Grade 9 Math 2
Alix Stocking
Our free math worksheets cover the full range of elementary school math skills from numbers and counting through fractions, decimals, word problems and more. All worksheets are printable files with answers on the 2nd page.
Waldorf is at its core a holistic method based on the development of the whole child. In the human being, thinking, feeling, and willing (doing) are integrated and Waldorf methods take advantage of that by including academic, artistic, and active parts in every lesson. In other words, we are educating the head, heart, and hands to provide a much deeper learning experience than if we focused only on the head.
I want to zero in today on what holistic learning looks like in first grade math lessons. For an overview of the essentials of first grade please see this post and to read more about the first grade math main lesson blocks please see here and here.
How do you teach counting and skip counting? You can work with movement and rhythm, using your body to march, skip, gallop, walk, stomp, clap, toss beanbags, etc. as you speak. See this post for ideas on how to incorporate active math in circle. You can work with imagination, pretending that you are crossing a stream on stepping stones or chopping wood with an axe. You can work with verse and poetry (for example with the Strange Family verse).
How do you teach the four processes? You can start with an imaginative story to show the ways that numbers can be related to each other. You can use characters in your story to represent each process and present it in a rich way, drawing on temperament, verse, and real problems that must be solved. You can work with manipulatives including fingers, acorns, or counting stones to make each problem very concrete, visual, and kinesthetic. You can draw the problems as well using little pictures before moving into the more abstract with dots and then numbers and symbols. You can move into practicing math facts and multiplication tables using movement and rhythm once the concepts are understood. You can keep the four processes in the holistic realm by learning not just the mechanics and not just the facts, but also learning how the processes are related, how they undo each other, how the amazing patterns in numbers and shapes translate into these relationships.
Making Math Meaningful by Jamie York is an excellent overview of the Waldorf math curriculum for grades 1-4. The opening chapters on how to teach math effectively and avoid math phobia are priceless. The curriculum and objectives for each grade and main lesson block are given in detail but the particulars on how to bring the subject to life (with games, verses, art, stories, and so on) are left up to the teacher.
Your child will learn and develop mathematical ways of thinking through (mathematical practices). Some examples of math practices are using math to model authentic situations, persevering in solving problems, constructing and critiquing mathematical justifications, and representing mathematical ideas visually. Read more about the Standards for Mathematical Practices.
Effective math instruction begins by building a strong conceptual understanding of how numbers work (number sense). This is the foundation that leads students towards procedural fluency (using flexible, efficient, and accurate strategies). Effective math instruction includes opportunities for students to apply their understanding and fluency to real-world mathematical problems.
When your child goes to 5th grade this knowledge will serve as the foundation for their continued growth in learning with fractions, decimals, volume, and sense-making when solving problems involving these concepts.
Learning Standards are for all of us: students, principals, community partners, teachers, families, and the public. They provide an equitable benchmark of what is important for students to learn as they progress through school. Introduction to the Common Core Math Standards: Achieve the Core
The 2023 Mathematics Standards of Learning were approved by the Virginia Board of Education on August 31, 2023. The 2023 Mathematics Standards of Learning represent "best in class" standards and comprise the mathematics content that teachers in Virginia are expected to teach and students are expected to learn. The 2023 Mathematics Standards of Learning will be fully implemented during the 2024-2025 school year.
The 2016 Mathematics Standards of Learning Curriculum Framework, a companion document to the 2016 Mathematics Standards of Learning, amplifies the standards and further defines the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The standards and Curriculum Framework are not intended to encompass the entire curriculum for a given grade level or course. School divisions are encouraged to incorporate the standards and Curriculum Framework into a broader, locally designed curriculum. The Curriculum Framework delineates in greater specificity the minimum content that all teachers should teach and all students should learn. Teachers are encouraged to go beyond the standards as well as to select instructional strategies and assessment methods appropriate for all students.
The content of the mathematics standards is intended to support the following five process goals for students: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations. Practical situations include real-world problems and problems that model real-world situations.
In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.
(1) Students will develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They will use a variety of models, including discrete objects and length-based models (for example, cubes connected to form lengths), to model add-to, take-from, put-together, and take-apart; compare situations to develop meaning for the operations of addition and subtraction; and develop strategies to solve arithmetic problems with these operations. Students will understand connections between counting and addition and subtraction (for example, adding two is the same as counting on two). They will use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (for example, "making tens") to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children will build their understanding of the relationship between addition and subtraction.
(2) Students will develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They will compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They will think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they will understand the order of the counting numbers and their relative magnitudes.
(3) Students will develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.
(4) Students will compose and decompose plane or solid figures (for example, put two triangles together to make a quadrilateral) and build understanding of part-whole relationships, as well as the properties of the original and composite shapes. As they combine shapes, they will recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.
Strand: MATHEMATICAL PRACTICES (1.MP)
The Standards for Mathematical Practice in first grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes (Standards 1.MP. 1-8).
Standard 1.MP.1
Make sense of problems and persevere in solving them. Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.
Standard 1.MP.2
Reason abstractly and quantitatively. Make sense of quantities and their relationships in problem situations. Contextualize quantities and operations by using images or stories. Decontextualize a given situation and represent it symbolically. Interpret symbols as having meaning, not just as directions to carry out a procedure. Know and flexibly use different properties of operations, numbers, and geometric objects.
Standard 1.MP.3
Construct viable arguments and critique the reasoning of others. Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.