Starting the Multiplication Unit

We believe there are 3 non-negotiable skills for fifth graders moving on to sixth grade:

  • Fractions
  • Multiplication
  • Division

Accordingly, we spend more time on these 3 units than most schools do, although we work in a handful of additional topics as well. The payoff comes later —  middle school (and high school!) teachers don’t have to reteach these topics. A goal in itself! Continue reading Starting the Multiplication Unit

Review Lesson: Fractions, Word Problems and Patterns.

These 4 problems actually took a whole period! Problem-solving takes time.

CW review

We did this review in groups of 3, with some students rotating after each problem, but the rotation is not necessary. (See Alpha Beta Gamma post from Sept) Rotation breaks up the period with a little movement, and decreases group competition.

Problem #1: Claire has 4 cookies more than Max. Max has 3 times as many cookies as Oliver. Altogether they have 81 cookies. How many does Claire have?

VERDICT: The kids have got it now. Continue reading Review Lesson: Fractions, Word Problems and Patterns.

3 Investigations and 3 Homeworks – Investigating Patterns

INVESTIGATION 1:   Visual Patterns

We spend one lesson investigating patterns we choose from this website:

It is best to start with patterns like #2, #15, #18,  that add a constant number of objects at each step.

Concrete/pictorial students will spend the time they need to build or draw the next few steps in a pattern, and count the new totals at each step. Watch for leaps of intuition when a student gradually begins to see a pattern emerging, and takes the risk of predicting the 10th or the 43rd term. Continue reading 3 Investigations and 3 Homeworks – Investigating Patterns

The Collatz Conjecture via Mathpickle

Unbeatable! Combining a Greek myth with an investigation with a reward attached!

We start our investigation of patterns every year with this contest offered by Mathpickle:

We start with any youtube video of the tale of Icarus. Then we show the video from mathpickle (link above). They claim to be offering a $1,000,000 prize to any child who can find a number that does NOT end with one when we follow these 2 rules: Continue reading The Collatz Conjecture via Mathpickle

Can ‘Not Knowing’ be Engaging? Can ‘Figuring it Out’ Be Fun?

Once again, this investigation is not about the answers, it’s about the seeing, thinking, talking, and discovery of patterns. It takes weeks to break students’ misconceptions that math is all about the answers at the back of the book. Children need daily excursions into the territory of “I wonder…”, “What if…”, and “I don’t know; what shall I do?” (best answer – an intrigued shrug!) . As they discover that the patterns are there, on the table (or floor, if that’s where they’re working!) – that they’re there, to be seen, their confidence grows.
We have to be careful not to push, not to squash the delicate tendrils of discovery. We mustn’t judge one student’s work as better than another’s because it is more abstract. Everyone sees what they see. Trust that insights are happening. Continue reading Can ‘Not Knowing’ be Engaging? Can ‘Figuring it Out’ Be Fun?

More on Assessment – Takeaways from our Second Quiz

Quiz 2 Word doc here:   Quiz 2

This quiz only had 3 questions, since Quiz 1 took too long.


This student has made progress since last quiz (when he had all the bars different sizes. This time, 2 of his bars are the same, but the 3rd bar has a different size. We’ll schedule time to work with him on this. Back to the Toblerones!


Continue reading More on Assessment – Takeaways from our Second Quiz

What Does a Daily Lesson Look Like? Four Days of Activities

October Unit: PATTERNS, especially squares. Homework will continue to review fractions and word problems visually.

What does a daily lesson look like?

1. HW

  • Every other day, students hand in HW, and retrieve and correct the last HW. We mark any mistakes on their HWs, but it is their job to correct them. We put an answer key on the board – it shows work – but they cannot bring a pencil if they come to look at it. They only read it, and return to their seats to correct. For each mistake, they write a “Note to Self” reflection.  “Draw more carefully”, “Only draw unit boxes the same size if they’re the same”, “When adding fractions in 12ths, make all the fraction bars the same size”, for example. HW corrections take 5 minutes or so.
  • We collect their binders about once a week to check corrections.
  • Here are HW #6, and #7 and their keys.

Continue reading What Does a Daily Lesson Look Like? Four Days of Activities