Unit 3: Grade 6: Number Sense and Numeration (Addition and Subtraction – with student work)

Overall Expectations

By the end of Grade 6, students will:

• solve problems involving the multiplication and division of whole numbers, and the addition and subtraction of decimal numbers to thousandths, using a variety of strategies;

Specific ExpectationsOperational Sense

- By the end of Grade 6, students will: – use a variety of mental strategies to solve addition, subtraction…multiplication, and division problems involving whole numbers (e.g., use the commutative property: 4 x 16 x 5 = 4 x 5 x 16, which gives 20 x 16 = 320; use the distributive property: (500 + 15) ÷ 5 = 500 ÷ 5 + 15 ÷ 5, which gives 100 + 3 = 103);

- add and subtract decimal numbers to thousandths, using concrete materials, estimation, algorithms, and calculators;

Lesson Plans:

Notes:

- addition - mental math strategies – a few intro questions- addition - estimating- addition - traditional- addition multiple numbers- addition using decimals (the same amount – all numbers to the thousandths)- addition using decimals (not all the same decimal place values: 1.543 + 4.2 + 2.34)- subtraction – mental math strategies – a few intro questions- subtraction - traditional- subtraction of larger numbers- subtraction using decimals

Lesson 1 – Addition: Mental Math Strategies (review)

Question 1 – Solve the following problem in as many different ways as you can (342 + 215 =)

Some students broke numbers up into their expanded form to answer the question. We later talked about how you can either expand both numbers, or just expand the second number (in which case it becomes a kind of “Add-on” strategy:

Some students (in one of the solutions) did what they called “rounding”, but what ended up being a kind of “compensation” strategy (which we labeled “Switcheroo” in our anchor chart during the consolidation):

Some students used a traditional strategy:

Consolidation: We took all the ideas and put them up on the board. The conversation then focused on mental math strategies (how we do math in our heads)

And so we made an anchor chart for the class:

Review Splitting Strategy (using expanded form)Add-on Strategy (start at biggest number, count up using expanded form of other number)Moving Strategy (move numbers from one number to the other number to make it friendly)Traditional

Lesson 2 – Addition: Estimation

Question 2 – Rocket Question

Some students “gamed” the system by answering the second question first, and the first question second:

Some students rounded, but rounded the numbers to different PVC’s. In this case rounding two of the numbers to the ten-thousands, and one to the hundred thousands:

Some students rounded to two numbers to the thousands, and one number to the ten thousands:

Some students correctly rounded all the numbers to the same PVC (ten thousands, thousands, or hundreds):

Consolidation: We focused our conversation around the idea that ALL numbers in a question that asks for rounding or estimations, have to be rounded to the same PVC in order to give a reasonable answer.

Practice: Grade 6 – Question 2 – Sheet 1 (estimation only)Grade 6 – Question 2 – Sheet 2 (estimation only)

Lesson 3 – Addition: Traditional

Teacher Directed – practice sheets for traditional addition

Lesson 4 – Addition: Multiple Numbers

Question 3 – Tesla Question – A 2 part question which traditionally would use addition and then subtraction to answer (but not necessarily):

Some students used subtraction to answer the question:

Some students used only addition to answer the question, finding the difference at the end by counting up to the higher number:

Some students did the addition steps one at a time (more accurate, less mistakes, less efficient):

Some students used an efficient addition strategy (stacking) and an efficient subtraction strategy:

Consolidation: We talked about when stacking to do addition there are 2 efficient ways to add…Traditional vs… adding hundreds PVC, then tens PVC, then ones PVC. Also we talked about the advantages of adding altogether as a stack, or adding one number at a time.

395 242+ 119 600 140 16 756

Practice:https://www.math-drills.com/addition/addition_column_3digit_3numbers_001.phphttps://www.math-drills.com/addition/addition_column_3digit_4numbers_001.phphttps://www.math-drills.com/addition/addition_column_xdigit_3numbers_001.phphttps://www.math-drills.com/addition/addition_column_4digit_4numbers_001.php

Lesson 5 – Addition with Decimals

Question 4 – Cups question

Sorry, forgot to take pictures of student work

Consolidation: Focus on lining up the decimals

Practice:https://www.math-drills.com/decimal/decimals_addition_ones_thousandths_001.php

Lesson 6 – Addition with Decimals of different PVCs

Question 5 – Bunny Contest Question

Some students added one step at a time in order to avoid mistakes:

Some students added zeros to the missing PVCs (in the hundredths and thousandths PVC – 2.1 becomes 2.100) in order to avoid making mistakes, and making it easier to get all the digits to line up:

Some students drew lines between PVCs in order to avoid making mistakes:

Some students just neatly stacked and added:

Consolidation – Our conversation focused on lining up decimals. We also discussed the question, “Can you use mental math strategies on decimal problems?” So we gave it a try

Practice:https://www.math-drills.com/decimal/decimals_addition_ones_mixed_001.php

Lesson 7 – Subtraction: Mental Math Strategies (Review)

Question 1 – School Library Question

First we talked about what important information they need from the question, and what information is not necessary.

The students came up with a number of different strategies:

Consolidation – We reviewed mental math strategies:

Review:Add-On strategy (count up from smaller number to larger number)Partial Subtraction Method (break up second number into its expanded form and subtract)Constant Difference Strategy (make the second number friendly by adding or subtracting, then do same

to first number)Traditional

Lesson 8 – Subtraction of Larger Numbers

Teacher directed: practice of traditional subtraction

Practice:subtract 3 digit numbershttps://www.math-drills.com/subtraction/subtraction_multidigit_0303_001.phpadd/subtract 4 digit numbershttps://www.math-drills.com/multiop/mixed_addition_subtraction_4digit_4digit_some_regrouping_001.phpadd/subtract 5 digit numbershttps://www.math-drills.com/multiop/mixed_addition_subtraction_5digit_5digit_some_regrouping_001.php

Lesson 9 - Subtraction problems – multiple steps

Question 2

Some students added did one step at a time (no stacking) which is less efficient, but you are also less likely to make mistakes:

Some students drew lines to separate the PVSs to make sure no silly mistakes would occur:

Some students simply stacked and added:

Some students used an inequity symbol to show their answer:

Some students took it a step further and showed exactly how close they were to their goal (the subtraction part of the question that I thought everybody would do). This is level 4 thinking:

Consolidation: We focused our conversation around strategies we use to keep ourselves organized, and to prevent silly errors. We also discussed the idea of taking our work one extra step forward by doing a bit more than what is asked

Practice:Sheet: Grade 6 - Subtraction - Question 2 sheet 1 - Multi step problemsSheet: Grade 6 - Subtraction - Question 2 sheet 2 - Multi step problems

Lesson 10 – Subtraction Using Decimals

Question 3 – Protein Powder

Consolidation:We focused on all the silly mistakes being made, and how they can lead to the wrong answer. The examples below show where the silly mistakes happened in several questions:

And what the answer should be if you are careful not to make mistakes

Lesson 11: More multi-step problems

Question 4:

Fun question, but again, I forgot to take pictures of the student work.

Consolidation: We discussed how time must be spent understanding the question, before attacking the math.

Lesson 12: Evaluation

Addition and Subtraction Test