Grade 3 - Math

In addition to the HFCS ‘Āina-based Learning Competencies (click to view), the PK-12 Mathematics Kahua is grounded in the belief that the purpose of math is to search for patterns and relationships in number, shapes and functions, to better appreciate the beauty of math in our world. It is the kuleana of every student to explore mathematics in their daily lives on ‘āina and share mo’olelo of their understanding. End of school year grade level benchmarks were crosswalked with the HFCS Vision of the Graduate (2013), CCSS, Nā Ana Aʻo Hawaiʻi DOE Kula Kaiapuni Content Standards and Benchmarks (Nā Ana ma ka Papa K-12), Student Achievement Partners (SAP) Essential Standards documents K-12, NCTM Catalyzing Change. K-12, Prioritizing Critical Areas In your Math Curriculum K-8 Prerequisites for Success, ALN High Leverage Concepts, CA Digital Learning Integration & Standard Guidance Jo Boaler & Cathy Williams and were prioritized using the following criteria (Reeves, 2004): 1) Endurance, 2) Leverage, 3) Readiness, 4) Assessment Requirements.

I. Sense of Place: ʻĀina Learning Competencies

Overarching goals for ʻāina-based curriculum designed to connect the learner to their cultural, linguistic and physical community

II. Sense of Belonging: Mathematical Practices - http://www.corestandards.org/Math/Practice/

Varieties of expertise students should develop and rest on important processes and proficiencies with longstanding importance in mathematics education.

III. Sense of Belonging: Discovering Shape and Space

Explore unit fractions, fractions, circles, and decimals and connect these concepts to problem solving. Analyze quadrilaterals, shapes, symmetry and layers of cubes.

IV. Sense of Community: Taking Wholes Apart, Putting Parts Together

Become flexible using fractions, seeing fractions relationships using visual fraction models. Explore unit fractions, fractions, circles, and decimals. Visualize and conceptualize division including powers of 10 and place value.

V. Sense of Community: Exploring Changing Quantities

Search for patterns in number, shape, addition and subtraction. Explore number flexibility with multi-digit numbers. Explore factor and area models and factor and groups. Investigate fraction connections. Model changing quantities found in the world. Continue telling a data story and making connections.

VI. Sense of Responsibility: Communicating Stories with Data

Represent, measure and plot multivariable data and look for patterns within the data. Explore fractions of shape and time, and investigate rectangles. Begin to tell a data story.

M.3.1Weave together ʻāina, ʻohana, and cultural components of moʻokūʻauhau (i.e. ʻohana genealogy, waʻa genealogy, Kumulipo, history, moʻolelo wahi pana)
M.3.2Interact with ‘āina by using ʻōlelo Hawaiʻi performance cartographies (i.e. oli, mele, hula, kaulana mahina, hoʻokele) and develop a stronger relationship with ʻāina.
M.3.3Understand the function and relationship between cultural protocols, cultural artifacts, and lawena (i.e piko/pū/reverence, mahalo/lei/gratitude).
M.3.4Know our place in the community ʻāina, its resources (mauna, awawa, wai , kai, one, wao) and the relationship with well-being.
M.3.5Understand the connection between moʻokūʻauhau, knowing deeply about a place, and fulfilling the ʻauamo to care for that place.

M.3.6Make sense of problems and persevere in solving them.
M.3.7Reason abstractly & quantitatively.
M.3.8Construct viable arguments and critique the reasoning of others.
M.3.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts
M.3.10Use appropriate tools strategically.
M.3.11Attend to precision.
M.3.12Look for and make use of structure.
M.3.13Look for and express regularity in repeated reasoning.

M.3.14Fractions of Shape & Time: Collect data by time of day, show time using a data visualization (ex: graph, table etc.). Think about fractions of time and of shape and space, expressing the base unit as a unit fraction of the whole.
M.3.15Unit Fraction Models: Compare unit fractions using different visual models including linear models (ex: number lines, tape measures, time, and clock) and area models (ex: shape diagrams, arrays) and encourage student justification with visual models.
M.3.16Analyze Quadrilaterals: Describe, analyze, and compare quadrilaterals. Explore the ways that area and perimeter change as side lengths change, by modeling real world problems. Use rounding strategies to approximate lengths where appropriate.

M.3.17Fractions of Shape & Time: Collect data by time of day, show time using a data visualization (ex: graph, table etc.). Think about fractions of time and of shape and space, expressing the base unit as a unit fraction of the whole.
M.3.18Square Tiles: Use square tiles to measure the area of shapes, finding an area of n squared units, and learn that one square represents 1/nth of the total area.
M.3.19Fractions as Relationships: Know that a fraction is a relationship between numerators and denominators - and it is important to consider the relationship in context and reason about their size. Understand why ½ = 2/4 = 3/6.
M.3.20Unit Fraction Models: Compare unit fractions using different visual models including linear models (ex: number lines, tape measures, time, and clock) and area models (ex: shape diagrams, arrays) and encourage student justification with visual models.

M.3.21Addition and Subtraction Patterns: Add and subtract within 1000 - Using student generated strategies and models, such as base 10 blocks. EX: use expanded notation to illustrate place value and justify results. Investigate patterns addition and multiplication tables, and use operation, and color-coding to generalize and justify findings.
M.3.22Number Flexibility to 100: Multiply and divide within 100 and justify answers using arrays and student generated visual representations. Encourage number sense and number flexibility - not “blind” memorization of number facts. Use estimation and rounding in number problems.