WELCOME TO THE NUMBER GARDEN
Little numbers.
Big ideas.
Build a number. Grow equal groups. Explore a fraction. There’s more than one way to show what you notice.
Untimed exploration. Grown-up help is welcome.
CHOOSE BY SKILL
What will you discover today?
Count & build
Make small groups, fill a ten-frame, and explore tens and ones.
Start with small numbers ↓Fraction Discoveries
Build equal parts, explore a number line, compare amounts, and find equivalent fractions.
Open the fraction pathway →Ratio Investigations
Scale a mixture, work with ratio tables and unit rates, and investigate proportional relationships.
Open the ratio pathway →Selected early, elementary and middle-school starters are available. Complete K–8 math coverage is still being developed.
MOVE IT. BUILD IT. EXPLAIN IT.
Your hands-on math labs
Build a number with Max
A blue rod is a group of ten. A yellow square is one. Start with 34, then change the number and explain what happens.
3 tens
4 ones
30 + 4 = 34
34 is 3 tens and 4 ones.
34 = 30 + 4: draw 3 ten-rods and 4 single squares. Add one square. Then draw a model for 40.
Try a little exchange
Build 39 and add 1. Ten ones can be exchanged for one ten, so 39 + 1 = 40. At 40, take 1 away: exchange one ten for ten ones, then remove one. You have 3 tens and 9 ones.
This model explores whole numbers from 0 to 99.
Grow equal groups with Aven
Choose how many garden beds to make and how many counters to put in each. Every bed has the same number.
3 × 4 = 12
3 beds with 4 counters each. 4 + 4 + 4 = 12.
Draw 3 beds with 4 counters in each: 4 + 4 + 4 = 12. That is 3 groups of 4, or 3 × 4 = 12.
Turn the idea around
If you share 12 counters equally among 3 beds, each bed gets 4. This is the related division fact: 12 ÷ 3 = 4.
Try 4 beds with 3 counters in each. The total is still 12, but the number of groups and the amount in each group have changed.
START WITH A LITTLE GROUP
Small numbers you can see.
Predict first, then use a toggle to see what changes. Try it again with blocks beside the screen.
Grow a group of five
Start with three yellow counters. Add two blue counters, then count them all.
3 yellow counters. How many will there be with 2 more?
3 + 2 = 5. Five counters altogether.
Fill the ten-frame
Seven spaces are filled. How many more counters will fill this frame?
7 filled spaces. 3 empty spaces.
7 + 3 = 10. The frame is full!
Try another way to make ten with blocks on your own paper.
A little take-away story
You have five apples. Put two aside. How many are left?
5 apples are here.
5 − 2 = 3. Three apples are left.
TAKE THE IDEA OFF THE SCREEN
Show it your own way.
Choose a challenge, draw or build your answer, and open the explanation after you try. Use large blocks with younger learners.
Count & compare
Make a group of 4 blocks and a group of 2. Which has more? How many altogether?
Check & explain
The group of 4 has more. There are 6 altogether. Touch each block once as you count.
Make ten
Start with 7 counters. How many more do you need to make 10?
Check & explain
You need 3 more. Count on 8, 9, 10, or use the empty spaces in a ten-frame. 7 + 3 = 10.
Add & take away
Start with 8 blocks and put 3 aside. How many remain? How can you check?
Check & explain
5 remain. Put the 3 back: 5 + 3 = 8.
Tens & ones
Draw bundles of ten and single dots for 34. Add 12. What changes?
Check & explain
34 is 3 tens and 4 ones. Add 1 ten and 2 ones to get 4 tens and 6 ones: 46.
Equal groups
Draw 3 plates with 4 dots on each. How many dots altogether? Share 12 equally among 3 plates.
Check & explain
3 groups of 4 make 12. Sharing 12 among 3 plates gives 4 per plate.
Fraction detective
Draw a rectangle, divide it into 4 equal parts, and shade 2. Name the shaded fraction two ways.
Check & explain
2/4 is shaded, which is the same amount as 1/2 of this rectangle. The parts must be equal in size.
Open your discovery star
“Today I noticed…” Tell your grown-up one strategy you tried or one idea you want to explore next.
FOR PARENTS & TEACHERS
Let the explanation matter.
Help your learner choose a start
Use skills as the guide. Begin with small quantities when counting is uncertain. Explore place value when groups of ten make sense. Choose fractions or ratios after checking the prerequisites in those pathways.
Ask “How do you know?”
Invite pointing, drawing, building, speaking or writing. Help the learner connect the model to the equation. A different method can be useful if it represents the same quantities correctly.
Use a model, then try without it
After a few supported examples, ask for a fresh example on paper. Return another day to see what the learner remembers. Completing an activity here does not establish mastery.
Keep the next step manageable.
Try one lab or a short part of a pathway. Take breaks freely. These tools do not save scores, create child profiles, or replace a full math curriculum.
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