# Ways of Knowing: Subtraction

## If you want to build proficiency with subtraction at any grade, you must not be afraid to move things in your head.

Start by moving things in real time and discuss the affects of the move. So here is a ChunkitZ puzzle. I see 3 and 2. That’s 5.

How do I know this is still 5? I turned the 2, (quarter turn left)  flipped it over (reflected) and slid it down to match the left hand side.

I see 8 = 8 because I see 6 + 2 in each of them.I turned the 6 (one quarter turn to the left). Then I slid the dot on the far left side of the middle row down below and lined up with the middle bottom dot. I slid the dot on the far right side of the middle row up. It is above and lined up with the middle top dot. It is still 6 and 2.

## NUMBER TWO: Subtraction is an action that emerges when you want to make things equal or maintain equality. These are not equal. One way to make them equal is to remove from one side.

IT IS CALLED SUBTRACTING not take away. first I did a quarter turn to the left. Then I removed one dot and pushed the other to the right. Yes, the action was a removing action but the mathematical term is subtract and the sign we use is a subtraction or minus sign. WHEN STUDENTS HAVE THE VOCABULARY, THEY CAN JOIN THE MATH COMMUNITY. Vocabulary is a part of community. You have to speak the language to join the club. we correct DA DA to become daddy or dad or even father but we leave take away??? I do not agree. You do not take away to solve every subtraction problem.

## Number 3: Addition and Subtraction are RELATED. Teach them together, first as a relationship.

If you can add, you can subtract. Since 1997, the Western Protocol for Mathematics and the Alberta Program of Studies for mathematics which emerged from it, has stated this as an outcome in mathematics. Students need to know and understand that addition and subtraction are related. In the 2004 revision, the statement think addition for subtraction was used as a strategy. HOWEVER, it is not just a strategy it is an actual property of our number system. The focus is relationships before equations. Understand the relationship, talk, describe explain the relationship. Then introduce the notation.  Not the same day, but once they can explain…..

INVERSE OPERATIONS, is a critical understanding students need to be able to apply when they work with integers, rational numbers and algebra.

# Finding Common Ground:

## “WAYS OF KNOWING: KNOWING WAYS”

Thinking101 Institutes are dedicated to fuelling the evolution of learning that is teaching. Every summer, every session deepens the connections between Numeracy, Literacy, Science and Math. The ARTS are INFUSED throughout, a little or a lot. An approach to teaching and assessing that values- no prizes visual/temporal spatial reasoning is an approach that includes EVERY LEARNER, EVERY CULTURE, EVERY BACKGROUND.

It embodies and encompasses a holistic world view, a holistic learning view… we all share the gift of coming to know as a body mind connection… Visual models can bridge any gap be it:  Literacy, Numeracy, Remembering or Recall.

Infographics is more than reading graphs and organizing data. It is an approach that makes connections and patterns burst forward as students discuss and COMPARE.

The focus is thinking and comparing: the teacher role is to prompt, probe, prod…. immerse students in the vocabulary, shape and mould the pathway from seeing and experiencing through thinking and doing to understanding the conventions of the discipline. We do not start from memorizing symbols and rules… but we can certainly end up with understandings of the symbols and rules.

# Finding Common Ground:

## “WAYS OF KNOWING: KNOWING WAYS”

Thinking101 Institutes are dedicated to fuelling the evolution. Every summer, every session deepens the connections between Numeracy, Literacy, Science and Math. The ARTS are INFUSED throughout, a little or a lot. An approach teaching and assessing that values- no prizes visual/temporal spatial reasoning is the BASIC SKILL for learning, anything even MATH FACTS!

This summer my new word is INFOGRAPHICS. The topic is huge and all encompassing. Making sense of the mathematics that is all around us, often used to influence us, often used to bias our decisions. Infographics refers to an approach to actively, deliberately teaching students to connect  and communicate the development of their literacy, numeracy and critical thinking skills through the use of graphics based artifacts. STEM, STEAM with a focus on learning to think, not a focus on making products.

Over the next few weeks I will share samples to demonstrate the breadth and scope of using INFOGRAPHICS as the organizer for curriculum. Here is one:

As a class we looked for connections between the problem told orally and the diagram this student created to share her solution. Here is what we came up with through that discussion. We can now use the information on the diagram to re write the problem or to improve our own solutions.

or to start building the number relationships that will support the kind of number practice Grade twos need to constantly engage in. Do you understand this table that we created from information in the picture?

# They will learn arithmetic faster, more fluently, with confidence, speed and accuracy.

### Here’s an article to consider:

order-of-operations-the-myth-and-the-math

# DO YOU UNDERSTAND NUMBER PROPERTIES??? Then how can you teach NUMBER SENSE?

The evolution has begun, WE WILL CHANGE THE WORLD… Join me for SUMMER INSTITUTES 2017…. Multiplication is not repeated ADDITION… It is much, much more and our KIDS DESERVE TO KNOW “why?” AND “Why DO they have to learn this?” Make the mathematics they learn meaningful in a way that leaves them wanting to LEARN MORE….

LITERACY IS NUMERACY, NUMERACY IS LITERACY and let’s not leave out SCIENCE.  Comprehension, reading and writing skills do not grow in a vacuum. We use the content of math and science in engaging, authentic and challenging explorations and experiments to develop the skills that link them all.

IT IS WELL PAST TIME FOR TEACHING TO EVOLVE OR GO EXTINCT…. THE  world demands it, our kids deserve it…

# Parent letters

I do not and will not support DreamBox or any other on line platform for teaching and learning mathematics but this is one of the components that we really really need to learn from…. Christopher writes a great blog, thanks

Overthinking my teaching

Here is an email that a friend of mine—father of a first grader in the Minneapolis Public Schools, and math-teacher-on-parental-leave—received from DreamBox, an “adaptive learning platform” for K—8 math.

Congratulations! [Child] successfully completed a group of DreamBox Learning lessons.

Are you familiar with the concept of compensation? This is a strategy that can be used to make addition problems “friendlier”. To use it, just subtract a “bit” from one number and add that same “bit” to the other to create two new numbers that are easier to add mentally.

[Child] learned this strategy by completing a series of lessons using the special DreamBox tool, Compensation BucketsTM. For example, when shown the problem 29 + 64, [Child] turned it into 30 + 63. Towards the end of this unit, [Child] was adding 3-digit numbers with sums up to 200!

On the Run: Friendly Numbers

Take turns supplying two numbers to add. The other player has…

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# So what did you see in math class today?

fixed my spleling (ha,ha)

Thinking 101

## So here’s my point folks. We present math ideas with a perspective that pushes students’ focus to the wrong place in the picture or in the manipulative. Then we say see that didn’t work and go back to telling them what to think. Instead, I want you to get rid of “fill in the blank math sheets.” Start giving students fully finished equations and have them learn to read, demonstrate and compare them. What can you change and not affect the outcome.

### What happens if you move the collection around? Knowing 9 is the answer is not the same knowledge as “knowing” 9.  Think about it. We have to do the right job in…

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