Observational Assessment : Pages 9-11 of this document Math Pod1
Day 1: Exploring 3D Solids Students will be given time to explore, in small groups, the 3D materials that they brought to school. As they are exploring, record the language that they use such as rolls, slides, stack, etc. Document through the use of photos. Once they have had had time to explore and documentation of all of the groups have been completed, meet in full group.
We will co-construct criteria together for our learning target. Let students know that in their grade they need to be able to sort 3D solids according to an attribute and explain the sorting rule. Discuss what sorting means. Discuss what attribute means. What do you need to know or understand about 3D solids to sort? (criteria) What would that look like? (details) What would you have to understand to explain how they are sorted? Fill in the criteria and details as they speak.
Have students return to their solids and small groups and find a collection or set of 3D solids that belong together and be prepared to explain the sorting rule.
Revist the criteria and add to it if necessary. This co- constructed criteria will be used to assess future work.
I am preparing for my next block in a combined grade 3-4 classroom. The classroom teacher would like to focus on outcomes SS3.3 and SS4.2 I would like to begin with a discussion/ understanding why we need standard units of length.
SS3.3. Demonstrate an understanding of linear measurement (cm and m) including selecting and justifying referents generalizing the relationship between cm and m estimating length and perimeter using referents; measuring and recording length, width, height, and perimeter ; constructing 2-D shapes with a given perimeter or given lengths.
• Volume is the three-dimensional space that a certain object takes up while capacity refers to how much a container or object can hold or accommodate.
• Volume is measured mostly using cubic centimeter or cubic meters and can be determined by multiplying the object’s length, width and height; while capacity is measured by the liters, gallons, milliliters, etc. depending on how much the container can accommodate.
Date: 05/01/2002 at 18:55:51
From: Lydia Saxton
Subject: Volume vs. Capacity
Can you explain the difference between the terms "volume" and
"capacity"? Most sources I've researched seem to lean toward reserving
the use of the term "volume" for solids (measured in cubic units) and
the term "capacity" for liquids. Is this accurate?
Also, can you define the distinction between "weight" and "mass"? Many
texts use these terms interchangeably. I know that weight is a
function of gravity and mass has to do with atomic structure, which is
not affected by gravity.
Learning by Doing- Chapter 4 How Will We Respond When Some Students Don`t Learn
DuFour, Richard, 2009 Learning by doing : a handbook for professional learning communities at work / Richard DuFour … [et al.] Hawker Brownlow Education, Moorabbin, Vic. :
This chapter confronts a ‘problem’ that many, if not all schools are presently encountering.
What do we do with the students that are failing? The case study was interesting in that it shows frequent monitoring and timely interventions are critical to student success. What the case studies also confront is the differences among teachers and the ‘lottery’ of all teachers/classrooms are not created equal. By providing additional time and support within the school day, without students missing new instruction is necessary. This may be seen as a difficult task to modify schedules and have teachers assume new roles and responsibilities. “Intervention systems do not require additional resources, but they do require schools to use their existing resources—time, personnel, and material—differently” (p. 101).
Effective intervention is NOT more of the same but in pull out groups. It requires differentiated instruction knowing what the precise reason(s) why the student is failing. Intervention does not exclude the responsibility of the teacher “I taught it… so let the intervention people deal with it” (p. 115). Empower the teachers that work with the student so ongoing timely interventions happen daily.
Great chapter!
So what can we do with students who struggle with the basic math facts?
First: What data do you presently have on each of these students?
What deficits do they have? Remember: Effective intervention is NOT more of the same but in pull out groups. It requires differentiated instruction knowing what the precise reason(s) why the student is failing. Use existing materials you already have.
Do you have Power of Ten? If so, in All the Facts sheets where are they struggling? http://poweroften.ca/index.php?option=com_content&view=article&id=38&Itemid=102
Can your students verbalize the strategy that they use? If so, is it an efficient strategy? Do they need to experience more efficient strategies?
When assessing your student begin with the concrete. Remember DO NOT only assess paper pencil- symbolic representations and make evaluation judgements based on this data, especially with your struggling students. concrete_abstract March 31 The Concrete to Abstract Continuum
It is important that, in learning mathematics, students be allowed to explore and develop understandings by moving along a concrete to abstract continuum. As understanding develops, this movement along the continuum is not necessarily linear. Students may at one point be working abstractly but when a new idea or context arises, they need to return to a concrete starting point. Therefore, the teacher must be prepared to engage students at different points along the continuum.
How can we self-educate to best understand the developmental process of mathematical understanding?
These are two approved resources that you will find valuable. Our library has these resources for borrowing.
VanDe Walle :Teaching Student Centered Math
NCTM Teaching Children Math journals
Another book I like is Guiding Children’s Learning of Mathematics – 12th Edition by Steve Tipps, Art Johnson, Leonard M
Small Group Instruction or PODS may be the answer to differentiate instruction to meet the needs of all learners.
Earlier post: http://blogs.gssd.ca/smuir/?tag=math-pods
Debbie Diller has a great resource ( K-3) . You can view her entire book on line.
Talk Points for math stations: Simple buttons record and replay up to 10 seconds of clear sound. Use for activity instructions, reminder messages, word or sound practice, math fact exercises, speech therapy and more. Provide immediate self-assessment. Record and re-record instantly, or flip the switch to lock. Five bright colors. Measures 1 3/4″ in diameter. Grades PreK+
P4.2 Demonstrate an understanding of equations involving symbols to represent unknown values by: * writing an equation to represent a problem * solving one step equations.
Represent and solve a multiplication or divison problem involving equal grouping or partitioning (equal sharing) using a symbol to represent the unknown.
P3.2 Demonstrate understanding of equality by solving one-step addition and subtraction equations involving symbols representing an unknown quantity.
Some Indicators: [C, CN, ME, R]
a. Share, compare, and distinguish between understandings and uses of the word equal, including those represented in First Nations and Métis worldviews.
b. Observe and describe situations relevant to self, family, or community in which a symbol could be used to represent an unknown quantity.
c. Explain the purpose of the symbol, such as a triangle or a circle, in an addition or subtraction equation
f. Verify (concretely, pictorially, or physically) which of a set of given quantities is the solution to one-step addition or
h. Explain why the unknown in a given addition or subtraction equation has only one value.
i. Create and solve one-step equations related to situational questions.
We will use variables, or symbols, to represent numbers in equations, also equality and inequality.
We will be asking the third grade students ” What does this ( = ) mean? Many students think that the equal sign means ‘the answer is…’. Most students think that they should carry out the calculation and the answer follows. Many grade three students do not see the equal sign as a symbol that expresses the relationship of quality or the same as.
We will be exploring the concept of balance or equality by solving one step equations.
To demonstrate this concept we will be playing games using the Power of Ten (Salute and Advanced Salute) along with representing using the mathematical tools such as ten frames and the part-part whole model.
An Entrance Slip will be given the following day to asess their understanding.
Virtual Tools and concrete pan balance tools will be used to solve situational problems:
one red square = one red square, or 1s = 1s, using variables. This demonstrates the Reflexive Property of Equality, a = a.Remind students to “Reset” the balance to show 2 pink triangles = 2 pink triangles, or one yellow diamond on each side.This property may also be demonstrated with with a pan balance in the classroom, placing 3 blue blocks in the left pan, and 3 blue blocks in the right pan. To develop kinesthetic understanding of the Reflexive Property of Equality, have students hold 3 cubes in their left hand, and 3 cubes in their right hand.When demonstrating to the class, you may use the following linkto keep a constant set of relationships, which may be helpful when leading the discussion.
To demonstrate the Symmetric Property of Equality, if a = b, then b = a,place 1 red square in the left pan and 2 blue circles in the right pan. Ask students, “What if I put 2 blue circles in the left pan? What must I put in the right pan?”
[1 red square].
Reset, and demonstrate 1 pink triangle = 3 yellow diamonds. Using the Symmetric Property of Equality, ask students, “What will balance 3 yellow diamonds placed in the left pan?
Thinking Blocks I really like Thinking blocks as it gives a great problem and allows you to build the problem based on what you know and do not know. It models the math problem to help you find the unknown.
Students will be given time to explore, in small groups, the 3D materials that they brought to school. As they are exploring, record the language that they use such as rolls, slides, stack, etc. Document through the use of photos. Once they have had had time to explore and documentation of all of the groups have been completed, meet in full group.
