li><li>What stories can data tell us?</li></ul></li></ul></li></ul> can be described as likely or unlikely and compared.
