# MATH STUFF #13

## 2ND 9 WEEKS - SKILLS BLOCK 5TH GRADE WEEK 7

· Multiplication/Division Fact Fluency-each student is working on activities to support their individual goal

· Mini-lessons for Math Practice – Comparing Fractions pg 24 – Do not use the “Extending the Activity” section at this time

· Support Activity #30: Money, Fractions & Decimals - See Eduphoria-Fact Fluency Tab – 5th Grade Fluency pg 279

· Repeat Support Activity #27: Fraction Race Game from Last week and/or Wipe Out Game from week 5

## Direct Instruction…Do We Need It? By Donna Boucher

I thought that would get your attention! Now just hear me out. I want you to consider that there is really very little in math that students must learn through direct instruction, that is explicit instruction from a teacher. Let me give two examples, and then I’m sure you can think of others.

Take, for example, expanded notation [eg., 234 = (2 x 100) + (3 x 10) + (4 x 1)]. Yes, students need to be directly taught the conventions for writing a number in expanded notation. They would have no way of knowing that we put parenthesis around each multiplication expression, nor could they discover it through exploration. But they can construct their own learning about what expanded notation is (describing the value of each digit using a multiplication expression) through exploration with base-ten blocks and careful questioning by the teacher. Be sure to check out this blog post for more on that.

Another great example is decimal equivalencies. Say, for example, you are trying to teach the concept that 0.4 and 0.40 are equivalent. That is a very abstract concept for students to grasp through direct teaching. Instead, have students use base-ten blocks to build 0.4 and 0.40. Note that when using base-ten blocks for decimal values, we typically use the flat to represent ones, the rod for tenths, and the unit for hundredths. If they build those two numbers, how could the not see the equivalence? Have them build a few more similar pairs (0.7 and 0.70, etc.) and then have them explain why the two numbers in each pair are equivalent.

Need decimal place value mats? Grab the ones pictured for free by clicking here.

In her book What’s Math Got to Do with It?, Jo Boaler describes traditional teaching methods as passive learning. She cites years of research that underscore how ineffective the lecture-demonstrate-practice cycle of teaching is for student learning. I love this quote: “Students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems.” If we want deeper understanding (and don’t we?), we must move past stand and deliver teaching.

The idea of direct teaching vs inquiry is not really a debate about small group instruction vs whole group instruction. It’s more a teaching style and philosophy. Unfortunately, direct instruction happens as often in a small group setting as in whole group instruction. The shift we need is more toward facilitating learning through thoughtful questioning and away from telling and showing students what they need to learn.

Do you notice the other common thread that is a must for learning through discovery? Students must be allowed to explore concepts with concrete materials for discovery to occur!

## 2ND 9 WEEKS - SKILLS BLOCK 4TH GRADE WEEK 7

· Multiplication Fact Fluency-each student is working on activities to support their individual goal

· Investigation Unit 4 Session 1.1: Measurement Benchmarks – Create anchor charts of items that are about 1 cm, 1 yd, etc… Important note: Linear measurements are recording the measurement of a 1-d object or part of the object. This is important when differentiating between area and perimeter. Perimeter measures length, just one dimension. Area measures the space in the middle which has 2 dimensions, length and width. Make sure to do the discussion about “Why do our measurements differ?”

· Repeat Last Equation Wins or Racing Fractions from daily lessons

In her book How Children Learn Number Concepts, Kathy Richardson devotes an entire chapter to composing and decomposing numbers. It may surprise you that the title of the chapter is Understanding Addition and Subtraction: Parts of Numbers. This quote sums it up beautifully:

## “If basic facts are to be foundational, they must be based on an understanding of the composition and decomposition of numbers.”

Both the CCSSM and Texas TEKS have a number of standards in Kindergarten and 1st Grade related to composing and decomposing numbers, as shown in this table.

One important feature of the standards that is often overlooked is that they describe the level of concrete or pictorial support a student should receive. Notice that K.OA.3, for example, states that students should use “objects or drawings” and record the decomposition using a “drawing or equation.” In that one standard, you hear each phase in the concrete, representational, abstract (CRA) sequence of instruction. Notice how the concrete and pictorial are tied to the abstract (equation) to help students make that important connection. Rushing students to abstract, or purely symbolic, learning is a recipe for disaster, and that is recognized in the standards.

Composing and decomposing numbers is such a critical component of number sense that it should constitute a a major part of the learning that takes place in Kindergarten and 1st Grade. Richardson states, “As children learn the combinations that make up the numbers to 10, they will reach the point where they know the parts so well, they can identify a missing part when they know the total and one part.” In other words, students need lots of practice composing numbers, working with the various combinations of each number, before they will be able to decompose numbers, or find a missing part. In your bag of instructional tricks, you will want to have a wide variety of activities to practice composing and decomposing numbers.

These blog posts will give you ideas for activities as well as freebies you can use this week!

For all of these activities, it’s important to understand that students should master the combinations for one number before moving on to the next. It does no good for a child to practice composing and decomposing 6 if he does not know the combinations for 5. That’s where differentiation comes in. Richardson describes using the “hiding assessment” to determine a child’s fluency with each number. To determine if a child knows all the combinations for 3, ask the child to count out 3 counters or linking cubes. Hide some counters and show some, asking the student to identify how many are hidden. For example, hide 1 counter and show 2. “If I have 3 counters and 2 are showing, how many are hidden?” Continue this routine for each combination for 3 (hide 3, show 0; hide 2, show 1; hide 0, show 3). If the student can name all the missing parts for 3, try the combinations for 4. When the student can no longer easily name the missing parts, that becomes her number. Use a recording sheet to keep track of each student’s number so you can differentiate activities, such as those described above, based on each student’s needs. For example, all students might be using Shake and Spill in a workstation this week, but each child is using his or her own target number. Every few weeks, “test” your students to determine if they are ready to move on to a new number.

While it might seem daunting to differentiate based on each student’s number, the good news is that a few engaging activities go a long way. Constantly rotating the activities keeps engagement high and allows you to meet the needs of each student without a great deal of prep work. For more great activities, check out Building Number Sense: Games and Activities to Practice Combinations for 10 or these other blog posts tagged with the key word “compose.”

## 2ND 9 WEEKS - SKILLS BLOCK 3RD GRADE WEEK 7

· Wrap up addition /subtraction fact fluency- Identify students who have not met expectations and need extra support-create a plan to meet their needs

· Continue Decomposing Facts

· Continue Multiplying by 10 and multiples of 10 (20,30,40,etc…) Do NOT use the phrase “put a 0 on the end” it forms misconceptions in student understanding

· The Relationship Between Multiplication and Division – See Unit 5 pg 148 & 175 Problems can be solved by either operation if you can justify your thinking…

## MATH APPS

CuriousRuler | How to use the app
iPad Apps For Kids: Oh No Fractions!