Conceptual Understanding in Mathematics Grades 3-5 January 30th, 2016

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Norms Be on time Be present Spread joy! Norms

Today we will… Learn how pattern blocks can be used to teach fractions in mathematics using a conceptual approach. Helping kids connect the concrete to the abstract

Every child can and must learn at grade level and beyond. OUR COMMITMENT, OUR BOLD STAND, OUR EXPECTATION 5 Every child can and must learn at grade level and beyond. 1 min. 1 min. In order to move students forward, a significant shift in beliefs and mindsets regarding math instruction has to occur. We are charged with making math work for a much greater proportion of students. Thus math classes must reflect a different set of instructional practices – productive struggle, alternative approaches and multiple representations, discourse, explanations, etc. Students move a minimum of a grade level per year.

Five Tenets Culture of Learning with High Expectations Challenging Content Ownership Supporting all students Demonstrating learning 2 min By aligning our instruction to the claims we are ensuring that our students will be engaging in challenging content and our lessons reflect the shifts required by the CCSS for Math, which include the content and math practice standards.

Domain Progressions

Fractional Concepts Flexible representations with pattern blocks How many of each block will fit on a hexagon? What is the fractional value of each block? Fractions as division of the whole 6/6 = 1 whole 2/6 (explain the symbolic notation) Changing the size of the whole If 2 hexagons equal one whole, what will be the value of the other blocks? Spatially the larger the number of parts, the smaller the parts will be (Comparing & Ordering 1/3 and 1/6) Equivalent fractions: show 2 examples of how equivalent fractions can be visualized Write number sentences on the board and have kids prove/disprove equivalencies 2/6 = 1/3, ½ > 2/3, etc. (2 hexagons = 1) Mixed Numbers: Rename fractional remainders, 6/4 = 1 ½

Fractional Relationships = 1/3 = ? = 1/4 = ? = 1/5 Build the whole = 1 Create a design worth 2 1/2

Equivalency Equivalent fractions: show 2 examples of how equivalent fractions can be visualized Write number sentences on the board and have kids prove/disprove equivalencies 2/6 = 1/3, ½ > 2/3, etc.

Mixed Numbers   Each partner does one

Operations with Fractions   Numerators combine or separate but denominator stays the same (patterns) 2/3 + 5/3 = 7/3= 2 1/3 7/4 – 5/4 = 2/4 = 1/2 Think Smarter- Can lay fractions over the top when solving for a missing part

Operations with Fractions   Students could create their own equations: Write an equation that equals 3 1/3 using any combination of pattern blocks

Operations with Fractions  

Operations with Fractions   2 hexagons = 1 whole (in order to work with fourths, twelfths) Trapazoid (1/4) into thirds triangles, 1 triangle = 1/12 of the total pan Hexagon (1/2) into sixths, 5 triangles = 5/12 of the total pan

Video Example 5-6th grade classroom (Students explore part and whole relationships with part blocks) How could Mr. D. extend this lesson to develop students’ thinking around adding and subtracting fractions or decomposition of fractions?

Conceptual Tools Set Models Linear Models Area Models 12/6/2019 Remember pattern blocks are just one of many tools that can be utilized to conceptualize fractions. 12/6/2019

Eight Math Practices What math practices does the use of a Rekenrek reinforce? MP 1, 3, 5, 7