Advice for making addition and multiplication tables for my kid

Question

I'm working with my 6 year old on understanding and mastering addition. As a result, I want to be able to make some custom addition (and eventually multiplication) tables for her to fill out.

Specifically, I'd like to be able to black out some cells, such as every other one in a row or all odd numbers, and then leave the remaining ones blank for her to fill out. The goal is for her to see the patterns embedded within the table. I am, however, finding it difficult to do and I'd appreciate some input.

1) What's the best way to make a table? I've messed around with the Grid[] function, but have issues. For example, I can't get the column and row values enclosed in heavy grid lines while the rest are in light grid lines.

Here's my code:

xmin = 0;
xmax = 10;
ymin = xmin;
ymax = xmax;
fontSize = 18;

xFrameStyle = 
  Join[{1 -> Thickness[5]}, 
    Table[i -> Thin, {i, xmin + 2, xmax + 1}]] // Reverse;

tableInterior = Table[x + y, {x, xmin, xmax}, {y, ymin, ymax}];
tableInterior[[1, 1]] = "+";
fullTable = Grid[tableInterior, 
  Frame -> {xFrameStyle, xFrameStyle}, 
  BaseStyle -> {FontSize -> fontSize}]

I'm wondering, would using Table and TableHeading be wiser. Some other function?

2) What's a good way of putting black boxes in individual cells? I can see how I could use a Replace or Map function to replace all even or odd numbers with, say, a black box, but that generally wouldn't take up the entire cell.

Much obliged.

Answer 1

How about randomly blanking out cells to be filled in.

hideCells = 30; (* Number of cells to blank out *)

tableInterior = Table[x + y, {x, xmin, xmax}, {y, ymin, ymax}] // 
  ReplacePart[RandomInteger[{2, xmax + 1}, {hideCells, 2}] -> ""]

tableInterior[[1, 1]] = "+";

fullTable = Grid[tableInterior,
  Frame -> {xFrameStyle, xFrameStyle}, 
  BaseStyle -> {FontSize -> fontSize}]

Answer 2

Thanks for your input Rohit, it got me thinking.

As a result, here's what I've come up with

(*formatting values *)
fontSize = 20;
frameThickness = 5;
itemSize = 1.5;

(* Value Ranges *)
xmin = 0;
xmax = 10;
ymin = xmin;
ymax = xmax;

(* Functions *)
(* Determine which cells for student to fill in *)

testFunc[x_, y_] := Mod[(x + y), 3] == 0 

(* Define style for input row and column *)

headerItem[z_] = 
 Item[ Style[z, Bold], FrameStyle -> Thickness[frameThickness]]

renderingFunc[x_, y_] := If[
   (x == xmin || y == ymin),(*input values*) 
   headerItem[x + y],
   If[
    testFunc[x, y],
    Item[""],
    Item["", Background -> Black]
    ]
   ];

(*determine which cells for student to fill in*)
(*set up table*)

fullTable = Table[
   renderingFunc[x, y], {x, xmin, xmax}, {y, ymin, ymax}];
fullTable[[1, 1]] = headerItem["+"];

formattedTable = Grid[fullTable, 
  Frame -> All,
  ItemSize -> {itemSize, itemSize}, 
  BaseStyle -> {FontSize -> fontSize}]