1. Subtraction using the standard algorithm
4th Grade
Subtraction using the standard algorithm

2. Transition to 4th Grade 4.NBT.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
show standard, then show objectives written from the standard on next slide

3. Possible Objectives
Add multi-digit whole numbers using the standard algorithm.
Subtract multi-digit whole numbers using the standard algorithm.
Have standard written out on chart paper and post for reference when looking at the objectives.

4. Objective:
Today we will subtract multi-digit whole numbers using the standard algorithm.

5. Prior Knowledge
562 – 115
3.NBT.2-Fluently add and subtract within 1000 using strategies based and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Students, you already know how to add and subtract within 1000 using concrete models, drawings, and various strategies. Before we move on to today’s lesson, you must prove to me that you can subtract within 1000 using a strategy of your choice.
Matched pairs- Model 1st with a strategy, have participants do second one. Record both problems on the whiteboard for reference during skill development to make the connection between the strategy and why we do what we do with the standard algorithm.
Today we will subtract multi-digit whole numbers using the standard algorithm.

6. Concept
Multi-digit whole numbers-numbers made up of three or more place values. Standard algorithm-a set of predefined steps that gives the correct result in every case when the steps are carried out correctly.
Today we will subtract multi-digit whole numbers using the standard algorithm.

7. Skill Development-I Do
Steps:
Read the problem and write it vertically, if needed.
Subtract the ones place.
Subtract the tens place.
Subtract the hundreds place.
Today we will subtract multi-digit whole numbers using the standard algorithm.

8. Skill Development-We Do
Steps:
Read the problem and write it vertically, if needed.
Subtract the ones place.
Subtract the tens place.
Subtract the hundreds place.
Today we will subtract multi-digit whole numbers using the standard algorithm.

9. Skill Development-I Do
Steps:
Read the problem and write it vertically, if needed.
Subtract the ones place.
Subtract the tens place.
Subtract the hundreds place.
Today we will subtract multi-digit whole numbers using the standard algorithm.

10. Skill Development-We Do
Steps:
Read the problem and write it vertically, if needed.
Subtract the ones place.
Subtract the tens place.
Subtract the hundreds place.
Today we will subtract multi-digit whole numbers using the standard algorithm.

11. Possible Next Steps
Continue with variations that require exchanging/decomposing more than once. (over multiple place values)
Using Mobi- show how each of these might look without getting into the skill steps. Just a snapshot of the final product.

12. Multiplication using area model
4th Grade
Multiplication using area model

13. 4.NBT.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

14. Possible Objectives Multiply whole numbers using an area model.
Multiply whole numbers using strategies based on place value.
Multiply whole numbers using the properties of operations.
Have standard written out on chart paper and post for reference when looking at the objectives.
Remind teachers of the parameters set out in the standard: a whole number of up to 4 digits by a one-digit whole number, and two 2-digit numbers.

15. Objective:
Today we will multiply whole numbers using an area model.

16. Prior Knowledge
8 X 7
5 x 7 9 x 3 4 x 10
3.OA.7
Fluently multiply and divide with 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Students, you already know how to use various strategies to multiply within Some of the strategies you have learned include using drawing/picture/arrays, decomposing numbers, fact families, doubles, etc. Before we can move on to today’s lesson, you must prove to me that you can multiply within 100 using the strategies you have learned.
Matched pairs-Model 1st 8 x x 2 = 56
Have participants do 2nd
Today we will multiply whole numbers using an area model.

17. Concept 7 4 28 Example: Product Factors
Area model of multiplication-a pictorial way of representing multiplication.
The length and width of a rectangle represent factors.
The area of the rectangle represents their product.
Example:
Factors 7
Product 4 28
This is an example because it shows the two factors represented as length and width on a rectangular array, with the area representing the product.
Today we will multiply whole numbers using an area model.

18. Concept 4 x 7 Non-example:
Area model of multiplication-a pictorial way of representing multiplication.
The length and width of a rectangle represent factors.
The area of the rectangle represents their product.
Non-example:
4 x 7
This is NOT an example of an area model of multiplication because it shows the equal groups representation. 4 groups of 7
Today we will multiply whole numbers using an area model.

19. Skill Development-I Do
Steps:
Read the problem.
Build the length and width factors.
Fill in the area.
(record the “draw” on graph paper)
Record the solution. 34 x8
34 x 8
Model under the doc camera using Base 10 blocks, record the “draw” on graph paper with colored pencils, and write/record the solution.
As adult learners, I am pushing all three to make sure participants have a chance to interact with all three components of BDW for multiplication. Mention that in the classroom we would not do the build, draw, write all at the same time. Start with build and record, then transition to draw and record.
Today we will multiply whole numbers using an area model.

20. Skill Development-We Do
Steps:
Read the problem.
Build the length and width factors.
Fill in the area.
(record the “draw” on graph paper)
Record the solution.
14 x 7 14 x7
28 x 3 28 x3
Today we will multiply whole numbers using an area model.

21. Skill Development-I Do
Steps:
Read the problem.
Build the length and width factors.
Fill in the area.
(record the “draw” on graph paper)
Record the solution. 25
x17
25 x 17
Model under the doc camera using Base 10 blocks, record the “draw” on graph paper with colored pencils, and write/record the solution.
Today we will multiply whole numbers using an area model.

22. Skill Development-We Do
Steps:
Read the problem.
Build the length and width factors.
Fill in the area.
(record the “draw” on graph paper)
Record the solution.
14 x 16 14
x16
26 x 18 26
x18
Today we will multiply whole numbers using an area model.

23. Order of Introduction in the classroom
One-digit whole number by two-, three-, and four-digit whole numbers, and two-digit by two-digit whole numbers using:
Area models
Rectangular arrays
Strategies based on place value
Properties of operations
Using Mobi-show how each of these might look without getting into the skill steps. Just a snapshot of the final product.

24. Generating equivalent fractions using an area model
4th Grade
Generating equivalent fractions using an area model

25. 4.NF.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
*denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 100
*visual fraction models include area models, number lines, and set models
show standard, then show objectives written from the standard on next slide

26. Possible Objectives
Explain why fractions are equivalent using an area model.
Explain why fractions are equivalent using a number line.
Explain why fractions are equivalent using a set model.
Generate equivalent fractions using an area model.
Generate equivalent fractions using a number line.
Generate equivalent fractions using a set model.
Have standard written out on chart paper and post for reference when looking at the objectives.

27. Objective:
Today we will generate equivalent fractions using an area model.

28. Prior Knowledge 1 3 2 6 3 4 6 8 2 4 3 8 2 3 3 4 and and
3.NF.3a-Understand two fractions as equivalent (equal) if they are the same size or the same point on a number line.
Students, you already know how to determine if two fractions are equivalent using a number line, which is a visual model. Before we move on to today’s lesson, you must prove to me that you can determine if two fractions are equivalent using a number line.
Matched pairs- Model 1st with written/recording method, have participants do second
Today we will generate equivalent fractions using an area model.

29. Concept
Area model-the shaded portion of a rectangle that represents the fractional amount.
Example:
Today we will generate equivalent fractions using an area model.

30. Skill Development-I Do
Steps:
Partition the rectangle into an equal number of parts, based on the denominator.
Shade the number of parts based on the numerator.
Generate an equivalent fraction.
Model using Mobi
Examples from NC unpacked content
Today we will generate equivalent fractions using an area model.

31. Skill Development-We Do
Steps:
Partition the rectangle into an equal number of parts, based on the denominator.
Shade the number of parts based on the numerator.
Generate an equivalent fraction.
Guide using the Mobi, with gradual release
Examples from NC unpacked content
Today we will generate equivalent fractions using an area model.