Grade 4 - 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.4.1Weave together ʻāina, ʻohana, and cultural components of moʻokūʻauhau (i.e. ʻohana genealogy, waʻa genealogy, Kumulipo, history, moʻolelo wahi pana)
M.4.2Interact with ‘āina by using ʻōlelo Hawaiʻi performance cartographies (i.e. oli, mele, hula, kaulana mahina, hoʻokele) and develop a stronger relationship with ʻāina.
M.4.3Understand the function and relationship between cultural protocols, cultural artifacts, and lawena (i.e piko/pū/reverence, mahalo/lei/gratitude).
M.4.4Know our place in the community ʻāina, its resources (mauna, awawa, wai , kai, one, wao) and the relationship with well-being.
M.4.5Understand the connection between moʻokūʻauhau, knowing deeply about a place, and fulfilling the ʻauamo to care for that place.

M.4.6Make sense of problems and persevere in solving them.
M.4.7Reason abstractly & quantitatively.
M.4.8Construct viable arguments and critique the reasoning of others.
M.4.9Model with mathematics. ✰Critical emphasis to connect to ‘Āina Learning Concepts
M.4.10Use appropriate tools strategically.
M.4.11Attend to precision.
M.4.12Look for and make use of structure.
M.4.13Look for and express regularity in repeated reasoning.

M.4.14Visual Fraction Models: Use different ways of seeing and visualizing fractions to compare fractions using student generated visual fraction models. Use >, < and = to compare fraction size, through linear and area models, and determine whether fractions are greater or less than benchmark numbers such as ½ and 1.
M.4.15Shapes & Symmetries: Draw and identify shapes, looking at the relationships between rays, lines, and angles. Explore symmetry through folding activities.
M.4.16Connected Problem Solving: Solve problems with perimeter, area, volume, distance, and symmetry, using operations and measurements.

M.4.17Fraction Flexibility: Understand that additions and subtraction of fractions as joining and separating parts that are referring to the same whole. Decompose fractions and mixed numbers into unit fractions and whole numbers and express mixed numbers as a sum of unit fractions.
M.4.18Visual Fraction Models: Use different ways of seeing and visualizing fractions to compare fractions using student generated visual fraction models. Use >, < and = to compare fraction size, through linear and area models, and determine whether fractions are greater or less than benchmark numbers such as ½ and 1.
M.4.19Circles, Fractions & Decimals: Understand, compare, and visualize fractions expressed as decimals.Recognize fractions with denominators of 10 and 100, ex: 25 cents can be written as 0.25 or 25/100. Connect a circle fraction model to the clock face. Example 3/10 + 4?100 = 30/100 +4/100 = 34/100.

M.4.20Number & Shape Patterns: generalize number and shape patterns that follow a given rule. Communicate understanding how the pattern changes in words, symbols, and diagrams - working with multi-digit numbers.
M.4.21Factors & Area Models: Break numbers inside of 100 into factors. Illustrate whole number multiplication and division calculations as area models and rectangular arrays that illustrate factors.
M.4.22Multi-Digit Numbers: Read and write multi-digit whole numbers in expanded form and express each number component of the expanded form as a multiple of a power of ten.
M.4.23Multi-Digit Numbers: Use place value understanding and properties of operations to perform multi-digit arithmetic.