What Goes Together
Grade 1 teacher guide. All 36 weeks, with the words to say out loud, every answer, and the wrong turn each week produces.
Read the say-this line out loud. The student page carries exactly one sentence, written for a reader who may not read on their own yet. The sentence on the page and the line in this guide are not the same words: the page is written to be decoded, this one is written to be heard.
Every answer below is recomputed from the problem as the workbook states it by verify.py, which ships with the source and runs on every build. It also fails the build if any answer in this guide is left unchecked.
Week 1. One Pile or the Other
Sorting & Rules · In class: Sorting and describing objects
Say thisLook at all the shapes. Some are round and some are not. Put every single one in a hoop.
The first act of the year: hold a rule in your head and use it. Nobody is asked what the rule is, because that is Grade 2 week 1.
On the page
Put every shape in one pile or the other.
Answers
| Round shapes | 3 |
| Blue shapes | 3 |
| Not blue | 5 |
| Shapes in all | 8 |
| Left over | 0 |
| Groups for both rules | 4 |
Watch for. Children who invent a third pile for the ones they are unsure about. The rule has exactly two answers, and saying so is the lesson.
If it stalls. Hand them one shape and ask only about that shape. Then the next one.
Week 2. What Is the Same?
Sorting & Rules · In class: Comparing objects
Say thisLook at these two. Say one way they are the same.
Naming a shared attribute out loud, in a sentence. The sentence is the work.
On the page
Say one way these two are the same.
Watch for. One-word answers. 'Blue' is not yet an answer; 'they are both blue' is.
If it stalls. Give them the sentence frame and let them fill the end: they are both ___.
Week 3. What Is Different?
Sorting & Rules · In class: Comparing objects
Say thisLook at the same two. Now say one way they are different.
Same and different are one skill, asked from two sides.
On the page
Say one way these two are different.
Watch for. Children who repeat the sameness answer with a 'not' in front of it.
If it stalls. Point at one, then the other, and ask what changed between your fingers.
Week 4. Does It Belong?
Sorting & Rules · In class: Organizing objects into categories (1.MD.4)
Say thisEvery shape in this group has three corners. Here are three more. Which ones belong?
Applying a stated rule to something new, and saying why.
On the page
Which of these belong in the group?
Answers
| Belong, second set | 1 |
| Red shapes of four | 3 |
| Not red | 1 |
| Does not belong, red rule | yellow triangle |
Watch for. Children who put a shape in because they like it. Ask for the rule back.
If it stalls. Count the corners out loud together, touching each one.
Week 5. Sort It Two Ways
Sorting & Rules · In class: Organizing objects into categories (1.MD.4)
Say thisSort these six by color. Now push them all back together and sort them again, by shape.
The objects did not change. The piles did. Sorting is a choice, and that is what makes a rule a rule.
On the page
Sort them by color.
Answers
| Red | 3 |
| Blue | 3 |
| Round | 2 |
| Shapes in all | 6 |
| Same piles both times | No |
Watch for. Children who leave the first sort in place and try to make the second one fit around it. Physically sweep the piles together between sorts.
If it stalls. Do the color sort with them, mix them up, then hand them the shape rule.
Week 6. One for Each
Matching · In class: Comparison word problems (1.OA.1)
Say thisHere are the children and here are the chairs. Draw a line from each child to a chair.
One-to-one matching, which is what counting rests on and is worth doing before counting is fluent.
On the page
Draw a line to match each one.
Answers
| Children | 6 |
| Chairs | 4 |
| Children with no chair | 2 |
| Chairs still needed | 2 |
| Children after two more arrive | 8 |
| More chairs needed then | 4 |
Watch for. Children who count both rows and subtract. That is a fine answer and not this week's. Ask them to show it with lines too.
If it stalls. Cover one row with your hand and ask if they can still answer. Then draw one line together.
Week 7. More, Fewer, or Same
Matching · In class: Comparison word problems (1.OA.1)
Say thisMatch them up one to one. When one row runs out, the other row has more.
Comparing two sets without counting either one.
On the page
Which row has more?
Answers
| Red | 7 |
| Blue | 5 |
| Yellow | 4 |
| Green | 4 |
| Row with more, yellow or green | Neither, the same |
| Row with fewer, third pair | Blue |
| More in the long row, third pair | 3 |
Watch for. Children who say 'they are the same' for the 4 and 4 pair without matching. Right answer, no method. Ask for the lines.
If it stalls. Draw the first two lines for them and let them finish.
Week 8. Which Row Ran Out?
Matching · In class: Ordering three groups by matching
Say thisMatch red with yellow. Then match yellow with blue. Now put all three rows in order without counting any of them.
Two matchings settle three rows when they go through the middle row: red beat yellow and yellow beat blue, so red beats blue without a third matching. The first time this year that one fact is used to get another.
On the page
Put the three rows in order.
Answers
| Red | 6 |
| Yellow | 5 |
| Blue | 3 |
| Order, most to fewest | Red, Yellow, Blue |
| Matchings needed | 2 |
| Matchings, four rows in a chain | 3 |
| Fewest of four | Green |
Watch for. Children who count. It works and it is not the point. Ask them to prove it again with lines only.
If it stalls. Ask which row beat yellow, and which row yellow beat. Then ask where yellow goes.
Week 9. What Comes Next?
Patterns · In class: Patterns and reasoning
Say thisSay the pattern out loud with me, pointing. Then draw the next two.
Repeating patterns: AB, then AAB, then ABB. Saying it aloud is what finds it.
On the page
Draw the next two.
Answers
| Next two, first strip | red circle, blue square |
| Next two, second strip | yellow triangle, yellow triangle |
| Next two, page 2 | blue star, red circle |
| After those two | red circle |
Watch for. Children who copy the last two shapes rather than continuing the pattern.
If it stalls. Chant it with them. The voice finds the pattern before the eye does.
Week 10. Find the Part That Repeats
Patterns · In class: Patterns and reasoning
Say thisThis pattern says the same thing over and over. Circle the part that says itself again.
Naming the unit of repeat, which is the thing that makes a pattern a pattern rather than a list.
On the page
Circle the part that repeats.
Answers
| Repeating part, first strip | 2 |
| Repeating part, second strip | 3 |
| Shapes in the repeating part | 4 |
| Times it repeats | 2 |
| 12th shape | red square |
| 16th shape | red square |
Watch for. Circling one shape instead of the group. Ask them to check by covering it and asking whether the rest still works.
If it stalls. Chant it and clap on the first shape of each repeat.
Week 11. It Grows
Patterns · In class: Counting on to add (1.OA.5)
Say thisThis one does not repeat. It grows. Draw the next picture.
A growing pattern is a different animal from a repeating one, and a child who has only met repeating ones will try to start it over.
On the page
Draw the next one.
Answers
| Dots in the fourth picture, first pattern | 4 |
| Dots in the fourth picture, second pattern | 8 |
| Growth each step, second pattern | 2 |
| Dots in the fifth picture, second pattern | 10 |
| Next in 1, 3, 5, 7 | 9 |
Watch for. Children who draw the first picture again, because every pattern they have seen so far came back around.
If it stalls. Write the count under each picture. The numbers make it obvious.
Week 12. Sorting Fair
Sorting & Rules · In class: Review & reasoning
Say thisSort these ten however you like. Then tell me your rule.
Review of weeks 1 to 11. The child picks the rule for the first time, which is a step toward Grade 2 and not yet Grade 2.
On the page
Sort these into two groups your own way.
Answers
| Shapes to sort | 10 |
| Red row | 5 |
| Blue row | 8 |
| Row with more | Blue |
| Next two | green square, yellow circle |
Watch for. There is no wrong sort here, only a sort with no rule behind it. The rule is the answer.
If it stalls. Ask what is the same about the ones in the first hoop.
Week 13. Line Them Up
Order & Time · In class: Ordering three objects by length (1.MD.1)
Say thisLook at the three. Write 1 on the shortest and 3 on the longest.
Ordering by length by direct comparison (1.MD.1). No ruler, no numbers.
On the page
Write 1 on the shortest and 3 on the longest.
Answers
| Shortest of three | Clip |
| Longest of three | Ribbon |
| Shortest of four | Straw |
| Longest of four | Stick |
| Order of four, shortest first | Straw, Spoon, Rope, Stick |
| Longer, straw or spoon | Spoon |
| Closest in length | Rope and Spoon |
| Side-by-side checks, five in a line | 4 |
Watch for. Children who compare the right-hand ends. Every bar starts at the same left edge here, on purpose, so point at the start line.
If it stalls. Cover all but two bars and ask only about those two.
Week 14. Longer Than the Pencil
Order & Time · In class: Comparing lengths using a third object (1.MD.1)
Say thisYou never see the rope and the clip side by side. Use the pencil to work it out.
Indirect comparison (1.MD.1), which is the first genuinely transitive argument in the line.
On the page
Which one is longer?
Answers
| The rope is longer than the | pencil, and so the clip |
| Longer, spoon or nail | Spoon |
| Pencil | 5 |
| Clip | 3 |
| Rope | 8 |
| Straw | 4 |
| Spoon | 6 |
| Nail | 2 |
Watch for. Children who guess. Ask which picture the pencil is in, and then the other picture the pencil is in.
If it stalls. Put a real pencil on the desk and act it out with two objects.
Week 15. How Many Paper Clips?
Order & Time · In class: Length as same-size units (1.MD.2)
Say thisLay the clips end to end with no gaps. Then count them.
Length as a count of same-size units (1.MD.2). The gaps are the lesson.
On the page
How many clips long is it?
Answers
| First bar, in clips | 6 |
| Second bar | 4 |
| Third bar | 9 |
| Third bar minus second bar | 5 |
| Eight clips, in erasers | 16 |
Watch for. Gaps between the clips, and overlaps. Both give a wrong count and both look fine to a six-year-old.
If it stalls. Do it with real paper clips and let them see the gap problem happen.
Week 16. Sort the Shapes
Shape & Space · In class: Defining attributes of shapes (1.G.1)
Say thisCount the sides on each shape. Three sides go in this hoop.
Sorting shapes by a stated attribute (1.G.1).
On the page
Put the shapes with three sides here.
Answers
| Three sides | 3 |
| Four sides | 3 |
| No sides | 2 |
| Corners on a five-sided shape | 5 |
Watch for. Children who count a corner as a side, or count the same side twice going around.
If it stalls. Put a finger on one corner as a start mark and go around once.
Week 17. What Makes It a Triangle?
Shape & Space · In class: Defining attributes of shapes (1.G.1)
Say thisA big red triangle and a small blue one are both triangles. What has to be true?
Defining against non-defining attributes (1.G.1). Three sides matters. Color and size do not.
On the page
Color every shape that is a triangle.
Answers
| Triangles in the first row | 4 |
| Sides on a triangle | 3 |
| Corners on a triangle | 3 |
Watch for. Children who reject a triangle sitting on its point. Orientation is not a defining attribute either, and this week is the place to say so.
If it stalls. Turn the page around and ask if it is still a triangle.
Week 18. Two Shapes Make One
Shape & Space · In class: Composing shapes (1.G.2)
Say thisTwo of these triangles make one square. Show me.
Composing shapes (1.G.2), and the first hint that a whole can be cut and put back with nothing lost.
On the page
Draw two shapes that make this one.
Answers
| Triangles per square | 2 |
| Triangles for two squares | 4 |
| Small squares for two big squares | 8 |
Watch for. Children who overlap the pieces. The pieces have to meet, not cover.
If it stalls. Cut a paper square corner to corner and hand them the two halves.
Week 19. Cut It Fair
Shape & Space · In class: Halves and fourths (1.G.3)
Say thisFold it so both parts are exactly the same. Then draw the fold line.
Halves and fourths by folding (1.G.3). Equal is checked by matching, not by looking.
On the page
Fold it, then draw the fold line.
Answers
| Equal parts after two folds | 4 |
| One fourth, more or less than half | Less |
| Fourths that make the whole | 4 |
| Halves that make the whole | 2 |
Watch for. Folds that are close but not equal, called equal because they look it. Hold it to the light.
If it stalls. Fold it with them once, then let them do the second fold.
Week 20. Around the Table
Dots & Lines · In class: Who sits next to whom
Say thisDraw a line to every friend you sit beside. Only the ones right next to you.
Adjacency drawn as a picture. The word graph is not used here and arrives in Grade 2.
On the page
Draw a line to every friend you sit beside.
Answers
| Lines, four at the table | 4 |
| Lines, five at the table | 5 |
| Neighbors each person has | 2 |
| Lines, six at the table | 6 |
Watch for. Children who draw a line to everyone. Beside means next to, and the distinction is the week.
If it stalls. Sit four children in a circle and ask each who they can touch.
Week 21. Everybody Waves
Dots & Lines · In class: Counting every pair
Say thisEveryone waves at everyone. A wave between two people is one wave, not two.
The handshake problem at n = 3 and n = 4, drawn rather than counted by formula. Grade 3 finds the rule.
On the page
Draw every wave one time only.
Answers
| Waves, three friends | 3 |
| Waves, four friends | 6 |
| Waves each friend sends, four friends | 3 |
| Waves, five friends | 10 |
| Double the answer for four | 12 |
| Five friends, more or less than double | Less |
Watch for. Double counting. A to B and B to A get drawn as two lines and the total comes out doubled.
If it stalls. Do all of A's waves, then cover A and start again with B.
Week 22. Do Not Touch the Same Color
Dots & Lines · In class: Coloring so touching parts differ
Say thisColor it so that no two parts that touch are the same color.
Proper coloring. Two colors are enough on this picture, A and D one color and B and C the other, because parts that meet only at a corner are not touching. That is the challenge's answer. How few colors in general is Grade 2 week 18.
On the page
Color it so no two touching parts match.
Answers
| Regions | 4 |
| Do A and D touch? | No |
| Fewest colors that work | 2 |
| Two colors enough? | Yes |
Watch for. Children who treat a shared corner as touching. It is not, and saying so is worth doing here.
If it stalls. Color one region, then ask what it touches, and rule those out together.
Week 23. Three Buckets
Pictures & Data · In class: Organizing data in three categories (1.MD.4)
Say thisPut each shape in the right bucket. Then draw one dot for each shape you found.
Organizing data into three categories and representing it (1.MD.4).
On the page
Sort them into the three buckets.
Answers
| Circles | 4 |
| Squares | 3 |
| Stars | 2 |
| Shapes in all | 9 |
| Most | Circles |
| Red, sorted by color | 4 |
| Blue, sorted by color | 2 |
| Yellow, sorted by color | 3 |
Watch for. Miscounts from not crossing shapes off as they go.
If it stalls. Cross the first three off together, out loud.
Week 24. Which Bucket Has More?
Pictures & Data · In class: Interpreting data in three categories (1.MD.4)
Say thisLook at the picture. Which row goes farthest?
Reading a picture graph back and comparing (1.MD.4). The comparison is visual before it is numeric.
On the page
Which bucket has the most?
Answers
| Dogs | 6 |
| Cats | 4 |
| Fish | 7 |
| Pets in all | 17 |
| More fish than cats | 3 |
| Cats and fish together | 11 |
| Fewest | Cats |
| More dogs than cats and fish together? | No |
| Cats after two arrive | 6 |
| Most after two cats arrive | Fish |
Watch for. Children who count every dot for the first question. The row that reaches farther has more, and they can see it.
If it stalls. Put a ruler down the ends of the rows.
Week 25. Getting There
Steps & Paths · In class: Finding a path on a grid
Say thisDraw a path from the dot to the flag. One square at a time, no jumping.
Any path, found and drawn. Shortest paths with weights are Grade 2 week 9. The blocks on page 2 do not make the shortest path longer. Closing every path takes two more blocks, for example the top and bottom squares of the middle column, or the two squares next to the dot. Accept any two that leave no way through.
On the page
Draw a path from the dot to the flag.
Answers
| Fewest steps | 7 |
| Fewest steps around the blocks | 7 |
| More squares to block every path | 2 |
Watch for. Diagonal moves. The rule is up, down, left, right, and it needs saying.
If it stalls. Trace one path with your finger first and let them draw a different one.
Week 26. The Short Way
Steps & Paths · In class: Counting and comparing steps
Say thisCount the steps on the first path. Now count the steps on the second.
Counting and comparing two given paths. Both are the same length on purpose.
On the page
Count the steps on each path.
Answers
| Steps, first path | 7 |
| Steps, second path | 7 |
| Shorter path | Neither, both are 7 |
| Fewest possible | 7 |
| Fewer steps than both? | No |
Watch for. Children who assume the wiggly path is longer because it looks longer. It is not, and the surprise is the point.
If it stalls. Have them mark a dot on every square the path enters and count the dots.
Week 27. Follow the Arrows
Steps & Paths · In class: Following steps in order
Say thisDo the arrows in order. Put your finger on the new square each time.
Executing a short program. Grade 2 adds repetition.
On the page
Do the arrows and color where you land.
Answers
| Landing square, first set | 2 right, 1 up from the dot |
| Landing square, second set | 2 right, 2 up from the dot |
| Steps up, second set | 2 |
| Same square in another order? | Yes |
| Four arrows back, one answer | up, right, down, left |
Watch for. Children who read all three arrows and jump. One at a time, finger down.
If it stalls. Do the first arrow for them and hand the page back.
Week 28. Write the Arrows
Steps & Paths · In class: Finding an unknown number to add (1.OA.8)
Say thisYou know where you start and where you finish. Write the arrows yourself.
The inverse problem, and the first missing-addend shape of the year (1.OA.8).
On the page
Write the arrows that get you there.
Answers
| Arrows needed, first grid | 4 |
| Going right, first grid | 2 |
| Going up, first grid | 2 |
| Arrows needed, second grid | 5 |
| Going right, second grid | 3 |
| Going up, second grid | 2 |
| Orders of 2 right and 2 up | 6 |
Watch for. Children who write the arrows in an order that walks off the grid. The order matters even though the totals do not.
If it stalls. Count the squares across, write those arrows, then count up.
Week 29. A Ten and Some More
Numbers & Tens · In class: Tens and ones (1.NBT.2)
Say thisFill the first frame all the way. Then start the second one.
A teen number as one ten and some ones (1.NBT.2), seen in the frames rather than told.
On the page
Write how many tens and how many ones.
Answers
| First number | 13 |
| Tens in it | 1 |
| Ones in it | 3 |
| Second number | 17 |
| Third number | 10 |
| Ones in the second frame, third number | 0 |
| Frames to show 20 | 2 |
Watch for. Children who fill both frames unevenly. The first ten has to be complete before the second frame starts, or the picture says nothing.
If it stalls. Fill the first frame with them, counting to ten out loud.
Week 30. Ten More, Ten Less
Numbers & Tens · In class: Ten more, ten less (1.NBT.5)
Say thisTen more is one row down. Ten less is one row up.
Ten more and ten less on a hundred chart (1.NBT.5), as a move rather than an addition.
On the page
Circle ten more, then circle ten less.
Answers
| Ten more than 34 | 44 |
| Ten less than 34 | 24 |
| Ten more than 55 | 65 |
| Ten less than 55 | 45 |
| Same about 45, 55 and 65 | All end in 5 |
| Twenty more than 34 | 54 |
| Rows for twenty more | 2 |
Watch for. Children who count ten squares along the row and land in the wrong place.
If it stalls. Put a finger on the number and slide straight down.
Week 31. Rows of Ten
Numbers & Tens · In class: Counting to 120 (1.NBT.1)
Say thisColor every number that ends in zero. Then look at where they are.
The structure of the 120 chart (1.NBT.1): ten in a row is why the columns line up.
On the page
Color every number that ends in zero.
Answers
| Numbers in one row | 10 |
| Numbers ending in zero, first forty | 4 |
| Where the zeros are | One column, the last one |
| Directly below 27 | 37 |
Watch for. Children who color 10, 20, 30 but miss that they form a column.
If it stalls. Ask them to put a finger on each colored number at the same time.
Week 32. Every Way to Make 6
Ways of Counting · In class: Adding within 10: every way to make 6 (1.OA.6)
Say thisStart with 0 and go down the column one at a time. The second number takes care of itself.
Systematic listing, which is the whole of Grade 3, arriving here in its smallest form (1.OA.6).
On the page
Write every way to make 6.
Answers
| Ways to make 6 | 7 |
| Ways to make 5 | 6 |
| Ways to make 10 | 11 |
| Ways to make 9 | 10 |
| The way that repeats a number, for 6 | 3 |
| 2 and 4, 4 and 2: two ways? | Yes, two rows of the table |
Watch for. Children who stop at 3 and 3 because it feels like the middle. The list runs to 6 and 0.
If it stalls. Fill in the first two rows with them and ask what comes next in column one.
Week 33. Two Hats, Two Scarves
Ways of Counting · In class: Counting every combination
Say thisEvery box is one outfit. Fill in every box and you have them all.
Every combination, drawn. The grid is what guarantees none is missed. Grade 3 week 3 replaces the drawing with multiplication.
On the page
Draw every outfit one time only.
Answers
| Outfits, two and two | 4 |
| Outfits using the red hat | 2 |
| Outfits, two and three | 6 |
| Outfits, three and three | 9 |
| Outfits with shoes as well | 8 |
Watch for. Children who draw four outfits at random and miss one while repeating another. The grid prevents exactly this.
If it stalls. Do the top row together, keeping the hat the same all the way across.
Week 34. Three Friends, Two Chairs
Ways of Counting · In class: Counting every pair
Say thisPick one friend. Pair them with everyone else. Then move on and skip the pairs you already have.
Every pair from a small group, with order not mattering. Same object as week 21, asked as pairs rather than waves.
On the page
Draw every pair of friends.
Answers
| Pairs from three | 3 |
| Pairs from four | 6 |
| Pairs from five | 10 |
| Left out each time, three friends | 1 |
Watch for. Children who count A with B and B with A as two pairs. Point back at week 21.
If it stalls. Ask who is left standing. There is exactly one, and that counts the pairs.
Week 35. First, Next, Last
Order & Time · In class: Telling time to the hour (1.MD.3)
Say thisThe short hand points at the hour. These three clocks are all morning times. Read them, then put them in order.
Time to the hour (1.MD.3), and sequencing events, which is ordering applied to something that is not a length.
On the page
Write 1, 2, and 3 in order.
Answers
| Earliest clock | 7 |
| Latest clock | 11 |
| Order of the clocks as printed | 3, 1, 2 |
| Clock on page 2 | 6 |
| Four hours after 3 o'clock | 7 |
Watch for. Children who read the long hand as the hour. It points straight up on every clock here, which is the clue.
If it stalls. Cover the long hand with your thumb.
Week 36. The Last Sort
Sorting & Rules · In class: Review & reasoning
Say thisSort these however you like. Then tell me the rule you used.
The last week. The child chooses the rule, which is the step Grade 2 opens with, and this is the handoff.
On the page
Sort these your own way, and say the rule.
Answers
| Shapes to sort | 8 |
| Next two | red star, blue circle |
| Waves, three friends | 3 |
| Ways to make 5 | 6 |
| One rule that puts exactly three in one hoop | blue or round |
Watch for. A sort with no rule behind it. Every week this year ends the same way: say the reason. For the challenge, every single color and every single shape here gives a hoop of 2, so exactly three needs a rule that puts two things together. Blue or round is one; triangles and stars that are not green is another. Accept any rule that really puts three in the hoop.
If it stalls. Ask what is the same about everything in the first hoop.