Having successfully decoded the Wumanian number system (and further developed their understanding of place value), the preservice teachers begin to explore the concepts of composing and decomposing numbers. This is done through the use of centers - an instructional approach used successfully in many elementary classrooms. In this post, I share some of the more popular activities.

**Yiwu Go Fish**

As with many of the Wumanian center activities, this game has an Earth equivalent.

**Summing Yiwu-yi Cubes**

- With a partner, take turns rolling the dot cubes;
- Using symbols, write the amount shown on each individual cube (see example below);
- Write the total of the cubes combined (see example below); and
- Pass the cubes to your partner and repeat.

**Collecting Coins**

- Use a pencil and a paper clip to create a spinner out of the sectioned circle provided below;
- Take turns using the spinner to determine how many coins to add to your collection;
- Each turn, say how much you had, what you spun, and your new total after adding your spin.
- Keep track of the total worth of the collected coins using the rekenrek;
- Keep spinning until you reach a total of erwuwu pents; and
- If you finish early, play the game in reverse - giving the amount spun away until you reach na pents.

**Fact Finding**

On the addition table, identify which facts fit into which categories (note that some facts will need more than one color):

- Doubles
- Doubles plus or minus yi
- Count up yi
- Sums of yiwu
- Bounce off yiwu

**Story Problems**

In this center, learners work to solve a selection of Cognitively Guided Instruction "Joining" stories.

- There are si people in this group and si people in another group. How many rekenreks will I need if every person gets a rekenrek?
- I have er dot cubes. This center requires si dot cubes. How many more dot cubes do I need?
- A puzzle is made up of yiwu-yi pieces. Some of the pieces are already put together. There are san pieces left to complete the puzzle. How many pieces are already put together?

**Yiwu Fingers**

Yiwu is a benchmark number in the Wumanian system. Students who learn the different ways to decompose this benchmark are often more successful learning their facts and later on developing efficient mental strategies for larger numbers. This song and the accompanying motions (putting up the appropriate number of fingers and spinning around at "Now it's time for turn-arounds") is one way to support students in this area.

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After the preservice teachers rotate through the centers, they are asked to reflect on the experience. I have them focus on how they might apply what they did in each activity to teaching composing and decomposing numbers in our system. Their responses form an assessment that allows me to evaluate whether or not they are able to transfer their experiences in base-yiwu to our base-tem system. Then I can then plan future learning activities based on their current level of understanding, not just what comes next in the curriculum.

My 6th graders work with different bases too, but you take this to a full functional level that's quite lovely. The Center activities nicely reinforce and challenge one's ability to adapt/transfer knowledge from one task to another. I've thoroughly enjoyed your Wumanian series, and I'm sure your preservice teachers appreciated this great PD! Thank you!

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