Arithmancy

Week of Inspirational Math

Every year I start the math period demolishing my students' stereotypes about being or not being a "math person" with the help of Jo Boaler's "Week of Inspirational Math". I find it is important to make my students understand that everybody can learn math, that math surrounds us, and that making mistakes is part of the process of learning. I want them to have a growth mindset about learning, and to understand how their brains work. I also want them to have fun, investigate, wonder, and find more than one way to get to the answer. I want them to use models, and think like mathematicians. That prepares the ground for successful growth of their math skills, and is a fantastic way to make my students feel confident to tackle any mathematical challenge. Check out the Youcubed website, and the resources for parents here:
www.youcubed.org/resource/parent-resources/

Number Talks

Once we finish the Week of Inspirational Math, we begin every morning with some number talks. Number talks change along the year, but to give you an idea of the process of a number talk, I will give you a brief example: I post a series of related simple equations and I ask my students to look for patterns on those equations. At the beginning of the year it is normal that my students find very simple patterns, and focus their attention on only one equation at a time, but with guidance and practice, they soon become comfortable with seeing interrelations between equations, movement of quantities, and mathematical processes that in the future will help them make mathematical claims that will lead them to the rules we all learned to memorize when we were kids. I find this approach more organic, and immensely more effective in understanding math, as my students find agency in their discoveries and learn to be flexible and to play with numbers. However, number talks don´t end with numbers, along the year we will work with shapes, measurement, fractions and more! To learn more about number talks, check out this blog post in Scholastic
www.scholastic.com/teachers/blog-posts/alycia-zimmerman/number-talks-grow-mathematical-minds/

Math Fridays

To learn about our Math Fridays, check out the Camp Volunteers page, and join us for fun mathematical games that will challenge your child´s mind while having a lot of fun.

Go Math Curriculum

The core of our math learning will be done through this district wide resource. In third grade we will go through 11 units that will cover addition and subtraction, multiplication, division, data, fractions, measurement and geometry. Each student will have one workbook per unit, that contains a pretest, mid-chapter checkpoint, and end of chapter checkpoint, along with the individual lessons. I will remove the quizzes from the books before handing them to my students, and they will be placed in their goal binders after being completed and graded. You will notice along the year that some, or in some cases many of the activities and problems in the workbook appear undone, the reason being that, during my math block I will use some of the activities in the book to practice in the classroom using whiteboards and markers instead of the workbook, and other times we will use other resources to learn certain skills. Regardless the tool, your child will finish the school year with a strong mathematical content knowledge on the areas highlighted on the common core standards for third grade.

Common Core Standards and Mathematical Practices (source: corestandards.org)

In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division.
Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators.
Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle.
Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole.

Grade 3 Overview
Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Number and Operations in Base Ten

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations—Fractions

Develop understanding of fractions as numbers.

Measurement and Data

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Represent and interpret data.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometry

Reason with shapes and their attributes.

Mathematical Practices